%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW325+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 : n009.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 18:07:29 EDT 2024 % Result : Theorem 186.05s 186.61s % Output : CNFRefutation 186.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SWW325+1 : TPTP v8.2.0. Released v5.2.0. % 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jun 19 04:16:24 EDT 2024 % 0.13/0.34 % CPUTime : % 0.45/0.61 start to proof:theBenchmark % 185.58/186.45 %------------------------------------------- % 185.58/186.45 % File :CSE---1.7 % 185.58/186.45 % Problem :theBenchmark % 185.58/186.45 % Transform :cnf % 185.58/186.45 % Format :tptp:raw % 185.58/186.45 % Command :java -jar mcs_scs.jar %d %s % 185.58/186.45 % 185.58/186.45 % Result :Theorem 167.100000s % 185.58/186.45 % Output :CNFRefutation 167.100000s % 185.58/186.45 %------------------------------------------- % 185.61/186.46 %------------------------------------------------------------------------------ % 185.61/186.46 % File : SWW325+1 : TPTP v8.2.0. Released v5.2.0. % 185.61/186.46 % Domain : Software Verification % 185.61/186.46 % Problem : Hoare's Logic with Procedures 435085, 5000 axioms selected % 185.61/186.46 % Version : Especial. % 185.61/186.46 % English : % 185.61/186.46 % 185.61/186.46 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 185.61/186.46 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 185.61/186.46 % Source : [Bla11] % 185.61/186.46 % Names : hoare_435085.5000.p [Bla11] % 185.61/186.46 % 185.61/186.46 % Status : ContradictoryAxioms % 185.61/186.46 % Rating : 0.81 v8.2.0, 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 185.61/186.46 % Syntax : Number of formulae : 5206 (1705 unt; 0 def) % 185.61/186.46 % Number of atoms : 12606 (4534 equ) % 185.61/186.46 % Maximal formula atoms : 13 ( 2 avg) % 185.61/186.46 % Number of connectives : 8491 (1091 ~; 158 |; 712 &) % 185.61/186.46 % ( 875 <=>;5655 =>; 0 <=; 0 <~>) % 185.61/186.46 % Maximal formula depth : 22 ( 6 avg) % 185.61/186.46 % Maximal term depth : 19 ( 2 avg) % 185.61/186.46 % Number of predicates : 141 ( 140 usr; 1 prp; 0-7 aty) % 185.61/186.46 % Number of functors : 388 ( 388 usr; 57 con; 0-10 aty) % 185.61/186.46 % Number of variables : 16774 (16645 !; 129 ?) % 185.61/186.46 % SPC : FOF_CAX_RFO_SEQ % 185.61/186.46 % 185.61/186.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 185.61/186.46 % 2011-03-01 11:52:50 % 185.61/186.46 %------------------------------------------------------------------------------ % 185.61/186.46 %----Relevant facts (4983) % 185.61/186.46 fof(fact_ext,axiom, % 185.61/186.46 ! [V_g_2,V_f_2] : % 185.61/186.46 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 185.61/186.46 => V_f_2 = V_g_2 ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_OWhileFalse,axiom, % 185.61/186.46 ! [V_n_2,V_ca_2,V_s_2,V_ba_2] : % 185.61/186.46 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.46 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_s_2) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_OWhileTrue,axiom, % 185.61/186.46 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_ba_2] : % 185.61/186.46 ( hBOOL(hAPP(V_ba_2,V_s0_2)) % 185.61/186.46 => ( c_Natural_Oevaln(V_ca_2,V_s0_2,V_n_2,V_s1_2) % 185.61/186.46 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s1_2,V_n_2,V_s2_2) % 185.61/186.46 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_Oequations_I7_J,axiom, % 185.61/186.46 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 185.61/186.46 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2) % 185.61/186.46 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.46 => ? [B_s1] : % 185.61/186.46 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 185.61/186.46 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_Oequations_I8_J,axiom, % 185.61/186.46 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 185.61/186.46 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2) % 185.61/186.46 <=> ( ( V_a6_2 = V_a2_2 % 185.61/186.46 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 185.61/186.46 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.46 & ? [B_s1] : % 185.61/186.46 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 185.61/186.46 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I5_J,axiom, % 185.61/186.46 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 185.61/186.46 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 185.61/186.46 <=> ( V_fun_2 = V_fun_H_2 % 185.61/186.46 & V_com_2 = V_com_H_2 ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_triple__valid__def2,axiom, % 185.61/186.46 ! [V_Q_2,V_ca_2,V_Pa_2,V_n_2,T_b] : % 185.61/186.46 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)) % 185.61/186.46 <=> ! [B_Z,B_s] : % 185.61/186.46 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.61/186.46 => ! [B_s_H] : % 185.61/186.46 ( c_Natural_Oevaln(V_ca_2,B_s,V_n_2,B_s_H) % 185.61/186.46 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln__WHILE__case,axiom, % 185.61/186.46 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_ba_2] : % 185.61/186.46 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_t_2) % 185.61/186.46 => ( ( V_t_2 = V_s_2 % 185.61/186.46 => hBOOL(hAPP(V_ba_2,V_s_2)) ) % 185.61/186.46 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.46 => ! [B_s1] : % 185.61/186.46 ( c_Natural_Oevaln(V_ca_2,V_s_2,V_n_2,B_s1) % 185.61/186.46 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),B_s1,V_n_2,V_t_2) ) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_triple__valid__Suc,axiom, % 185.61/186.46 ! [V_t,V_n,T_a] : % 185.61/186.46 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 185.61/186.46 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_hoare__valids__def,axiom, % 185.61/186.46 ! [V_ts_2,V_Ga_2,T_b] : % 185.61/186.46 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) % 185.61/186.46 <=> ! [B_n] : % 185.61/186.46 ( ! [B_x] : % 185.61/186.46 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) % 185.61/186.46 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) % 185.61/186.46 => ! [B_x] : % 185.61/186.46 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 185.61/186.46 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I69_J,axiom, % 185.61/186.46 ! [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) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_OSkip,axiom, % 185.61/186.46 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln__elim__cases_I1_J,axiom, % 185.61/186.46 ! [V_t,V_n,V_s] : % 185.61/186.46 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) % 185.61/186.46 => V_t = V_s ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_triple_Oinject,axiom, % 185.61/186.46 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 185.61/186.46 ( 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) % 185.61/186.46 <=> ( V_fun1_2 = V_fun1_H_2 % 185.61/186.46 & V_com_2 = V_com_H_2 % 185.61/186.46 & V_fun2_2 = V_fun2_H_2 ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I64_J,axiom, % 185.61/186.46 ! [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 ). % 185.61/186.46 % 185.61/186.46 fof(fact_triples__valid__Suc,axiom, % 185.61/186.46 ! [V_n_2,V_ts_2,T_b] : % 185.61/186.46 ( ! [B_x] : % 185.61/186.46 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 185.61/186.46 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 185.61/186.46 => ! [B_x] : % 185.61/186.46 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 185.61/186.46 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln__Suc,axiom, % 185.61/186.46 ! [V_s_H,V_n,V_s,V_c] : % 185.61/186.46 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) % 185.61/186.46 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_Oequations_I1_J,axiom, % 185.61/186.46 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I17_J,axiom, % 185.61/186.46 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I16_J,axiom, % 185.61/186.46 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 185.61/186.46 % 185.61/186.46 fof(fact_triple_Orecs,axiom, % 185.61/186.46 ! [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) ). % 185.61/186.46 % 185.61/186.46 fof(fact_triple_Osimps_I2_J,axiom, % 185.61/186.46 ! [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) ). % 185.61/186.46 % 185.61/186.46 fof(fact_n__not__Suc__n,axiom, % 185.61/186.46 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 185.61/186.46 % 185.61/186.46 fof(fact_Suc__n__not__n,axiom, % 185.61/186.46 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 185.61/186.46 % 185.61/186.46 fof(fact_nat_Oinject,axiom, % 185.61/186.46 ! [V_nat_H_2,V_nat_2] : % 185.61/186.46 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 185.61/186.46 <=> V_nat_2 = V_nat_H_2 ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_Suc__inject,axiom, % 185.61/186.46 ! [V_y,V_x] : % 185.61/186.46 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 185.61/186.46 => V_x = V_y ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln_OSemi,axiom, % 185.61/186.46 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 185.61/186.46 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) % 185.61/186.46 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2) % 185.61/186.46 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Orecs_I1_J,axiom, % 185.61/186.46 ! [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 ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Osimps_I67_J,axiom, % 185.61/186.46 ! [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) ). % 185.61/186.46 % 185.61/186.46 fof(fact_com_Orecs_I6_J,axiom, % 185.61/186.46 ! [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)) ). % 185.61/186.46 % 185.61/186.46 fof(fact_evaln__elim__cases_I5_J,axiom, % 185.61/186.46 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] : % 185.61/186.46 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2) % 185.61/186.46 => ( ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.46 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) ) % 185.61/186.46 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.46 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ). % 185.61/186.46 % 185.61/186.47 fof(fact_evaln_OIfFalse,axiom, % 185.61/186.47 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_ba_2] : % 185.61/186.47 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.47 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2) % 185.61/186.47 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_evaln_OIfTrue,axiom, % 185.61/186.47 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_ba_2] : % 185.61/186.47 ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.47 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2) % 185.61/186.47 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I44_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I45_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I3_J,axiom, % 185.61/186.47 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 185.61/186.47 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 185.61/186.47 <=> ( V_com1_2 = V_com1_H_2 % 185.61/186.47 & V_com2_2 = V_com2_H_2 ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I4_J,axiom, % 185.61/186.47 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 185.61/186.47 ( 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) % 185.61/186.47 <=> ( V_fun_2 = V_fun_H_2 % 185.61/186.47 & V_com1_2 = V_com1_H_2 % 185.61/186.47 & V_com2_2 = V_com2_H_2 ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Orecs_I4_J,axiom, % 185.61/186.47 ! [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)) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Orecs_I5_J,axiom, % 185.61/186.47 ! [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)) ). % 185.61/186.47 % 185.61/186.47 fof(fact_evaln_Oequations_I5_J,axiom, % 185.61/186.47 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 185.61/186.47 ( 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) % 185.61/186.47 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.47 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) % 185.61/186.47 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.47 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_evaln_Oequations_I6_J,axiom, % 185.61/186.47 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 185.61/186.47 ( 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) % 185.61/186.47 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.47 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) % 185.61/186.47 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.47 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I53_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I52_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_evaln_Oequations_I4_J,axiom, % 185.61/186.47 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 185.61/186.47 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2) % 185.61/186.47 <=> ? [B_s1] : % 185.61/186.47 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) % 185.61/186.47 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I15_J,axiom, % 185.61/186.47 ! [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 ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I14_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I46_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I47_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I13_J,axiom, % 185.61/186.47 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I12_J,axiom, % 185.61/186.47 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I68_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_evaln__elim__cases_I4_J,axiom, % 185.61/186.47 ! [V_t,V_n,V_s,V_c2,V_c1] : % 185.61/186.47 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t) % 185.61/186.47 => ~ ! [B_s1] : % 185.61/186.47 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1) % 185.61/186.47 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 185.61/186.47 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 185.61/186.47 ( class_Rings_Osemiring__1(T_b) % 185.61/186.47 => 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)) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_nat__case__Suc,axiom, % 185.61/186.47 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 185.61/186.47 % 185.61/186.47 fof(fact_nat__rec__Suc,axiom, % 185.61/186.47 ! [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)) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WTs__elim__cases_I4_J,axiom, % 185.61/186.47 ! [V_c2,V_c1] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 185.61/186.47 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 185.61/186.47 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I66_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I71_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WTs__elim__cases_I5_J,axiom, % 185.61/186.47 ! [V_c2_2,V_c1_2,V_ba_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2))) % 185.61/186.47 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 185.61/186.47 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I65_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WTs__elim__cases_I6_J,axiom, % 185.61/186.47 ! [V_ca_2,V_ba_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2))) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I70_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WTs__elim__cases_I3_J,axiom, % 185.61/186.47 ! [V_ca_2,V_a_2,V_Y_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WTs__elim__cases_I8_J,axiom, % 185.61/186.47 ! [V_a_2,V_Pa_2,V_X_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2))) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OCall,axiom, % 185.61/186.47 ! [V_a_2,V_X_2,V_pn_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OLocal,axiom, % 185.61/186.47 ! [V_a_2,V_Y_2,V_ca_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I2_J,axiom, % 185.61/186.47 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 185.61/186.47 ( 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) % 185.61/186.47 <=> ( V_loc_2 = V_loc_H_2 % 185.61/186.47 & V_fun_2 = V_fun_H_2 % 185.61/186.47 & V_com_2 = V_com_H_2 ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I7_J,axiom, % 185.61/186.47 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 185.61/186.47 ( 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) % 185.61/186.47 <=> ( V_vname_2 = V_vname_H_2 % 185.61/186.47 & V_pname_2 = V_pname_H_2 % 185.61/186.47 & V_fun_2 = V_fun_H_2 ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I1_J,axiom, % 185.61/186.47 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 185.61/186.47 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 185.61/186.47 <=> ( V_vname_2 = V_vname_H_2 % 185.61/186.47 & V_fun_2 = V_fun_H_2 ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I6_J,axiom, % 185.61/186.47 ! [V_pname_H_2,V_pname_2] : % 185.61/186.47 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 185.61/186.47 <=> V_pname_2 = V_pname_H_2 ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I8_J,axiom, % 185.61/186.47 ! [V_a3_2,V_a1_2,V_a2_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 185.61/186.47 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I3_J,axiom, % 185.61/186.47 ! [V_a1_2,V_a3_2,V_a2_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 185.61/186.47 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I2_J,axiom, % 185.61/186.47 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I42_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I43_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I23_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I33_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I40_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I63_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I22_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I32_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I30_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I41_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I62_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I31_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OAssign,axiom, % 185.61/186.47 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I58_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I59_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I54_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I55_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I48_J,axiom, % 185.61/186.47 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I49_J,axiom, % 185.61/186.47 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I18_J,axiom, % 185.61/186.47 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I19_J,axiom, % 185.61/186.47 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 185.61/186.47 % 185.61/186.47 fof(fact_While,axiom, % 185.61/186.47 ! [V_ba_2,V_ca_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2))) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I6_J,axiom, % 185.61/186.47 ! [V_a1_2,V_a2_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 185.61/186.47 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OIf,axiom, % 185.61/186.47 ! [V_ba_2,V_c1_2,V_c0_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 185.61/186.47 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2))) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I5_J,axiom, % 185.61/186.47 ! [V_a2_2,V_a1_2,V_a3_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 185.61/186.47 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 185.61/186.47 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OSemi,axiom, % 185.61/186.47 ! [V_c1,V_c0] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 185.61/186.47 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 185.61/186.47 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I4_J,axiom, % 185.61/186.47 ! [V_a2_2,V_a1_2] : % 185.61/186.47 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 185.61/186.47 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 185.61/186.47 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_OSkip,axiom, % 185.61/186.47 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 185.61/186.47 % 185.61/186.47 fof(fact_WT_Oequations_I1_J,axiom, % 185.61/186.47 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I29_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I28_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I38_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I61_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I39_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I60_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I27_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I26_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I36_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I37_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.47 fof(fact_com_Osimps_I56_J,axiom, % 185.61/186.47 ! [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) ). % 185.61/186.47 % 185.61/186.48 fof(fact_com_Osimps_I57_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I25_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I24_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I8_J,axiom, % 185.61/186.48 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I9_J,axiom, % 185.61/186.48 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I34_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I51_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I35_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I50_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I20_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I10_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I21_J,axiom, % 185.61/186.48 ! [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 ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osimps_I11_J,axiom, % 185.61/186.48 ! [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 ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Orecs_I7_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Orecs_I2_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Orecs_I3_J,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Orecs_I8_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Body__triple__valid__0,axiom, % 185.61/186.48 ! [V_Q_2,V_pn_2,V_Pa_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln__elim__cases_I2_J,axiom, % 185.61/186.48 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] : % 185.61/186.48 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2) % 185.61/186.48 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln_OAssign,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Body__triple__valid__Suc,axiom, % 185.61/186.48 ! [V_Q_2,V_pn_2,V_Pa_2,V_n_2,T_b] : % 185.61/186.48 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 185.61/186.48 <=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_def__nat__rec__Suc,axiom, % 185.61/186.48 ! [V_n_2,V_h_2,V_ca_2,T_b,V_f_2] : % 185.61/186.48 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n) % 185.61/186.48 => hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_h_2,V_n_2),hAPP(V_f_2,V_n_2)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln_Oequations_I2_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln_OBody,axiom, % 185.61/186.48 ! [V_s1,V_n,V_s0,V_pn] : % 185.61/186.48 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) % 185.61/186.48 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln_Oequations_I9_J,axiom, % 185.61/186.48 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 185.61/186.48 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2) % 185.61/186.48 <=> 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) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 185.61/186.48 ! [V_i_2,V_inc_2,T_b] : % 185.61/186.48 ( class_Rings_Osemiring__1(T_b) % 185.61/186.48 => 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 ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__rec__0,axiom, % 185.61/186.48 ! [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 ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OSkip,axiom, % 185.61/186.48 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc__elim__cases_I1_J,axiom, % 185.61/186.48 ! [V_t,V_s] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 185.61/186.48 => V_t = V_s ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OWhileFalse,axiom, % 185.61/186.48 ! [V_ca_2,V_s_2,V_ba_2] : % 185.61/186.48 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OWhileTrue,axiom, % 185.61/186.48 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_ba_2] : % 185.61/186.48 ( hBOOL(hAPP(V_ba_2,V_s0_2)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s1_2),V_s2_2)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OIfFalse,axiom, % 185.61/186.48 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_ba_2] : % 185.61/186.48 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OIfTrue,axiom, % 185.61/186.48 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_ba_2] : % 185.61/186.48 ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc__elim__cases_I5_J,axiom, % 185.61/186.48 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 185.61/186.48 => ( ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.48 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 185.61/186.48 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.48 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OSemi,axiom, % 185.61/186.48 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OAssign,axiom, % 185.61/186.48 ! [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)))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc__elim__cases_I2_J,axiom, % 185.61/186.48 ! [V_t_2,V_s_2,V_a_2,V_X_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) % 185.61/186.48 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc__elim__cases_I6_J,axiom, % 185.61/186.48 ! [V_s1,V_s,V_P] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_OBody,axiom, % 185.61/186.48 ! [V_s1,V_s0,V_pn] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com__det,axiom, % 185.61/186.48 ! [V_u,V_t,V_s,V_c] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 185.61/186.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 185.61/186.48 => V_u = V_t ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I9_J,axiom, % 185.61/186.48 ! [V_a3_2,V_a2_2,V_a1_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 185.61/186.48 <=> 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)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I2_J,axiom, % 185.61/186.48 ! [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)))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Suc__neq__Zero,axiom, % 185.61/186.48 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Zero__neq__Suc,axiom, % 185.61/186.48 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat_Osimps_I3_J,axiom, % 185.61/186.48 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Suc__not__Zero,axiom, % 185.61/186.48 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat_Osimps_I2_J,axiom, % 185.61/186.48 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 185.61/186.48 % 185.61/186.48 fof(fact_Zero__not__Suc,axiom, % 185.61/186.48 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 185.61/186.48 % 185.61/186.48 fof(fact_eval__eq,axiom, % 185.61/186.48 ! [V_t_2,V_s_2,V_ca_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 185.61/186.48 <=> ? [B_n] : c_Natural_Oevaln(V_ca_2,V_s_2,B_n,V_t_2) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln__evalc,axiom, % 185.61/186.48 ! [V_t,V_n,V_s,V_c] : % 185.61/186.48 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 185.61/186.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I7_J,axiom, % 185.61/186.48 ! [V_a2_2,V_a3_2,V_a1_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 185.61/186.48 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 => ? [B_s1] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I8_J,axiom, % 185.61/186.48 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 185.61/186.48 <=> ( ( V_a5_2 = V_a2_2 % 185.61/186.48 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 185.61/186.48 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 & ? [B_s1] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I5_J,axiom, % 185.61/186.48 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 185.61/186.48 ( 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)) % 185.61/186.48 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 185.61/186.48 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I6_J,axiom, % 185.61/186.48 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 185.61/186.48 ( 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)) % 185.61/186.48 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 185.61/186.48 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I4_J,axiom, % 185.61/186.48 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 185.61/186.48 <=> ? [B_s1] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 185.61/186.48 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc_Oequations_I1_J,axiom, % 185.61/186.48 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__case__0,axiom, % 185.61/186.48 ! [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 ). % 185.61/186.48 % 185.61/186.48 fof(fact_triple_Osize_I1_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_triple_Osize_I2_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evaln__elim__cases_I6_J,axiom, % 185.61/186.48 ! [V_s1,V_n,V_s,V_P] : % 185.61/186.48 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) % 185.61/186.48 => ~ ! [B_n] : % 185.61/186.48 ( V_n = hAPP(c_Nat_OSuc,B_n) % 185.61/186.48 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_evalc__elim__cases_I4_J,axiom, % 185.61/186.48 ! [V_t,V_s,V_c2,V_c1] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 185.61/186.48 => ~ ! [B_s1] : % 185.61/186.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 185.61/186.48 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I1_J,axiom, % 185.61/186.48 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I8_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I2_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I7_J,axiom, % 185.61/186.48 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I9_J,axiom, % 185.61/186.48 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I16_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I10_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I15_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I11_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I12_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I3_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I4_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I13_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I5_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I14_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_com_Osize_I6_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_WT_OBody,axiom, % 185.61/186.48 ! [V_pn] : % 185.61/186.48 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 185.61/186.48 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_WT_Oequations_I7_J,axiom, % 185.61/186.48 ! [V_a_2] : % 185.61/186.48 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 185.61/186.48 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__right__imp__eq,axiom, % 185.61/186.48 ! [V_c,V_a,V_b,T_a] : % 185.61/186.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 185.61/186.48 => ( 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) % 185.61/186.48 => V_b = V_c ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__imp__eq,axiom, % 185.61/186.48 ! [V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 185.61/186.48 => ( 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) % 185.61/186.48 => V_b = V_c ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__left__imp__eq,axiom, % 185.61/186.48 ! [V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 185.61/186.48 => ( 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) % 185.61/186.48 => V_b = V_c ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__right__cancel,axiom, % 185.61/186.48 ! [V_ca_2,V_a_2,V_ba_2,T_b] : % 185.61/186.48 ( class_Groups_Ocancel__semigroup__add(T_b) % 185.61/186.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2) % 185.61/186.48 <=> V_ba_2 = V_ca_2 ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__left__cancel,axiom, % 185.61/186.48 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.48 ( class_Groups_Ocancel__semigroup__add(T_b) % 185.61/186.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2) % 185.61/186.48 <=> V_ba_2 = V_ca_2 ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 185.61/186.48 ! [V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Groups_Oab__semigroup__add(T_a) % 185.61/186.48 => 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)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__add__commute,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__add__left__commute,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__add__assoc,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__add__left__cancel,axiom, % 185.61/186.48 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.48 ( 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) % 185.61/186.48 <=> V_m_2 = V_n_2 ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_nat__add__right__cancel,axiom, % 185.61/186.48 ! [V_n_2,V_k_2,V_m_2] : % 185.61/186.48 ( 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) % 185.61/186.48 <=> V_m_2 = V_n_2 ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add_Ocomm__neutral,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Groups_Ocomm__monoid__add(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__0__right,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Groups_Omonoid__add(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_double__zero__sym,axiom, % 185.61/186.48 ! [V_a_2,T_b] : % 185.61/186.48 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.48 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 185.61/186.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__0,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Groups_Ocomm__monoid__add(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__0__left,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Groups_Omonoid__add(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_plus__nat_Oadd__0,axiom, % 185.61/186.48 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 185.61/186.48 % 185.61/186.48 fof(fact_Nat_Oadd__0__right,axiom, % 185.61/186.48 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__is__0,axiom, % 185.61/186.48 ! [V_n_2,V_m_2] : % 185.61/186.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__eq__self__zero,axiom, % 185.61/186.48 ! [V_n,V_m] : % 185.61/186.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 185.61/186.48 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__Suc__shift,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__Suc,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__Suc__right,axiom, % 185.61/186.48 ! [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)) ). % 185.61/186.48 % 185.61/186.48 fof(fact_one__is__add,axiom, % 185.61/186.48 ! [V_n_2,V_m_2] : % 185.61/186.48 ( 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) % 185.61/186.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.61/186.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__is__1,axiom, % 185.61/186.48 ! [V_n_2,V_m_2] : % 185.61/186.48 ( 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)) % 185.61/186.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.61/186.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_zero__reorient,axiom, % 185.61/186.48 ! [V_x_2,T_b] : % 185.61/186.48 ( class_Groups_Ozero(T_b) % 185.61/186.48 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 185.61/186.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_WT__bodiesD,axiom, % 185.61/186.48 ! [V_b,V_pn] : % 185.61/186.48 ( c_Com_OWT__bodies % 185.61/186.48 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 185.61/186.48 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_WTs__elim__cases_I7_J,axiom, % 185.61/186.48 ! [V_P] : % 185.61/186.48 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 185.61/186.48 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_the_Osimps,axiom, % 185.61/186.48 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 185.61/186.48 % 185.61/186.48 fof(fact_not__None__eq,axiom, % 185.61/186.48 ! [T_b,V_x_2] : % 185.61/186.48 ( V_x_2 != c_Option_Ooption_ONone(T_b) % 185.61/186.48 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_not__Some__eq,axiom, % 185.61/186.48 ! [T_b,V_x_2] : % 185.61/186.48 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y) % 185.61/186.48 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_option_Osimps_I3_J,axiom, % 185.61/186.48 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 185.61/186.48 % 185.61/186.48 fof(fact_option_Osimps_I2_J,axiom, % 185.61/186.48 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 185.61/186.48 % 185.61/186.48 fof(fact_option_Osize_I2_J,axiom, % 185.61/186.48 ! [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))) ). % 185.61/186.48 % 185.61/186.48 fof(fact_double__eq__0__iff,axiom, % 185.61/186.48 ! [V_a_2,T_b] : % 185.61/186.48 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_add__0__iff,axiom, % 185.61/186.48 ! [V_a_2,V_ba_2,T_b] : % 185.61/186.48 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.61/186.48 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) % 185.61/186.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 185.61/186.48 ! [V_c,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 185.61/186.48 ! [V_d,V_c,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 185.61/186.48 ! [V_d,V_c,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 185.61/186.48 ! [V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 185.61/186.48 ! [V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 185.61/186.48 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => 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)) ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_option_Osize_I1_J,axiom, % 185.61/186.48 ! [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) ). % 185.61/186.48 % 185.61/186.48 fof(fact_option_Oinject,axiom, % 185.61/186.48 ! [V_a_H_2,V_a_2,T_b] : % 185.61/186.48 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2) % 185.61/186.48 <=> V_a_2 = V_a_H_2 ) ). % 185.61/186.48 % 185.61/186.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 185.61/186.48 ! [V_a,T_a] : % 185.61/186.48 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.61/186.48 % 185.61/186.49 fof(fact_nat_Osize_I2_J,axiom, % 185.61/186.49 ! [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))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat_Osize_I4_J,axiom, % 185.61/186.49 ! [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))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Osize_I4_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Osize_I3_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Orecs_I2_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Osimps_I5_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Orecs_I1_J,axiom, % 185.61/186.49 ! [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 ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Osimps_I4_J,axiom, % 185.61/186.49 ! [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 ). % 185.61/186.49 % 185.61/186.49 fof(fact_bool_Osize_I1_J,axiom, % 185.61/186.49 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.49 % 185.61/186.49 fof(fact_bool_Osize_I2_J,axiom, % 185.61/186.49 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.49 % 185.61/186.49 fof(fact_is__none__code_I2_J,axiom, % 185.61/186.49 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat__size,axiom, % 185.61/186.49 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat_Osize_I3_J,axiom, % 185.61/186.49 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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat_Osize_I1_J,axiom, % 185.61/186.49 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.49 % 185.61/186.49 fof(fact_is__none__def,axiom, % 185.61/186.49 ! [V_x_2,T_b] : % 185.61/186.49 ( c_Option_Ois__none(T_b,V_x_2) % 185.61/186.49 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_is__none__code_I1_J,axiom, % 185.61/186.49 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_bool_Osize_I4_J,axiom, % 185.61/186.49 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.49 % 185.61/186.49 fof(fact_bool_Osize_I3_J,axiom, % 185.61/186.49 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.49 % 185.61/186.49 fof(fact_def__nat__rec__0,axiom, % 185.61/186.49 ! [V_h_2,V_ca_2,T_b,V_f_2] : % 185.61/186.49 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n) % 185.61/186.49 => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_ca_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_evalc__WHILE__case,axiom, % 185.61/186.49 ! [V_t_2,V_s_2,V_ca_2,V_ba_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_t_2)) % 185.61/186.49 => ( ( V_t_2 = V_s_2 % 185.61/186.49 => hBOOL(hAPP(V_ba_2,V_s_2)) ) % 185.61/186.49 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2)) % 185.61/186.49 => ! [B_s1] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pair__box_Osize_I1_J,axiom, % 185.61/186.49 ! [V_ba_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_ba_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_ba_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_evalc__evaln,axiom, % 185.61/186.49 ! [V_t,V_s,V_c] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 185.61/186.49 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osize_I1_J,axiom, % 185.61/186.49 ! [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))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osize_I2_J,axiom, % 185.61/186.49 ! [V_ba_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_ba_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_ba_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_option_Oexhaust,axiom, % 185.61/186.49 ! [T_a,V_y] : % 185.61/186.49 ( V_y != c_Option_Ooption_ONone(T_a) % 185.61/186.49 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zero__less__Suc,axiom, % 185.61/186.49 ! [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))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not0__implies__Suc,axiom, % 185.61/186.49 ! [V_n] : % 185.61/186.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.49 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__zeroE,axiom, % 185.61/186.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_lessI,axiom, % 185.61/186.49 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suc__mono,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat__less__cases,axiom, % 185.61/186.49 ! [V_Pa_2,V_n_2,V_m_2] : % 185.61/186.49 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.61/186.49 => ( ( V_m_2 = V_n_2 % 185.61/186.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.61/186.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.61/186.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.61/186.49 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__not__refl3,axiom, % 185.61/186.49 ! [V_t,V_s] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 185.61/186.49 => V_s != V_t ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__not__refl2,axiom, % 185.61/186.49 ! [V_m,V_n] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 185.61/186.49 => V_m != V_n ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__irrefl__nat,axiom, % 185.61/186.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__neqE__nat,axiom, % 185.61/186.49 ! [V_y,V_x] : % 185.61/186.49 ( V_x != V_y % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat__neq__iff,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( V_m_2 != V_n_2 % 185.61/186.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__not__refl,axiom, % 185.61/186.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pair__box_Oinject,axiom, % 185.61/186.49 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 185.61/186.49 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_ba_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) % 185.61/186.49 <=> ( V_a_2 = V_a_H_2 % 185.61/186.49 & V_ba_2 = V_b_H_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__cancel__right,axiom, % 185.61/186.49 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__cancel__left,axiom, % 185.61/186.49 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__strict__right__mono,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.49 => 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))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__strict__left__mono,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.49 => 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))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__strict__mono,axiom, % 185.61/186.49 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__imp__less__right,axiom, % 185.61/186.49 ! [V_b,V_c,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.49 => ( 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))) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__imp__less__left,axiom, % 185.61/186.49 ! [V_b,V_a,V_c,T_a] : % 185.61/186.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.49 => ( 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))) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_gr0I,axiom, % 185.61/186.49 ! [V_n] : % 185.61/186.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_gr__implies__not0,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__nat__zero__code,axiom, % 185.61/186.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_neq0__conv,axiom, % 185.61/186.49 ! [V_n_2] : % 185.61/186.49 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__less0,axiom, % 185.61/186.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__less__eq,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__Suc__eq,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.61/186.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.49 | V_m_2 = V_n_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suc__less__eq,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( 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))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__less__less__Suc__eq,axiom, % 185.61/186.49 ! [V_m_2,V_n_2] : % 185.61/186.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 185.61/186.49 <=> V_n_2 = V_m_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__antisym,axiom, % 185.61/186.49 ! [V_m,V_n] : % 185.61/186.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 185.61/186.49 => V_m = V_n ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__SucI,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suc__lessI,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__trans__Suc,axiom, % 185.61/186.49 ! [V_k,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__SucE,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => V_m = V_n ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suc__lessD,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suc__less__SucD,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__lessD1,axiom, % 185.61/186.49 ! [V_k,V_j,V_i] : % 185.61/186.49 ( 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)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__add__eq__less,axiom, % 185.61/186.49 ! [V_n,V_m,V_l,V_k] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 185.61/186.49 => ( 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) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__mono,axiom, % 185.61/186.49 ! [V_l,V_k,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 185.61/186.49 => 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))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__less__mono1,axiom, % 185.61/186.49 ! [V_k,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_trans__less__add2,axiom, % 185.61/186.49 ! [V_m,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_trans__less__add1,axiom, % 185.61/186.49 ! [V_m,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_nat__add__left__cancel__less,axiom, % 185.61/186.49 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.49 ( 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))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__add__less2,axiom, % 185.61/186.49 ! [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)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__add__less1,axiom, % 185.61/186.49 ! [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)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_even__less__0__iff,axiom, % 185.61/186.49 ! [V_a_2,T_b] : % 185.61/186.49 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.49 => ( 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))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__neg__neg,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__pos__pos,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 185.61/186.49 ! [V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.49 => ( 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))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 185.61/186.49 ! [V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__Suc__eq__0__disj,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.61/186.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.49 | ? [B_j] : % 185.61/186.49 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 185.61/186.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__Suc0,axiom, % 185.61/186.49 ! [V_n_2] : % 185.61/186.49 ( 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)))) % 185.61/186.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_gr0__conv__Suc,axiom, % 185.61/186.49 ! [V_n_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.61/186.49 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_add__gr__0,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( 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))) % 185.61/186.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.61/186.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__iff__Suc__add,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.49 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__add__Suc2,axiom, % 185.61/186.49 ! [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)))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__add__Suc1,axiom, % 185.61/186.49 ! [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)))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pair__box_Osize_I2_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pair__box_Orecs,axiom, % 185.61/186.49 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pair__box_Osimps_I2_J,axiom, % 185.61/186.49 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.61/186.49 % 185.61/186.49 fof(fact_pos__add__strict,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Inl__not__Inr,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osimps_I3_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Inr__not__Inl,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osimps_I4_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osize_I3_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osize_I4_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_termination__basic__simps_I1_J,axiom, % 185.61/186.49 ! [V_z,V_y,V_x] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__neqE__linordered__idom,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.49 => ( V_x != V_y % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Inr__inject,axiom, % 185.61/186.49 ! [V_y,V_x,T_a,T_b] : % 185.61/186.49 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y) % 185.61/186.49 => V_x = V_y ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osimps_I2_J,axiom, % 185.61/186.49 ! [V_b_H_2,V_ba_2,T_b,T_c] : % 185.61/186.49 ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_ba_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2) % 185.61/186.49 <=> V_ba_2 = V_b_H_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Inl__inject,axiom, % 185.61/186.49 ! [V_y,V_x,T_b,T_a] : % 185.61/186.49 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y) % 185.61/186.49 => V_x = V_y ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Osimps_I1_J,axiom, % 185.61/186.49 ! [V_a_H_2,V_a_2,T_c,T_b] : % 185.61/186.49 ( 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) % 185.61/186.49 <=> V_a_2 = V_a_H_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_termination__basic__simps_I2_J,axiom, % 185.61/186.49 ! [V_y,V_z,V_x] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Projl_Osimps,axiom, % 185.61/186.49 ! [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 ). % 185.61/186.49 % 185.61/186.49 fof(fact_Projr_Osimps,axiom, % 185.61/186.49 ! [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 ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Orecs_I1_J,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_sum_Orecs_I2_J,axiom, % 185.61/186.49 ! [V_ba_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_ba_2)) = hAPP(V_f2_2,V_ba_2) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suml_Osimps,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Sumr_Osimps,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__0__less__iff,axiom, % 185.61/186.49 ! [V_n_2,T_b] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__imp__Suc__add,axiom, % 185.61/186.49 ! [V_n,V_m] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__imp__add__positive,axiom, % 185.61/186.49 ! [V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.49 => ? [B_k] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k)) % 185.61/186.49 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_gr0__implies__Suc,axiom, % 185.61/186.49 ! [V_n] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.49 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__eq__iff,axiom, % 185.61/186.49 ! [V_n_2,V_m_2,T_b] : % 185.61/186.49 ( class_Nat_Osemiring__char__0(T_b) % 185.61/186.49 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) % 185.61/186.49 <=> V_m_2 = V_n_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Suml__inject,axiom, % 185.61/186.49 ! [V_g_2,V_f_2,T_c,T_d,T_b] : % 185.61/186.49 ( 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) % 185.61/186.49 => V_f_2 = V_g_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Sumr__inject,axiom, % 185.61/186.49 ! [V_g_2,V_f_2,T_b,T_d,T_c] : % 185.61/186.49 ( 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) % 185.61/186.49 => V_f_2 = V_g_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_int__eq__0__conv,axiom, % 185.61/186.49 ! [V_n_2] : % 185.61/186.49 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.49 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_int__0,axiom, % 185.61/186.49 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zless__iff__Suc__zadd,axiom, % 185.61/186.49 ! [V_z_2,V_w_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 185.61/186.49 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zless__int,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__int__left,axiom, % 185.61/186.49 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__int,axiom, % 185.61/186.49 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zero__less__int__conv,axiom, % 185.61/186.49 ! [V_n_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__less__0__iff,axiom, % 185.61/186.49 ! [V_m,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__0,axiom, % 185.61/186.49 ! [T_a] : % 185.61/186.49 ( class_Rings_Osemiring__1(T_a) % 185.61/186.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__less__imp__less,axiom, % 185.61/186.49 ! [V_n,V_m,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__imp__of__nat__less,axiom, % 185.61/186.49 ! [V_n,V_m,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__less__iff,axiom, % 185.61/186.49 ! [V_n_2,V_m_2,T_b] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__nat__add,axiom, % 185.61/186.49 ! [V_n,V_m,T_a] : % 185.61/186.49 ( class_Rings_Osemiring__1(T_a) % 185.61/186.49 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_lift__Suc__mono__less__iff,axiom, % 185.61/186.49 ! [V_m_2,V_n_2,V_f_2,T_b] : % 185.61/186.49 ( class_Orderings_Oorder(T_b) % 185.61/186.49 => ( ! [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)))) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_lift__Suc__mono__less,axiom, % 185.61/186.49 ! [V_n_H_2,V_n_2,V_f_2,T_b] : % 185.61/186.49 ( class_Orderings_Oorder(T_b) % 185.61/186.49 => ( ! [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)))) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2)) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 185.61/186.49 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 185.61/186.49 ! [V_y_2,V_x_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 185.61/186.49 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__irrefl,axiom, % 185.61/186.49 ! [V_x,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__neq__iff,axiom, % 185.61/186.49 ! [V_y_2,V_x_2,T_b] : % 185.61/186.49 ( class_Orderings_Olinorder(T_b) % 185.61/186.49 => ( V_x_2 != V_y_2 % 185.61/186.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_not__less__iff__gr__or__eq,axiom, % 185.61/186.49 ! [V_y_2,V_x_2,T_b] : % 185.61/186.49 ( class_Orderings_Olinorder(T_b) % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 185.61/186.49 | V_x_2 = V_y_2 ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__less__linear,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Olinorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 | V_x = V_y % 185.61/186.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__antisym__conv3,axiom, % 185.61/186.49 ! [V_x_2,V_y_2,T_b] : % 185.61/186.49 ( class_Orderings_Olinorder(T_b) % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.49 <=> V_x_2 = V_y_2 ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_int__less__0__conv,axiom, % 185.61/186.49 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 185.61/186.49 ! [V_y_2,V_x_2] : % 185.61/186.49 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 185.61/186.49 <=> V_x_2 = V_y_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_int__int__eq,axiom, % 185.61/186.49 ! [V_n_2,V_m_2] : % 185.61/186.49 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 185.61/186.49 <=> V_m_2 = V_n_2 ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__assoc,axiom, % 185.61/186.49 ! [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)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__left__commute,axiom, % 185.61/186.49 ! [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)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__commute,axiom, % 185.61/186.49 ! [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) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__0,axiom, % 185.61/186.49 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__0__right,axiom, % 185.61/186.49 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 185.61/186.49 % 185.61/186.49 fof(fact_zadd__strict__right__mono,axiom, % 185.61/186.49 ! [V_k,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.61/186.49 => 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))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zless__linear,axiom, % 185.61/186.49 ! [V_y,V_x] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 185.61/186.49 | V_x = V_y % 185.61/186.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__cases,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Olinorder(T_a) % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => ( V_x != V_y % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__asym,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_xt1_I10_J,axiom, % 185.61/186.49 ! [V_z,V_x,V_y,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__trans,axiom, % 185.61/186.49 ! [V_z,V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_xt1_I2_J,axiom, % 185.61/186.49 ! [V_c,V_a,V_b,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.49 => ( V_b = V_c % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_ord__less__eq__trans,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Orderings_Oord(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.49 => ( V_b = V_c % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_xt1_I1_J,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( V_a = V_b % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_ord__eq__less__trans,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Orderings_Oord(T_a) % 185.61/186.49 => ( V_a = V_b % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_xt1_I9_J,axiom, % 185.61/186.49 ! [V_a,V_b,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__asym_H,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__imp__not__eq2,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => V_y != V_x ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__imp__not__eq,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => V_x != V_y ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__imp__not__less,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_order__less__not__sym,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Opreorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__imp__neq,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Oorder(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => V_x != V_y ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_linorder__neqE,axiom, % 185.61/186.49 ! [V_y,V_x,T_a] : % 185.61/186.49 ( class_Orderings_Olinorder(T_a) % 185.61/186.49 => ( V_x != V_y % 185.61/186.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zero__less__imp__eq__int,axiom, % 185.61/186.49 ! [V_k] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.61/186.49 => ? [B_n] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 185.61/186.49 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__int__0__less__iff,axiom, % 185.61/186.49 ! [V_z_2,T_b] : % 185.61/186.49 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_of__int__less__0__iff,axiom, % 185.61/186.49 ! [V_z_2,T_b] : % 185.61/186.49 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zmult__zless__mono2__lemma,axiom, % 185.61/186.49 ! [V_k,V_j,V_i] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.61/186.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_negative__zless__0,axiom, % 185.61/186.49 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_split__nat,axiom, % 185.61/186.49 ! [V_i_2,V_Pa_2] : % 185.61/186.49 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 185.61/186.49 <=> ( ! [B_n] : % 185.61/186.49 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 185.61/186.49 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 185.61/186.49 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.49 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_zero__less__nat__eq,axiom, % 185.61/186.49 ! [V_z_2] : % 185.61/186.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_negative__zless,axiom, % 185.61/186.49 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 185.61/186.49 % 185.61/186.49 fof(fact_int__Suc,axiom, % 185.61/186.49 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 185.61/186.49 % 185.61/186.49 fof(fact_odd__less__0,axiom, % 185.61/186.49 ! [V_z_2] : % 185.61/186.49 ( 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))) % 185.61/186.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 185.61/186.49 ! [V_m,V_a,T_a] : % 185.61/186.49 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.49 => 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) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 185.61/186.49 ! [V_a,V_m,T_a] : % 185.61/186.49 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.49 => 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) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 185.61/186.49 ! [V_m,T_a] : % 185.61/186.49 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.49 => 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) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_less__1__mult,axiom, % 185.61/186.49 ! [V_n,V_m,T_a] : % 185.61/186.49 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 185.61/186.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 185.61/186.49 => 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))) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_square__eq__iff,axiom, % 185.61/186.49 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.49 ( class_Rings_Oidom(T_b) % 185.61/186.49 => ( 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_ba_2),V_ba_2) % 185.61/186.49 <=> ( V_a_2 = V_ba_2 % 185.61/186.49 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_square__eq__1__iff,axiom, % 185.61/186.49 ! [V_x_2,T_b] : % 185.61/186.49 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.61/186.49 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 185.61/186.49 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 185.61/186.49 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_minus__mult__minus,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Rings_Oring(T_a) % 185.61/186.49 => 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) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_minus__mult__commute,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Rings_Oring(T_a) % 185.61/186.49 => 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)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_minus__mult__left,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Rings_Oring(T_a) % 185.61/186.49 => 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) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_minus__mult__right,axiom, % 185.61/186.49 ! [V_b,V_a,T_a] : % 185.61/186.49 ( class_Rings_Oring(T_a) % 185.61/186.49 => 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)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 185.61/186.49 ! [V_c,V_b,V_a,T_a] : % 185.61/186.49 ( class_Groups_Oab__semigroup__mult(T_a) % 185.61/186.49 => 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)) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_neg__equal__iff__equal,axiom, % 185.61/186.49 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Ogroup__add(T_b) % 185.61/186.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.61/186.49 <=> V_a_2 = V_ba_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_minus__equation__iff,axiom, % 185.61/186.49 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Ogroup__add(T_b) % 185.61/186.49 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_ba_2 % 185.61/186.49 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) = V_a_2 ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_equation__minus__iff,axiom, % 185.61/186.49 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.49 ( class_Groups_Ogroup__add(T_b) % 185.61/186.49 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.61/186.49 <=> V_ba_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_mult_Ocomm__neutral,axiom, % 185.61/186.49 ! [V_a,T_a] : % 185.61/186.49 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.61/186.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_mult__1__right,axiom, % 185.61/186.49 ! [V_a,T_a] : % 185.61/186.49 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.61/186.49 % 185.61/186.49 fof(fact_one__reorient,axiom, % 185.61/186.49 ! [V_x_2,T_b] : % 185.61/186.49 ( class_Groups_Oone(T_b) % 185.61/186.50 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 185.61/186.50 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__1,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.61/186.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__1__left,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__minus,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 185.61/186.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 185.61/186.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 185.61/186.50 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 185.61/186.50 ! [V_rx,V_ly,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__assoc,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 185.61/186.50 ! [V_rx,V_ly,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__eq__iff,axiom, % 185.61/186.50 ! [V_z_2,V_w_2,T_b] : % 185.61/186.50 ( class_Int_Oring__char__0(T_b) % 185.61/186.50 => ( 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) % 185.61/186.50 <=> V_w_2 = V_z_2 ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__zminus,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 185.61/186.50 ! [V_ry,V_rx,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 185.61/186.50 ! [V_ry,V_rx,V_lx,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__commute,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__1__right,axiom, % 185.61/186.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__1,axiom, % 185.61/186.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__mult,axiom, % 185.61/186.50 ! [V_z,V_w,T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__minus,axiom, % 185.61/186.50 ! [V_z,T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zminus__zminus,axiom, % 185.61/186.50 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 185.61/186.50 ! [V_x,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__ring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__1,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__nat__mult,axiom, % 185.61/186.50 ! [V_n,V_m,T_a] : % 185.61/186.50 ( class_Rings_Osemiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__nat__1,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Osemiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__of__nat,axiom, % 185.61/186.50 ! [V_k,T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.50 => 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)))) ) % 185.61/186.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.50 => 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)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__zminus__int,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__1,axiom, % 185.61/186.50 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_pos__zmult__eq__1__iff,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 185.61/186.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.50 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.50 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__zero,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__0__equal__iff__equal,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_b) % 185.61/186.50 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 185.61/186.50 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_equal__neg__zero,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.50 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 185.61/186.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__equal__0__iff__equal,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_b) % 185.61/186.50 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__equal__zero,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.50 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 185.61/186.50 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__less__iff__less,axiom, % 185.61/186.50 ! [V_a_2,V_ba_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__less__iff,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_less__minus__iff,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__add__distrib,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oab__group__add(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__add,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__minus__cancel,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => 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 ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__add__cancel,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => 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 ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__zero__left,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Omult__zero(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__zero__right,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Omult__zero(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__eq__0__iff,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Rings_Oring__no__zero__divisors(T_b) % 185.61/186.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_no__zero__divisors,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ono__zero__divisors(T_a) % 185.61/186.50 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_divisors__zero,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ono__zero__divisors(T_a) % 185.61/186.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_one__neq__zero,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Ozero__neq__one(T_a) % 185.61/186.50 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zero__neq__one,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Ozero__neq__one(T_a) % 185.61/186.50 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zminus__0,axiom, % 185.61/186.50 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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__int,axiom, % 185.61/186.50 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 185.61/186.50 ! [V_z,V_y,V_x,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_crossproduct__noteq,axiom, % 185.61/186.50 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.61/186.50 => ( ( V_a_2 != V_ba_2 % 185.61/186.50 & V_ca_2 != V_d_2 ) % 185.61/186.50 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_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_ba_2),V_ca_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 185.61/186.50 ! [V_b,V_m,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_crossproduct__eq,axiom, % 185.61/186.50 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 185.61/186.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.61/186.50 => ( 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)) % 185.61/186.50 <=> ( V_w_2 = V_x_2 % 185.61/186.50 | V_y_2 = V_z_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__semiring__class_Odistrib,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Ocomm__semiring(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_combine__common__factor,axiom, % 185.61/186.50 ! [V_c,V_b,V_e,V_a,T_a] : % 185.61/186.50 ( class_Rings_Osemiring(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zminus__zadd__distrib,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zadd__zmult__distrib2,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zadd__zmult__distrib,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_int__0__neq__1,axiom, % 185.61/186.50 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__int__eq,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_one__less__nat__eq,axiom, % 185.61/186.50 ! [V_z_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__less__nonneg,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__less__0__iff__less,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__0__less__iff__less,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_less__minus__self__iff,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__unique,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_ab__left__minus,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Oab__group__add(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_left__minus,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_eq__neg__iff__add__eq__0,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_b) % 185.61/186.50 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.61/186.50 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_right__minus,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Groups_Ogroup__add(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__0,axiom, % 185.61/186.50 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.50 % 185.61/186.50 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 185.61/186.50 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__square__less__zero,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__ring(T_a) % 185.61/186.50 => ~ 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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__less__cancel__right__disj,axiom, % 185.61/186.50 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2))) % 185.61/186.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 185.61/186.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__less__cancel__left__disj,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.61/186.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 185.61/186.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__less__cancel__left__pos,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__pos__pos,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__pos__neg,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__pos__neg2,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zero__less__mult__pos,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( 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))) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zero__less__mult__pos2,axiom, % 185.61/186.50 ! [V_a,V_b,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( 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))) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__less__cancel__left__neg,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__neg__pos,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__neg__neg,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__strict__right__mono,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__strict__left__mono,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_comm__mult__strict__left__mono,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__strict__right__mono__neg,axiom, % 185.61/186.50 ! [V_c,V_a,V_b,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__strict__left__mono__neg,axiom, % 185.61/186.50 ! [V_c,V_a,V_b,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__one__less__zero,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zero__less__one,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__scale__eq__noteq,axiom, % 185.61/186.50 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 185.61/186.50 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 185.61/186.50 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => ( ( V_a = V_b % 185.61/186.50 & V_c != V_d ) % 185.61/186.50 => 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)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sum__squares__eq__zero__iff,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( 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) % 185.61/186.50 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_less__add__one,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.50 => 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)))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zadd__zminus__inverse2,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_negative__eq__positive,axiom, % 185.61/186.50 ! [V_m_2,V_n_2] : % 185.61/186.50 ( 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) % 185.61/186.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__int__zless__negative,axiom, % 185.61/186.50 ! [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)))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zmult__zless__mono2,axiom, % 185.61/186.50 ! [V_k,V_j,V_i] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_int__0__less__1,axiom, % 185.61/186.50 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))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_odd__nonzero,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zless__add1__eq,axiom, % 185.61/186.50 ! [V_z_2,V_w_2] : % 185.61/186.50 ( 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)))) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 185.61/186.50 | V_w_2 = V_z_2 ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__0,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__0__eq__iff,axiom, % 185.61/186.50 ! [V_z_2,T_b] : % 185.61/186.50 ( class_Int_Oring__char__0(T_b) % 185.61/186.50 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 185.61/186.50 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__eq__0__iff,axiom, % 185.61/186.50 ! [V_z_2,T_b] : % 185.61/186.50 ( class_Int_Oring__char__0(T_b) % 185.61/186.50 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__less__iff,axiom, % 185.61/186.50 ! [V_z_2,V_w_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__add,axiom, % 185.61/186.50 ! [V_z,V_w,T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__of__nat__eq,axiom, % 185.61/186.50 ! [V_n,T_a] : % 185.61/186.50 ( class_Rings_Oring__1(T_a) % 185.61/186.50 => 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) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mono__iff,axiom, % 185.61/186.50 ! [V_w_2,V_z_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zless__nat__conj,axiom, % 185.61/186.50 ! [V_z_2,V_w_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zless__nat__eq__int__zless,axiom, % 185.61/186.50 ! [V_z_2,V_m_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 185.61/186.50 <=> 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__sum__squares__lt__zero,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__ring(T_a) % 185.61/186.50 => ~ 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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sum__squares__gt__zero__iff,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.50 => ( 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)))) % 185.61/186.50 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.50 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zero__less__two,axiom, % 185.61/186.50 ! [T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.50 => 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)))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__nat__Suc,axiom, % 185.61/186.50 ! [V_m,T_a] : % 185.61/186.50 ( class_Rings_Osemiring__1(T_a) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_int__Suc0__eq__1,axiom, % 185.61/186.50 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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__aux__def,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_negD,axiom, % 185.61/186.50 ! [V_x] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.50 => ? [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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sgn__if,axiom, % 185.61/186.50 ! [V_x,T_a] : % 185.61/186.50 ( class_Groups_Osgn__if(T_a) % 185.61/186.50 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 185.61/186.50 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 185.61/186.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sgn__neg,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sgn__1__neg,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.50 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zsgn__def,axiom, % 185.61/186.50 ! [V_i] : % 185.61/186.50 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.50 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 185.61/186.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 185.61/186.50 ! [V_z] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.50 => 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)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__less__iff,axiom, % 185.61/186.50 ! [V_m_2,V_w_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 185.61/186.50 <=> 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_convex__bound__lt,axiom, % 185.61/186.50 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 185.61/186.50 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 185.61/186.50 => 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)) ) ) ) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sgn__1__pos,axiom, % 185.61/186.50 ! [V_a_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.50 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__refl,axiom, % 185.61/186.50 ! [V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le0,axiom, % 185.61/186.50 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_negative__zle,axiom, % 185.61/186.50 ! [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))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__le__mono,axiom, % 185.61/186.50 ! [V_l,V_k,V_j,V_i] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__le__mono2,axiom, % 185.61/186.50 ! [V_k,V_j,V_i] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.50 => 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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__le__mono1,axiom, % 185.61/186.50 ! [V_k,V_j,V_i] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.50 => 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))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mult__assoc,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mult__eq__1__iff,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.61/186.50 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.61/186.50 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mult__commute,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mult__1__right,axiom, % 185.61/186.50 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__1__eq__mult__iff,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 185.61/186.50 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.61/186.50 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__mult__1,axiom, % 185.61/186.50 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__cube,axiom, % 185.61/186.50 ! [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)))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__square,axiom, % 185.61/186.50 ! [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))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__eq__self__implies__10,axiom, % 185.61/186.50 ! [V_n,V_m] : % 185.61/186.50 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 185.61/186.50 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.61/186.50 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__mult__le__cancel1,axiom, % 185.61/186.50 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zle__refl,axiom, % 185.61/186.50 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zle__linear,axiom, % 185.61/186.50 ! [V_w,V_z] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 185.61/186.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zle__trans,axiom, % 185.61/186.50 ! [V_k,V_j,V_i] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zle__antisym,axiom, % 185.61/186.50 ! [V_w,V_z] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 185.61/186.50 => V_z = V_w ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_sgn__sgn,axiom, % 185.61/186.50 ! [V_a,T_a] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.50 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__fun__def,axiom, % 185.61/186.50 ! [V_g_2,V_f_2,T_b,T_c] : % 185.61/186.50 ( class_Orderings_Oord(T_c) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.61/186.50 <=> ! [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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__linear,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__eq__iff,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Oorder(T_b) % 185.61/186.50 => ( V_x_2 = V_y_2 % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__eq__refl,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => ( V_x = V_y % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__funD,axiom, % 185.61/186.50 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 185.61/186.50 ( class_Orderings_Oord(T_c) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__antisym__conv,axiom, % 185.61/186.50 ! [V_x_2,V_y_2,T_b] : % 185.61/186.50 ( class_Orderings_Oorder(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> V_x_2 = V_y_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_ord__eq__le__trans,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oord(T_a) % 185.61/186.50 => ( V_a = V_b % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I3_J,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( V_a = V_b % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_ord__le__eq__trans,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oord(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => ( V_b = V_c % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I4_J,axiom, % 185.61/186.50 ! [V_c,V_a,V_b,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.50 => ( V_b = V_c % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__antisym,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => V_x = V_y ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__trans,axiom, % 185.61/186.50 ! [V_z,V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I5_J,axiom, % 185.61/186.50 ! [V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => V_x = V_y ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I6_J,axiom, % 185.61/186.50 ! [V_z,V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__funE,axiom, % 185.61/186.50 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 185.61/186.50 ( class_Orderings_Oord(T_c) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__le__cases,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__nat__le__iff,axiom, % 185.61/186.50 ! [V_n_2,V_m_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 185.61/186.50 ! [V_y_2,V_x_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_zle__int,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_of__int__le__iff,axiom, % 185.61/186.50 ! [V_z_2,V_w_2,T_b] : % 185.61/186.50 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_one__le__mult__iff,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> ( 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)) % 185.61/186.50 & 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)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__le__cancel1,axiom, % 185.61/186.50 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__le__cancel2,axiom, % 185.61/186.50 ! [V_n_2,V_k_2,V_m_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 185.61/186.50 ! [V_y_2,V_x_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.61/186.50 => ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I8_J,axiom, % 185.61/186.50 ! [V_z,V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__le__less__trans,axiom, % 185.61/186.50 ! [V_z,V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I7_J,axiom, % 185.61/186.50 ! [V_z,V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__less__le__trans,axiom, % 185.61/186.50 ! [V_z,V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I11_J,axiom, % 185.61/186.50 ! [V_a,V_b,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.50 => ( V_a != V_b % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__le__neq__trans,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => ( V_a != V_b % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__le__imp__less__or__eq,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.50 | V_x = V_y ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__antisym__conv2,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Olinorder(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> V_x_2 = V_y_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__less__imp__le,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Opreorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_leD,axiom, % 185.61/186.50 ! [V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_xt1_I12_J,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( V_a != V_b % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__neq__le__trans,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Orderings_Oorder(T_a) % 185.61/186.50 => ( V_a != V_b % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__antisym__conv1,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Olinorder(T_b) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> V_x_2 = V_y_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__leE,axiom, % 185.61/186.50 ! [V_x,V_y,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_leI,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__le__less,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Oorder(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 | V_x_2 = V_y_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_less__le__not__le,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Opreorder(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_order__less__le,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Oorder(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 & V_x_2 != V_y_2 ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__le__less__linear,axiom, % 185.61/186.50 ! [V_y,V_x,T_a] : % 185.61/186.50 ( class_Orderings_Olinorder(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__not__le,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Olinorder(T_b) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_linorder__not__less,axiom, % 185.61/186.50 ! [V_y_2,V_x_2,T_b] : % 185.61/186.50 ( class_Orderings_Olinorder(T_b) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__le__imp__le__left,axiom, % 185.61/186.50 ! [V_b,V_a,V_c,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.50 => ( 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))) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__le__imp__le__right,axiom, % 185.61/186.50 ! [V_b,V_c,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.50 => ( 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))) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__mono,axiom, % 185.61/186.50 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.61/186.50 => 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))) ) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__left__mono,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__right__mono,axiom, % 185.61/186.50 ! [V_c,V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__le__cancel__left,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__le__cancel__right,axiom, % 185.61/186.50 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__0,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__0__right,axiom, % 185.61/186.50 ! [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) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__is__0,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.50 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.50 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__cancel1,axiom, % 185.61/186.50 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.50 ( 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) % 185.61/186.50 <=> ( V_m_2 = V_n_2 % 185.61/186.50 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_mult__cancel2,axiom, % 185.61/186.50 ! [V_n_2,V_k_2,V_m_2] : % 185.61/186.50 ( 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) % 185.61/186.50 <=> ( V_m_2 = V_n_2 % 185.61/186.50 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__mult__cancel1,axiom, % 185.61/186.50 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.50 ( 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) % 185.61/186.50 <=> V_m_2 = V_n_2 ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 185.61/186.50 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__0__eq,axiom, % 185.61/186.50 ! [V_n_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 185.61/186.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__minus__iff,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_minus__le__iff,axiom, % 185.61/186.50 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_neg__le__iff__le,axiom, % 185.61/186.50 ! [V_a_2,V_ba_2,T_b] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__imp__neg__le,axiom, % 185.61/186.50 ! [V_b,V_a,T_a] : % 185.61/186.50 ( class_Groups_Oordered__ab__group__add(T_a) % 185.61/186.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.50 => 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))) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__mult__distrib2,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_add__mult__distrib,axiom, % 185.61/186.50 ! [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)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__leD,axiom, % 185.61/186.50 ! [V_n,V_m] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__SucE,axiom, % 185.61/186.50 ! [V_n,V_m] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 185.61/186.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.50 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__SucI,axiom, % 185.61/186.50 ! [V_n,V_m] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__le__mono,axiom, % 185.61/186.50 ! [V_m_2,V_n_2] : % 185.61/186.50 ( 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))) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_le__Suc__eq,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.50 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_not__less__eq__eq,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Suc__n__not__le__n,axiom, % 185.61/186.50 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 185.61/186.50 % 185.61/186.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 185.61/186.50 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))) ). % 185.61/186.50 % 185.61/186.50 fof(fact_termination__basic__simps_I5_J,axiom, % 185.61/186.50 ! [V_y,V_x] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.61/186.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 185.61/186.50 % 185.61/186.50 fof(fact_nat__less__le,axiom, % 185.61/186.50 ! [V_n_2,V_m_2] : % 185.61/186.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.51 & V_m_2 != V_n_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__eq__less__or__eq,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.51 | V_m_2 = V_n_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_less__imp__le__nat,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__neq__implies__less,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => ( V_m != V_n % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_less__or__eq__imp__le,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 | V_m = V_n ) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_termination__basic__simps_I4_J,axiom, % 185.61/186.51 ! [V_y,V_z,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_termination__basic__simps_I3_J,axiom, % 185.61/186.51 ! [V_z,V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__add2,axiom, % 185.61/186.51 ! [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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__add1,axiom, % 185.61/186.51 ! [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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__iff__add,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.51 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__add__left__cancel__le,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_trans__le__add1,axiom, % 185.61/186.51 ! [V_m,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_trans__le__add2,axiom, % 185.61/186.51 ! [V_m,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__le__mono1,axiom, % 185.61/186.51 ! [V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__le__mono,axiom, % 185.61/186.51 ! [V_l,V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__leD2,axiom, % 185.61/186.51 ! [V_n,V_k,V_m] : % 185.61/186.51 ( 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)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__leD1,axiom, % 185.61/186.51 ! [V_n,V_k,V_m] : % 185.61/186.51 ( 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)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__leE,axiom, % 185.61/186.51 ! [V_n,V_k,V_m] : % 185.61/186.51 ( 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)) % 185.61/186.51 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zless__le,axiom, % 185.61/186.51 ! [V_w_2,V_z_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 185.61/186.51 & V_z_2 != V_w_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zadd__left__mono,axiom, % 185.61/186.51 ! [V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_evaln__nonstrict,axiom, % 185.61/186.51 ! [V_m,V_t,V_n,V_s,V_c] : % 185.61/186.51 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.51 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__le__eq__zle,axiom, % 185.61/186.51 ! [V_z_2,V_w_2] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__distrib,axiom, % 185.61/186.51 ! [V_z_H,V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_of__int__0__le__iff,axiom, % 185.61/186.51 ! [V_z_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_of__int__le__0__iff,axiom, % 185.61/186.51 ! [V_z_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn__0__0,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.51 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn0,axiom, % 185.61/186.51 ! [T_a] : % 185.61/186.51 ( class_Groups_Osgn__if(T_a) % 185.61/186.51 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn__times,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__distrib__neg,axiom, % 185.61/186.51 ! [V_z_H,V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__nonneg__nonneg,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__nonneg__eq__0__iff,axiom, % 185.61/186.51 ! [V_y_2,V_x_2,T_b] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_b) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 185.61/186.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__increasing,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__increasing2,axiom, % 185.61/186.51 ! [V_a,V_b,V_c,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__nonpos__nonpos,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__mult__neg__le,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.61/186.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 185.61/186.51 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__mult__pos__le,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__ring(T_a) % 185.61/186.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 185.61/186.51 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__mono,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__mono_H,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__mono__neg,axiom, % 185.61/186.51 ! [V_c,V_a,V_b,T_a] : % 185.61/186.51 ( class_Rings_Oordered__ring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__right__mono__neg,axiom, % 185.61/186.51 ! [V_c,V_a,V_b,T_a] : % 185.61/186.51 ( class_Rings_Oordered__ring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_comm__mult__left__mono,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__comm__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__mono,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__right__mono,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__nonpos__nonpos,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__ring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__nonpos__nonneg,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__nonneg__nonpos2,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__nonneg__nonpos,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__nonneg__nonneg,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__le__0__iff,axiom, % 185.61/186.51 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.61/186.51 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__le__mult__iff,axiom, % 185.61/186.51 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.51 => ( 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_ba_2))) % 185.61/186.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.61/186.51 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__le__square,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__ring(T_a) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__le__less__mono,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__less__le__mono,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__le__one,axiom, % 185.61/186.51 ! [T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_not__one__le__zero,axiom, % 185.61/186.51 ! [T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.51 => ~ 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_neg__0__le__iff__le,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__minus__self__iff,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_neg__le__0__iff__le,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_minus__le__self__iff,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.61/186.51 => ( 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)) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__eq__1__iff,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( 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)) % 185.61/186.51 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.61/186.51 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_of__nat__0__le__iff,axiom, % 185.61/186.51 ! [V_n,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__le__imp__of__nat,axiom, % 185.61/186.51 ! [V_m,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__0__less__mult__iff,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__cancel1,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__cancel2,axiom, % 185.61/186.51 ! [V_n_2,V_k_2,V_m_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__mono1,axiom, % 185.61/186.51 ! [V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__mono2,axiom, % 185.61/186.51 ! [V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__mult__less__cancel1,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__Suc__right,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__Suc,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_One__nat__def,axiom, % 185.61/186.51 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_less__eq__Suc__le,axiom, % 185.61/186.51 ! [V_m_2,V_n_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_less__Suc__eq__le,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__le__eq,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__imp__less__Suc,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__leI,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__less__Suc__eq,axiom, % 185.61/186.51 ! [V_n_2,V_m_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 185.61/186.51 <=> V_n_2 = V_m_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__le__lessD,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__eq__plus1__left,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Suc__eq__plus1,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 185.61/186.51 ! [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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 185.61/186.51 ! [V_Pa_2] : % 185.61/186.51 ( ? [B_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.61/186.51 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.61/186.51 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 185.61/186.51 ! [V_Pa_2] : % 185.61/186.51 ( ! [B_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.61/186.51 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zero__zle__int,axiom, % 185.61/186.51 ! [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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 185.61/186.51 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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_ex__nat,axiom, % 185.61/186.51 ! [V_Pa_2] : % 185.61/186.51 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.61/186.51 <=> ? [B_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.61/186.51 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_all__nat,axiom, % 185.61/186.51 ! [V_Pa_2] : % 185.61/186.51 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.61/186.51 <=> ! [B_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 185.61/186.51 ! [V_y_2,V_x_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.61/186.51 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 185.61/186.51 <=> V_x_2 = V_y_2 ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_eq__nat__nat__iff,axiom, % 185.61/186.51 ! [V_z_H_2,V_z_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 185.61/186.51 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 185.61/186.51 <=> V_z_2 = V_z_H_2 ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zadd__zless__mono,axiom, % 185.61/186.51 ! [V_z,V_z_H,V_w,V_w_H] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmult__int,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__mult,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zle__iff__zadd,axiom, % 185.61/186.51 ! [V_z_2,V_w_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 185.61/186.51 <=> ? [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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 185.61/186.51 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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__1,axiom, % 185.61/186.51 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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 185.61/186.51 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__pos__nonneg,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__nonneg__pos,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__strict__increasing,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__strict__increasing2,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__neg__nonpos,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add__nonpos__neg,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__le__imp__le,axiom, % 185.61/186.51 ! [V_b,V_a,V_c,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__right__le__imp__le,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__imp__less__left,axiom, % 185.61/186.51 ! [V_b,V_a,V_c,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__less__imp__less,axiom, % 185.61/186.51 ! [V_b,V_a,V_c,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__imp__less__right,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__right__less__imp__less,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring(T_a) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__le__less__imp__less,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__less__le__imp__less,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__strict__mono_H,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__strict__mono,axiom, % 185.61/186.51 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.51 => 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))) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__le__cancel__left__neg,axiom, % 185.61/186.51 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__le__cancel__left__pos,axiom, % 185.61/186.51 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sum__squares__le__zero__iff,axiom, % 185.61/186.51 ! [V_y_2,V_x_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__ring__strict(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sum__squares__ge__zero,axiom, % 185.61/186.51 ! [V_y,V_x,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__ring(T_a) % 185.61/186.51 => 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)))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__le__one__le,axiom, % 185.61/186.51 ! [V_y,V_x,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.51 => 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)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__right__le__one__le,axiom, % 185.61/186.51 ! [V_y,V_x,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.51 => 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)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn__less,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn__greater,axiom, % 185.61/186.51 ! [V_a_2,T_b] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_one__less__mult,axiom, % 185.61/186.51 ! [V_m,V_n] : % 185.61/186.51 ( 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)) % 185.61/186.51 => ( 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)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_n__less__n__mult__m,axiom, % 185.61/186.51 ! [V_m,V_n] : % 185.61/186.51 ( 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)) % 185.61/186.51 => ( 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)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_n__less__m__mult__n,axiom, % 185.61/186.51 ! [V_m,V_n] : % 185.61/186.51 ( 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)) % 185.61/186.51 => ( 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)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__le__0__conv,axiom, % 185.61/186.51 ! [V_n_2] : % 185.61/186.51 ( 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))) % 185.61/186.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__0__iff,axiom, % 185.61/186.51 ! [V_i_2] : % 185.61/186.51 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__le__0,axiom, % 185.61/186.51 ! [V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__one__le__iff__zero__less,axiom, % 185.61/186.51 ! [V_z_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__0__le,axiom, % 185.61/186.51 ! [V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__eq__iff,axiom, % 185.61/186.51 ! [V_z_2,V_m_2] : % 185.61/186.51 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 185.61/186.51 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__nat__eq,axiom, % 185.61/186.51 ! [V_z] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => 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) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zless__imp__add1__zle,axiom, % 185.61/186.51 ! [V_z,V_w] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_add1__zle__eq,axiom, % 185.61/186.51 ! [V_z_2,V_w_2] : % 185.61/186.51 ( 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)) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zle__add1__eq__le,axiom, % 185.61/186.51 ! [V_z_2,V_w_2] : % 185.61/186.51 ( 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)))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_int__zle__neg,axiom, % 185.61/186.51 ! [V_m_2,V_n_2] : % 185.61/186.51 ( 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)))) % 185.61/186.51 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.51 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_negative__zle__0,axiom, % 185.61/186.51 ! [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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_convex__bound__le,axiom, % 185.61/186.51 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__semiring__1(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 185.61/186.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 185.61/186.51 => 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)) ) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__less__eq__zless,axiom, % 185.61/186.51 ! [V_z_2,V_w_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 185.61/186.51 ! [V_y_2,V_x_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__eq__iff,axiom, % 185.61/186.51 ! [V_m_2,V_w_2] : % 185.61/186.51 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 185.61/186.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__eq__iff2,axiom, % 185.61/186.51 ! [V_w_2,V_m_2] : % 185.61/186.51 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 185.61/186.51 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.61/186.51 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__add__distrib,axiom, % 185.61/186.51 ! [V_z_H,V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 185.61/186.51 => 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)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__imp__0__less,axiom, % 185.61/186.51 ! [V_z] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_not__zle__0__negative,axiom, % 185.61/186.51 ! [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))))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_of__nat__nat,axiom, % 185.61/186.51 ! [V_z,T_a] : % 185.61/186.51 ( class_Rings_Oring__1(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.51 => 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) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_sgn__pos,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.51 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_self__quotient__aux2,axiom, % 185.61/186.51 ! [V_q,V_r,V_a] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.51 => ( 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)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_self__quotient__aux1,axiom, % 185.61/186.51 ! [V_q,V_r,V_a] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.51 => ( 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)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_q__pos__lemma,axiom, % 185.61/186.51 ! [V_r_H,V_q_H,V_b_H] : % 185.61/186.51 ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_q__neg__lemma,axiom, % 185.61/186.51 ! [V_r_H,V_q_H,V_b_H] : % 185.61/186.51 ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_unique__quotient__lemma,axiom, % 185.61/186.51 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 185.61/186.51 ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zdiv__mono2__lemma,axiom, % 185.61/186.51 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 185.61/186.51 ( 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) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_unique__quotient__lemma__neg,axiom, % 185.61/186.51 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 185.61/186.51 ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zdiv__mono2__neg__lemma,axiom, % 185.61/186.51 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 185.61/186.51 ( 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) % 185.61/186.51 => ( 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))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__le__cancel1,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__refl,axiom, % 185.61/186.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__le__linear,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_eq__imp__le,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( V_m = V_n % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__trans,axiom, % 185.61/186.51 ! [V_k,V_j,V_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 185.61/186.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_le__antisym,axiom, % 185.61/186.51 ! [V_n,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.51 => V_m = V_n ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_less__fun__def,axiom, % 185.61/186.51 ! [V_g_2,V_f_2,T_b,T_c] : % 185.61/186.51 ( class_Orderings_Oord(T_c) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.61/186.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.61/186.51 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__eq__cancel__disj,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( 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) % 185.61/186.51 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.51 | V_m_2 = V_n_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_left__add__mult__distrib,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__eq__cancel1,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.51 => ( 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) % 185.61/186.51 <=> V_m_2 = V_n_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_nat__mult__less__cancel1,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_transfer__morphism__nat__int,axiom, % 185.61/186.51 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))) ). % 185.61/186.51 % 185.61/186.51 fof(fact_compl__le__compl__iff,axiom, % 185.61/186.51 ! [V_y_2,V_x_2,T_b] : % 185.61/186.51 ( class_Lattices_Oboolean__algebra(T_b) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_compl__mono,axiom, % 185.61/186.51 ! [V_y,V_x,T_a] : % 185.61/186.51 ( class_Lattices_Oboolean__algebra(T_a) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_ex__least__nat__less,axiom, % 185.61/186.51 ! [V_n_2,V_Pa_2] : % 185.61/186.51 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 185.61/186.51 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 185.61/186.51 => ? [B_k] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 185.61/186.51 & ! [B_i] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 185.61/186.51 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 185.61/186.51 & 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)))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_divmod__int__rel__mod__eq,axiom, % 185.61/186.51 ! [V_y,V_q_1,V_b_1,V_a_1] : % 185.61/186.51 ( 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) % 185.61/186.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.61/186.51 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmult2__lemma__aux2,axiom, % 185.61/186.51 ! [V_q,V_r,V_b,V_c] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmult2__lemma__aux1,axiom, % 185.61/186.51 ! [V_q,V_r,V_b,V_c] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmult2__lemma__aux4,axiom, % 185.61/186.51 ! [V_q,V_b,V_r,V_c] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mod__trivial,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__0,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__by__0,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__self,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__self2,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__self1,axiom, % 185.61/186.51 ! [V_a,V_b,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__right__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__left__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__simps_I2_J,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__simps_I1_J,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__add__cong,axiom, % 185.61/186.51 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.61/186.51 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.61/186.51 => 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) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__right__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__left__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__eq,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__mult1,axiom, % 185.61/186.51 ! [V_b,V_a,V_c,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__mult2,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__simps_I4_J,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__cong,axiom, % 185.61/186.51 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.61/186.51 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.61/186.51 => 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) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__minus__eq,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Oring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__minus__cong,axiom, % 185.61/186.51 ! [V_a_H,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Oring__div(T_a) % 185.61/186.51 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 185.61/186.51 => 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) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zero,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__self,axiom, % 185.61/186.51 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__simps_I3_J,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zmult1__eq,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zminus__zmod,axiom, % 185.61/186.51 ! [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) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zminus__zminus,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zminus2,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__self2__is__0,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__self1__is__0,axiom, % 185.61/186.51 ! [V_a,V_b,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__self2,axiom, % 185.61/186.51 ! [V_c,V_b,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult__self1,axiom, % 185.61/186.51 ! [V_b,V_c,V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__by__1,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Divides_Osemiring__div(T_a) % 185.61/186.51 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__le__nonneg__dividend,axiom, % 185.61/186.51 ! [V_k,V_m] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_neg__mod__bound,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_pos__mod__bound,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__eq__0__iff,axiom, % 185.61/186.51 ! [V_d_2,V_m_2] : % 185.61/186.51 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.51 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zminus2__not__zero,axiom, % 185.61/186.51 ! [V_l,V_k] : % 185.61/186.51 ( 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) % 185.61/186.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zminus1__not__zero,axiom, % 185.61/186.51 ! [V_l,V_k] : % 185.61/186.51 ( 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) % 185.61/186.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__neg__neg__trivial,axiom, % 185.61/186.51 ! [V_b,V_a] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 185.61/186.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_neg__mod__conj,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ( 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))) % 185.61/186.51 & 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_neg__mod__sign,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__pos__pos__trivial,axiom, % 185.61/186.51 ! [V_b,V_a] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.51 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_pos__mod__conj,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.51 => ( 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))) % 185.61/186.51 & 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)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_pos__mod__sign,axiom, % 185.61/186.51 ! [V_a,V_b] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.51 => 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))) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__left__idem,axiom, % 185.61/186.51 ! [V_b,V_a,T_a] : % 185.61/186.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.61/186.51 => 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) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mult__idem,axiom, % 185.61/186.51 ! [V_x,T_a] : % 185.61/186.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.61/186.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_times_Oidem,axiom, % 185.61/186.51 ! [V_a,T_a] : % 185.61/186.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.61/186.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_compl__eq__compl__iff,axiom, % 185.61/186.51 ! [V_y_2,V_x_2,T_b] : % 185.61/186.51 ( class_Lattices_Oboolean__algebra(T_b) % 185.61/186.51 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 185.61/186.51 <=> V_x_2 = V_y_2 ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_uminus__apply,axiom, % 185.61/186.51 ! [V_x_2,V_A_2,T_c,T_b] : % 185.61/186.51 ( class_Groups_Ouminus(T_b) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_double__compl,axiom, % 185.61/186.51 ! [V_x,T_a] : % 185.61/186.51 ( class_Lattices_Oboolean__algebra(T_a) % 185.61/186.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__pos__neg__trivial,axiom, % 185.61/186.51 ! [V_b,V_a] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.51 => ( 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))) % 185.61/186.51 => 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) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__zmod,axiom, % 185.61/186.51 ! [V_k_2,V_n_2,V_Pa_2] : % 185.61/186.51 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 185.61/186.51 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 185.61/186.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.51 => ! [B_i,B_j] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 185.61/186.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ! [B_i,B_j] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmult2__lemma__aux3,axiom, % 185.61/186.51 ! [V_q,V_b,V_r,V_c] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.61/186.51 => 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))) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_z3mod__def,axiom, % 185.61/186.51 ! [V_k,V_l] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.51 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.51 => 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)) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__pos__lemma,axiom, % 185.61/186.51 ! [V_n_2,V_Pa_2,V_k_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> ! [B_i,B_j] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__neg__lemma,axiom, % 185.61/186.51 ! [V_n_2,V_Pa_2,V_k_2] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ( 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))) % 185.61/186.51 <=> ! [B_i,B_j] : % 185.61/186.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zmod__zmult2__eq,axiom, % 185.61/186.51 ! [V_b,V_a,V_c] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.51 => 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)) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 185.61/186.51 ! [V_y,V_x] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.51 => 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))) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__zdiv,axiom, % 185.61/186.51 ! [V_k_2,V_n_2,V_Pa_2] : % 185.61/186.51 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 185.61/186.51 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.51 => ! [B_i] : % 185.61/186.51 ( ? [B_j] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 185.61/186.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 => ! [B_i] : % 185.61/186.51 ( ? [B_j] : % 185.61/186.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.51 & 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) ) % 185.61/186.51 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_divmod__int__rel__div__eq,axiom, % 185.61/186.51 ! [V_r_1,V_y,V_b_1,V_a_1] : % 185.61/186.51 ( 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) % 185.61/186.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 185.61/186.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.61/186.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 185.61/186.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.61/186.51 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.51 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_split__div_H,axiom, % 185.61/186.51 ! [V_n_2,V_m_2,V_Pa_2] : % 185.61/186.51 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 185.61/186.51 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.51 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.61/186.51 | ? [B_q] : % 185.61/186.51 ( 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)) % 185.61/186.51 & 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)))) % 185.61/186.51 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 185.61/186.51 % 185.61/186.51 fof(fact_div__add1__eq,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_zdiv__int,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_mod__mult2__eq,axiom, % 185.61/186.51 ! [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)) ). % 185.61/186.51 % 185.61/186.51 fof(fact_div__mult1__eq,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__le__mono,axiom, % 185.61/186.52 ! [V_k,V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__le__dividend,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zero,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult2__eq,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__less,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__less__eq__dividend,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__mult__distrib,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__mult__distrib2,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zminus2,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zminus__zminus,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__0,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__by__0,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__by__1,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__div__distrib,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__1,axiom, % 185.61/186.52 ! [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 ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__less,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__mult__div__cancel__disj,axiom, % 185.61/186.52 ! [V_n,V_m,V_k] : % 185.61/186.52 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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) ) % 185.61/186.52 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__Suc,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 185.61/186.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.52 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__1,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__less__divisor,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 185.61/186.52 ! [V_a_2,V_ba_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 185.61/186.52 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 185.61/186.52 ! [V_a_2,V_ba_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__neg__pos__less0,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__self,axiom, % 185.61/186.52 ! [V_a] : % 185.61/186.52 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__eq__0__iff,axiom, % 185.61/186.52 ! [V_d_2,V_m_2] : % 185.61/186.52 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_DIVISION__BY__ZERO,axiom, % 185.61/186.52 ! [V_a] : % 185.61/186.52 ( 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) % 185.61/186.52 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__zdiv__trivial,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__mult__self3,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zadd1__eq,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__int,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__mult1,axiom, % 185.61/186.52 ! [V_b,V_a,V_c,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__mult2,axiom, % 185.61/186.52 ! [V_b,V_a,V_c,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self1__is__id,axiom, % 185.61/186.52 ! [V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self2__is__id,axiom, % 185.61/186.52 ! [V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__mult1__if,axiom, % 185.61/186.52 ! [V_b,V_a,V_c,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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) ) % 185.61/186.52 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__self,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__div__trivial,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__le__mono2,axiom, % 185.61/186.52 ! [V_k,V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self__is__m,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self1__is__m,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__mult__div__cancel1,axiom, % 185.61/186.52 ! [V_n,V_m,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__less__dividend,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__eq__0__iff,axiom, % 185.61/186.52 ! [V_k_2,V_i_2] : % 185.61/186.52 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 185.61/186.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 185.61/186.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 185.61/186.52 ! [V_a_2,V_ba_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 185.61/186.52 => ( 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_ba_2))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 185.61/186.52 ! [V_i_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 185.61/186.52 => ( 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_ba_2))) % 185.61/186.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),V_a_2)) % 185.61/186.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__mono2,axiom, % 185.61/186.52 ! [V_b,V_b_H,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.61/186.52 => 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))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__nonneg__neg__le0,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__pos__pos__trivial,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 185.61/186.52 ! [V_a_2,V_ba_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( 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_ba_2))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__nonpos__pos__le0,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__mono2__neg,axiom, % 185.61/186.52 ! [V_b,V_b_H,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.61/186.52 => 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))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__neg__neg__trivial,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__mono1,axiom, % 185.61/186.52 ! [V_b,V_a_H,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__mono1__neg,axiom, % 185.61/186.52 ! [V_b,V_a_H,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__le__divisor,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_int__div__less__self,axiom, % 185.61/186.52 ! [V_k,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zmult2__eq,axiom, % 185.61/186.52 ! [V_b,V_a,V_c] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__mult__self4,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zmod__equality2,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zmod__equality,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zmult1__eq,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__zdiv__equality,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self1,axiom, % 185.61/186.52 ! [V_c,V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mult__self2,axiom, % 185.61/186.52 ! [V_c,V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__add__self1,axiom, % 185.61/186.52 ! [V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__add__self2,axiom, % 185.61/186.52 ! [V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mod__equality,axiom, % 185.61/186.52 ! [V_c,V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mod__equality2,axiom, % 185.61/186.52 ! [V_c,V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__div__equality,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__div__equality2,axiom, % 185.61/186.52 ! [V_a,V_b,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_split__div,axiom, % 185.61/186.52 ! [V_k_2,V_n_2,V_Pa_2] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 185.61/186.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.61/186.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => ! [B_i,B_j] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 185.61/186.52 => ( 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) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__lemma,axiom, % 185.61/186.52 ! [V_q,V_b,V_r,V_c] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_split__mod,axiom, % 185.61/186.52 ! [V_k_2,V_n_2,V_Pa_2] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 185.61/186.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 185.61/186.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => ! [B_i,B_j] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 185.61/186.52 => ( 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) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__times__mod__eq,axiom, % 185.61/186.52 ! [V_m,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__mod__distrib,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_split__div__lemma,axiom, % 185.61/186.52 ! [V_m_2,V_q_2,V_n_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.61/186.52 => ( ( 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)) % 185.61/186.52 & 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)))) ) % 185.61/186.52 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_z3div__def,axiom, % 185.61/186.52 ! [V_k,V_l] : % 185.61/186.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.52 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zminus1__eq__if,axiom, % 185.61/186.52 ! [V_a,V_b] : % 185.61/186.52 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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)) ) % 185.61/186.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiv__zminus2__eq__if,axiom, % 185.61/186.52 ! [V_a,V_b] : % 185.61/186.52 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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)) ) % 185.61/186.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__div__geq,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__div__decomp,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Osemiring__div(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 185.61/186.52 ! [V_y,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_incr__mult__lemma,axiom, % 185.61/186.52 ! [V_k_2,V_Pa_2,V_d_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.61/186.52 => ( ! [B_x] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.52 => ! [B_x] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.61/186.52 => 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)))) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_field__le__mult__one__interval,axiom, % 185.61/186.52 ! [V_y,V_x,T_a] : % 185.61/186.52 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.52 => ( ! [B_z] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.52 => 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)) ) ) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__commute,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__eq__diff__eq,axiom, % 185.61/186.52 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oab__group__add(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.61/186.52 => ( V_a_2 = V_ba_2 % 185.61/186.52 <=> V_ca_2 = V_d_2 ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_of__int__diff,axiom, % 185.61/186.52 ! [V_z,V_w,T_a] : % 185.61/186.52 ( class_Rings_Oring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__apply,axiom, % 185.61/186.52 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.61/186.52 ( class_Groups_Ominus(T_b) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_of__nat__diff,axiom, % 185.61/186.52 ! [V_m,V_n,T_a] : % 185.61/186.52 ( class_Rings_Oring__1(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__int,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__eq__diff__less__eq,axiom, % 185.61/186.52 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_right__minus__eq,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.52 <=> V_a_2 = V_ba_2 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_eq__iff__diff__eq__0,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oab__group__add(T_b) % 185.61/186.52 => ( V_a_2 = V_ba_2 % 185.61/186.52 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__self,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__0__right,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__eq__diff__less,axiom, % 185.61/186.52 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__diff__cancel,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__cancel,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__diff__eq,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oab__group__add(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__diff__right__eq,axiom, % 185.61/186.52 ! [V_c,V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Oring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__diff__left__eq,axiom, % 185.61/186.52 ! [V_c,V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Oring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__diff__eq,axiom, % 185.61/186.52 ! [V_c,V_b,V_a,T_a] : % 185.61/186.52 ( class_Divides_Oring__div(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__diff__cong,axiom, % 185.61/186.52 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.61/186.52 ( class_Divides_Oring__div(T_a) % 185.61/186.52 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.61/186.52 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.61/186.52 => 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) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__0__eq__0,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__nat_Odiff__0,axiom, % 185.61/186.52 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__self__eq__0,axiom, % 185.61/186.52 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diffs0__imp__equal,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => V_m = V_n ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__diff__diff,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__Suc,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__imp__diff__less,axiom, % 185.61/186.52 ! [V_n,V_k,V_j] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__less__mono2,axiom, % 185.61/186.52 ! [V_l,V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__if,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__geq,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__inverse2,axiom, % 185.61/186.52 ! [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 ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__inverse,axiom, % 185.61/186.52 ! [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 ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__diff__left,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__cancel,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__cancel2,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__diff__iff,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat_Odiff__diff__eq,axiom, % 185.61/186.52 ! [V_n,V_m,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_eq__diff__iff,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.61/186.52 => ( 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) % 185.61/186.52 <=> V_m_2 = V_n_2 ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__diff__cancel,axiom, % 185.61/186.52 ! [V_n,V_i] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__le__mono,axiom, % 185.61/186.52 ! [V_l,V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__le__mono2,axiom, % 185.61/186.52 ! [V_l,V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__le__self,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__mod__geq,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__zmult__distrib2,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__zmult__distrib,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__mult__distrib,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__mult__distrib2,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__zmod__right,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__zmod__left,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__diff__distrib,axiom, % 185.61/186.52 ! [V_z,V_z_H] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zdiff__int__split,axiom, % 185.61/186.52 ! [V_y_2,V_x_2,V_Pa_2] : % 185.61/186.52 ( 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)))) % 185.61/186.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 185.61/186.52 => 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)))) ) % 185.61/186.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__iff__diff__le__0,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__iff__diff__less__0,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_eq__add__iff1,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oring(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2) % 185.61/186.52 <=> 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_ba_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_eq__add__iff2,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oring(T_b) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2) % 185.61/186.52 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__0,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__minus__eq__add,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_ab__diff__minus,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oab__group__add(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__def,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Ogroup__add(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 185.61/186.52 ! [V_y,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__ring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__bin__lemma,axiom, % 185.61/186.52 ! [V_l_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 185.61/186.52 <=> 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zero__less__diff,axiom, % 185.61/186.52 ! [V_m_2,V_n_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__less,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__less__Suc,axiom, % 185.61/186.52 ! [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))) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__0,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__is__0__eq,axiom, % 185.61/186.52 ! [V_n_2,V_m_2] : % 185.61/186.52 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__is__0__eq_H,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__diff__conv,axiom, % 185.61/186.52 ! [V_k_2,V_j_2,V_i_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 185.61/186.52 <=> 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__diff__inverse,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__diff__le,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__diff__iff,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__less__mono,axiom, % 185.61/186.52 ! [V_c,V_b,V_a] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 185.61/186.52 => 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__assoc2,axiom, % 185.61/186.52 ! [V_i,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__diff__assoc2,axiom, % 185.61/186.52 ! [V_i,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__add__assoc,axiom, % 185.61/186.52 ! [V_i,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__imp__diff__is__add,axiom, % 185.61/186.52 ! [V_k_2,V_j_2,V_i_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.61/186.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 185.61/186.52 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__add__diff__inverse2,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__diff__conv2,axiom, % 185.61/186.52 ! [V_i_2,V_j_2,V_k_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__diff__assoc,axiom, % 185.61/186.52 ! [V_i,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__add__diff__inverse,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__add__diff,axiom, % 185.61/186.52 ! [V_m,V_n,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__diff__conv,axiom, % 185.61/186.52 ! [V_i_2,V_k_2,V_j_2] : % 185.61/186.52 ( 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)) % 185.61/186.52 <=> 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__diff__right,axiom, % 185.61/186.52 ! [V_i,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__int__def,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__int__def__symmetric,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__eq__diff__pred,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__1,axiom, % 185.61/186.52 ! [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 ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__mod__equality_H,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mult__div__cancel,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Divides_Omod__div__equality_H,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_tsub__eq,axiom, % 185.61/186.52 ! [V_x,V_y] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.61/186.52 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__add__iff1,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oordered__ring(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.61/186.52 <=> 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_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__add__iff2,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oordered__ring(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__add__iff1,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oordered__ring(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.61/186.52 <=> 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_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__add__iff2,axiom, % 185.61/186.52 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Oordered__ring(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__less,axiom, % 185.61/186.52 ! [V_i,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__pred,axiom, % 185.61/186.52 ! [V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__diff__split,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,V_Pa_2] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 185.61/186.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.61/186.52 & ! [B_d] : % 185.61/186.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__diff__split__asm,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,V_Pa_2] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 185.61/186.52 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.61/186.52 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.61/186.52 | ? [B_d] : % 185.61/186.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 185.61/186.52 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zle__diff1__eq,axiom, % 185.61/186.52 ! [V_z_2,V_w_2] : % 185.61/186.52 ( 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)))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__diff__eq2,axiom, % 185.61/186.52 ! [V_m,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__Suc__diff__eq1,axiom, % 185.61/186.52 ! [V_m,V_j,V_k] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__le__add__iff1,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__diff__add__eq1,axiom, % 185.61/186.52 ! [V_n,V_m,V_u,V_i,V_j] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__eq__add__iff1,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.61/186.52 => ( 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) % 185.61/186.52 <=> 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 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__le__add__iff2,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__diff__add__eq2,axiom, % 185.61/186.52 ! [V_n,V_m,V_u,V_j,V_i] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__eq__add__iff2,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.61/186.52 => ( 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) % 185.61/186.52 <=> 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__zminus2__eq__if,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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) ) % 185.61/186.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__zminus1__eq__if,axiom, % 185.61/186.52 ! [V_b,V_a] : % 185.61/186.52 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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) ) % 185.61/186.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmod__zdiv__equality_H,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zmult__div__cancel,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_tsub__def,axiom, % 185.61/186.52 ! [V_x,V_y] : % 185.61/186.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.61/186.52 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.61/186.52 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__diff__1,axiom, % 185.61/186.52 ! [V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Suc__pred_H,axiom, % 185.61/186.52 ! [V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__less__add__iff1,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__less__add__iff2,axiom, % 185.61/186.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__eq__if,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 185.61/186.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__if,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_div__geq,axiom, % 185.61/186.52 ! [V_m,V_n] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mult__eq__if,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_int__power__div__base,axiom, % 185.61/186.52 ! [V_k,V_m] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.61/186.52 => 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)))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_decr__mult__lemma,axiom, % 185.61/186.52 ! [V_k_2,V_Pa_2,V_d_2] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.61/186.52 => ( ! [B_x] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.61/186.52 => ! [B_x] : % 185.61/186.52 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.61/186.52 => 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)))) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_incr__lemma,axiom, % 185.61/186.52 ! [V_x,V_z,V_d] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_decr__lemma,axiom, % 185.61/186.52 ! [V_z,V_x,V_d] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__mod__eq__lemma,axiom, % 185.61/186.52 ! [V_y,V_n,V_x] : % 185.61/186.52 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 185.61/186.52 => ? [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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mod__induct__0,axiom, % 185.61/186.52 ! [V_i_2,V_Pa_2,V_p_2] : % 185.61/186.52 ( ! [B_i] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 185.61/186.52 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 185.61/186.52 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 185.61/186.52 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_expand__Suc,axiom, % 185.61/186.52 ! [V_v] : % 185.61/186.52 ( 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))) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__gcd_Osimps,axiom, % 185.61/186.52 ! [V_x,V_y] : % 185.61/186.52 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 185.61/186.52 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_of__int__power,axiom, % 185.61/186.52 ! [V_n,V_z,T_a] : % 185.61/186.52 ( class_Rings_Oring__1(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_of__int__number__of__eq,axiom, % 185.61/186.52 ! [V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__idempotent,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_eq__number__of,axiom, % 185.61/186.52 ! [V_y_2,V_x_2,T_b] : % 185.61/186.52 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.52 & class_Int_Oring__char__0(T_b) ) % 185.61/186.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.61/186.52 <=> V_x_2 = V_y_2 ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__reorient,axiom, % 185.61/186.52 ! [V_x_2,V_w_2,T_b] : % 185.61/186.52 ( class_Int_Onumber(T_b) % 185.61/186.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 185.61/186.52 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zero__le__zpower__abs,axiom, % 185.61/186.52 ! [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))) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__le__D1,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__ge__self,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__zero,axiom, % 185.61/186.52 ! [T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__eq__0,axiom, % 185.61/186.52 ! [V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.52 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__add__abs,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__mult__self,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__mult,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__minus__commute,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__one,axiom, % 185.61/186.52 ! [T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__minus__cancel,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 185.61/186.52 ! [V_q,V_y,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__of__nat,axiom, % 185.61/186.52 ! [V_n,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__int__eq,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 185.61/186.52 ! [V_q,V_p,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zpower__zpower,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 185.61/186.52 ! [V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zpower__zmod,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_of__nat__number__of__lemma,axiom, % 185.61/186.52 ! [V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => ( ( 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))) % 185.61/186.52 => 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) ) % 185.61/186.52 & ( ~ 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))) % 185.61/186.52 => 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) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__eq,axiom, % 185.61/186.52 ! [V_k,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__number__of,axiom, % 185.61/186.52 ! [V_x,T_a] : % 185.61/186.52 ( ( class_Int_Onumber__ring(T_a) % 185.61/186.52 & class_Rings_Olinordered__idom(T_a) ) % 185.61/186.52 => ( ( 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))) % 185.61/186.52 => 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)) ) % 185.61/186.52 & ( ~ 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))) % 185.61/186.52 => 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) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zero__less__zpower__abs__iff,axiom, % 185.61/186.52 ! [V_n_2,V_x_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.52 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__of__nonneg,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__le__zero__iff,axiom, % 185.61/186.52 ! [V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__ge__zero,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__not__less__zero,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ~ 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zero__less__abs__iff,axiom, % 185.61/186.52 ! [V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__of__pos,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__triangle__ineq,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__mult__less,axiom, % 185.61/186.52 ! [V_d,V_b,V_c,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 185.61/186.52 => 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))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__triangle__ineq2__sym,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__triangle__ineq2,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__triangle__ineq3,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__ge__minus__self,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__le__iff,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 185.61/186.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.61/186.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__leI,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__le__D2,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__less__iff,axiom, % 185.61/186.52 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 185.61/186.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.61/186.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__number__of__eq__not__less,axiom, % 185.61/186.52 ! [V_w_2,V_v_2,T_b] : % 185.61/186.52 ( ( class_Int_Onumber(T_b) % 185.61/186.52 & class_Orderings_Olinorder(T_b) ) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> ~ 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_left__distrib__number__of,axiom, % 185.61/186.52 ! [V_v,V_b,V_a,T_b] : % 185.61/186.52 ( ( class_Int_Onumber(T_b) % 185.61/186.52 & class_Rings_Osemiring(T_b) ) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_right__distrib__number__of,axiom, % 185.61/186.52 ! [V_c,V_b,V_v,T_b] : % 185.61/186.52 ( ( class_Int_Onumber(T_b) % 185.61/186.52 & class_Rings_Osemiring(T_b) ) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 185.61/186.52 ! [V_q,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 185.61/186.52 ! [V_q,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 185.61/186.52 ! [V_q,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_left__diff__distrib__number__of,axiom, % 185.61/186.52 ! [V_v,V_b,V_a,T_b] : % 185.61/186.52 ( ( class_Int_Onumber(T_b) % 185.61/186.52 & class_Rings_Oring(T_b) ) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_right__diff__distrib__number__of,axiom, % 185.61/186.52 ! [V_c,V_b,V_v,T_b] : % 185.61/186.52 ( ( class_Int_Onumber(T_b) % 185.61/186.52 & class_Rings_Oring(T_b) ) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_le__number__of,axiom, % 185.61/186.52 ! [V_y_2,V_x_2,T_b] : % 185.61/186.52 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.52 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 185.61/186.52 ! [V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 185.61/186.52 ! [V_q,V_p,V_x,T_a] : % 185.61/186.52 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__number__of,axiom, % 185.61/186.52 ! [V_y_2,V_x_2,T_b] : % 185.61/186.52 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.52 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.52 => ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__add,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__number__of__eq,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__number__of__left,axiom, % 185.61/186.52 ! [V_z,V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 185.61/186.52 ! [V_n,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mult__number__of__left,axiom, % 185.61/186.52 ! [V_z,V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_arith__simps_I32_J,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__mult,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__zmult__eq__1,axiom, % 185.61/186.52 ! [V_n,V_m] : % 185.61/186.52 ( 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) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__diff,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zpower__zadd__distrib,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__minus,axiom, % 185.61/186.52 ! [V_w,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_arith__simps_I30_J,axiom, % 185.61/186.52 ! [V_w,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_mult__sgn__abs,axiom, % 185.61/186.52 ! [V_x,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => 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 ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__sgn,axiom, % 185.61/186.52 ! [V_k,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__mult__pos,axiom, % 185.61/186.52 ! [V_y,V_x,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__eq__mult,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Rings_Oordered__ring__abs(T_a) % 185.61/186.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 185.61/186.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 185.61/186.52 => 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)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__diff__triangle__ineq,axiom, % 185.61/186.52 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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))))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__triangle__ineq4,axiom, % 185.61/186.52 ! [V_b,V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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)))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__of__nonpos,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__minus__le__zero,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__if,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oabs__if(T_a) % 185.61/186.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_abs__of__neg,axiom, % 185.61/186.52 ! [V_a,T_a] : % 185.61/186.52 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zabs__less__one__iff,axiom, % 185.61/186.52 ! [V_z_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__number__of__diff1,axiom, % 185.61/186.52 ! [V_c,V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zabs__def,axiom, % 185.61/186.52 ! [V_i] : % 185.61/186.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 185.61/186.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.52 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__number__of__mult,axiom, % 185.61/186.52 ! [V_z,V_w,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__abs__mult__distrib,axiom, % 185.61/186.52 ! [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))) ). % 185.61/186.52 % 185.61/186.52 fof(fact_diff__number__of__eq,axiom, % 185.61/186.52 ! [V_w,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_add__number__of__diff2,axiom, % 185.61/186.52 ! [V_w,V_c,V_v,T_a] : % 185.61/186.52 ( class_Int_Onumber__ring(T_a) % 185.61/186.52 => 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) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__strict__mono,axiom, % 185.61/186.52 ! [V_n,V_b,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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))) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_one__less__power,axiom, % 185.61/186.52 ! [V_n,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.52 => 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))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__increasing__iff,axiom, % 185.61/186.52 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__le__imp__le__exp,axiom, % 185.61/186.52 ! [V_n,V_m,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.52 => ( 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))) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__decreasing,axiom, % 185.61/186.52 ! [V_a,V_N,V_n,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.52 => 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))) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__strict__decreasing,axiom, % 185.61/186.52 ! [V_a,V_N,V_n,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.52 => 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))) ) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__Suc__less__one,axiom, % 185.61/186.52 ! [V_n,V_a,T_a] : % 185.61/186.52 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.52 => 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))) ) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_number__of__is__id,axiom, % 185.61/186.52 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__eq__number__of__int__code,axiom, % 185.61/186.52 ! [V_l_2,V_k_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_less__number__of__int__code,axiom, % 185.61/186.52 ! [V_l_2,V_k_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_plus__numeral__code_I9_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_times__numeral__code_I5_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__numeral__code_I5_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__Suc__0,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 185.61/186.52 ! [V_m_2,V_x_2] : % 185.61/186.52 ( 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)) % 185.61/186.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__power__less__imp__less,axiom, % 185.61/186.52 ! [V_n,V_m,V_i] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 185.61/186.52 => ( 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))) % 185.61/186.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__zero__less__power__iff,axiom, % 185.61/186.52 ! [V_n_2,V_x_2] : % 185.61/186.52 ( 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))) % 185.61/186.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 185.61/186.52 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_int__number__of__def,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__one__le__power,axiom, % 185.61/186.52 ! [V_n,V_i] : % 185.61/186.52 ( 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)) % 185.61/186.52 => 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))) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__number__of,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__number__of__def,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_int__power,axiom, % 185.61/186.52 ! [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) ). % 185.61/186.52 % 185.61/186.52 fof(fact_zpower__int,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 185.61/186.52 ! [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)) ). % 185.61/186.52 % 185.61/186.52 fof(fact_minus__numeral__code_I6_J,axiom, % 185.61/186.52 ! [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))) ). % 185.61/186.52 % 185.61/186.52 fof(fact_power__eq__if,axiom, % 185.61/186.52 ! [V_p,V_m] : % 185.61/186.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 185.61/186.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.52 => 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)))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_int__eq__iff__number__of,axiom, % 185.61/186.52 ! [V_v_2,V_m_2] : % 185.61/186.52 ( 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) % 185.61/186.52 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 185.61/186.52 & 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))) ) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 185.61/186.52 ! [V_n,V_x] : % 185.61/186.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.52 => 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)) ) ). % 185.61/186.52 % 185.61/186.52 fof(fact_nat__power__eq,axiom, % 185.61/186.52 ! [V_n,V_z] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_field__power__not__zero,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 185.61/186.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__commutes,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__mult__distrib,axiom, % 185.61/186.53 ! [V_n,V_b,V_a,T_a] : % 185.61/186.53 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__one,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_of__nat__power,axiom, % 185.61/186.53 ! [V_n,V_m,T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__mult,axiom, % 185.61/186.53 ! [V_n,V_m,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__div__nat__number__of,axiom, % 185.61/186.53 ! [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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__abs,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__one__right,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__le__power,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__mono,axiom, % 185.61/186.53 ! [V_n,V_b,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__less__power,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__eq__0__iff,axiom, % 185.61/186.53 ! [V_n_2,V_a_2,T_b] : % 185.61/186.53 ( ( class_Power_Opower(T_b) % 185.61/186.53 & class_Rings_Omult__zero(T_b) % 185.61/186.53 & class_Rings_Ono__zero__divisors(T_b) % 185.61/186.53 & class_Rings_Ozero__neq__one(T_b) ) % 185.61/186.53 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__le__power,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__0__Suc,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( ( class_Power_Opower(T_a) % 185.61/186.53 & class_Rings_Osemiring__0(T_a) ) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__inject__exp,axiom, % 185.61/186.53 ! [V_n_2,V_m_2,V_a_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 185.61/186.53 => ( 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) % 185.61/186.53 <=> V_m_2 = V_n_2 ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__Suc,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Power_Opower(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__Suc2,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__0,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Power_Opower(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__add,axiom, % 185.61/186.53 ! [V_n,V_m,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_abs__power__minus,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__less__imp__less__base,axiom, % 185.61/186.53 ! [V_b,V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__le__imp__le__base,axiom, % 185.61/186.53 ! [V_b,V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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)))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__inject__base,axiom, % 185.61/186.53 ! [V_b,V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.53 => V_a = V_b ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__gt1__lemma,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__less__power__Suc,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__0__left,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( ( class_Power_Opower(T_a) % 185.61/186.53 & class_Rings_Osemiring__0(T_a) ) % 185.61/186.53 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.53 => 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) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__gt1,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__strict__increasing,axiom, % 185.61/186.53 ! [V_a,V_N,V_n,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__less__imp__less__exp,axiom, % 185.61/186.53 ! [V_n,V_m,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => ( 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))) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__strict__increasing__iff,axiom, % 185.61/186.53 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_b) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__le__power__abs,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__increasing,axiom, % 185.61/186.53 ! [V_a,V_N,V_n,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__minus,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Oring__1(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__Suc__less,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__eq__imp__eq__base,axiom, % 185.61/186.53 ! [V_b,V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.53 => V_a = V_b ) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nitpick_Onat__lcm__def,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nitpick_Oint__gcd__def,axiom, % 185.61/186.53 ! [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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__mod__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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)) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__power__power,axiom, % 185.61/186.53 ! [T_b] : % 185.61/186.53 ( class_Power_Opower(T_b) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mod__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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))) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nitpick_Oint__lcm__def,axiom, % 185.61/186.53 ! [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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__0,axiom, % 185.61/186.53 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__int,axiom, % 185.61/186.53 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__1,axiom, % 185.61/186.53 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__eq__ge__0,axiom, % 185.61/186.53 ! [V_x_2] : % 185.61/186.53 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__def,axiom, % 185.61/186.53 ! [V_Z_2] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__nat,axiom, % 185.61/186.53 ! [V_z] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 185.61/186.53 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__nat,axiom, % 185.61/186.53 ! [V_z] : % 185.61/186.53 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 185.61/186.53 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power_Opower_Opower__0,axiom, % 185.61/186.53 ! [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 ). % 185.61/186.53 % 185.61/186.53 fof(fact_power_Opower_Opower__Suc,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__imp__number__of__eq__0,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__zminus__int,axiom, % 185.61/186.53 ! [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))))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H_2,V_v_2] : % 185.61/186.53 ( 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) % 185.61/186.53 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 185.61/186.53 => 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))) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 185.61/186.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 185.61/186.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 185.61/186.53 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__number__of__add__left,axiom, % 185.61/186.53 ! [V_k,V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.61/186.53 => 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) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_int__nat__number__of,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_of__nat__number__of__eq,axiom, % 185.61/186.53 ! [V_v,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__nat__number__of__number__of,axiom, % 185.61/186.53 ! [V_w,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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)) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__nat__number__of,axiom, % 185.61/186.53 ! [V_n,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__nat__number__of__add,axiom, % 185.61/186.53 ! [V_n,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__nat__number__of,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zmod__minus1,axiom, % 185.61/186.53 ! [V_b] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div__pos__neg__trivial,axiom, % 185.61/186.53 ! [V_b,V_a] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.53 => ( 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))) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat0__intermed__int__val,axiom, % 185.61/186.53 ! [V_k_2,V_f_2,V_n_2] : % 185.61/186.53 ( ! [B_i] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 185.61/186.53 => 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))) ) % 185.61/186.53 => ( 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)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.61/186.53 => ? [B_i] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.61/186.53 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_int__val__lemma,axiom, % 185.61/186.53 ! [V_k_2,V_f_2,V_n_2] : % 185.61/186.53 ( ! [B_i] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 185.61/186.53 => 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))) ) % 185.61/186.53 => ( 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)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.61/186.53 => ? [B_i] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.61/186.53 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__number__of__eq,axiom, % 185.61/186.53 ! [V_y_2,V_x_2,T_b] : % 185.61/186.53 ( class_Int_Onumber__ring(T_b) % 185.61/186.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.61/186.53 <=> 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I2_J,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nonzero__number__of__Min,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I24_J,axiom, % 185.61/186.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I7_J,axiom, % 185.61/186.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_iszero__def,axiom, % 185.61/186.53 ! [V_z_2,T_b] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_b) % 185.61/186.53 => ( c_Int_Oiszero(T_b,V_z_2) % 185.61/186.53 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_iszero__0,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__iszero__1,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_bin__less__0__simps_I2_J,axiom, % 185.61/186.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Int_OMin__def,axiom, % 185.61/186.53 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__Min,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__number__of__Min,axiom, % 185.61/186.53 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__minus1__right,axiom, % 185.61/186.53 ! [V_z,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__minus1,axiom, % 185.61/186.53 ! [V_z,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_arith__simps_I31_J,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__Min,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_abs__minus__one,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_a) % 185.61/186.53 & class_Rings_Olinordered__idom(T_a) ) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zmod__minus1__right,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zmult__eq__1__iff,axiom, % 185.61/186.53 ! [V_n_2,V_m_2] : % 185.61/186.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.53 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.53 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 185.61/186.53 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 185.61/186.53 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 185.61/186.53 ! [V_n,V_m] : % 185.61/186.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.53 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.61/186.53 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_of__int__m1,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zdiv__minus1__right,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__def,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_abs__power__minus__one,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_a) % 185.61/186.53 & class_Rings_Olinordered__idom(T_a) ) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div__eq__minus1,axiom, % 185.61/186.53 ! [V_b] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__succ,axiom, % 185.61/186.53 ! [V_k,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__1__add__number__of,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__number__of__add__1,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__special_I3_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( class_Int_Onumber__ring(T_b) % 185.61/186.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 <=> 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__special_I1_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( class_Int_Onumber__ring(T_b) % 185.61/186.53 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.61/186.53 <=> 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__number__of__pred__iff__0,axiom, % 185.61/186.53 ! [V_v_2] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 185.61/186.53 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__number__of__mult__left,axiom, % 185.61/186.53 ! [V_k,V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pred__Pls,axiom, % 185.61/186.53 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 185.61/186.53 % 185.61/186.53 fof(fact_Pls__def,axiom, % 185.61/186.53 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I19_J,axiom, % 185.61/186.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I2_J,axiom, % 185.61/186.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Pls,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Pls__right,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__Pls,axiom, % 185.61/186.53 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I1_J,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__Pls,axiom, % 185.61/186.53 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I37_J,axiom, % 185.61/186.53 c_Int_OPls != c_Int_OMin ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I40_J,axiom, % 185.61/186.53 c_Int_OMin != c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__pred,axiom, % 185.61/186.53 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__Pls,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_semiring__norm_I112_J,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__numeral__0,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__numeral__0__right,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_bin__less__0__simps_I1_J,axiom, % 185.61/186.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__number__of__Pls,axiom, % 185.61/186.53 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.61/186.53 % 185.61/186.53 fof(fact_semiring__norm_I113_J,axiom, % 185.61/186.53 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__is__num__zero,axiom, % 185.61/186.53 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__diff__number__of,axiom, % 185.61/186.53 ! [V_m,V_v] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I20_J,axiom, % 185.61/186.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I23_J,axiom, % 185.61/186.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I3_J,axiom, % 185.61/186.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I6_J,axiom, % 185.61/186.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__number__of__Pls__Min,axiom, % 185.61/186.53 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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__neg__number__of__Pls,axiom, % 185.61/186.53 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_iszero__Numeral0,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__Min,axiom, % 185.61/186.53 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__iff__pred__less,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pred__def,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Min__right,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Min,axiom, % 185.61/186.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__number__of__diff__1,axiom, % 185.61/186.53 ! [V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__0__number__of,axiom, % 185.61/186.53 ! [V_v_2] : % 185.61/186.53 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__number__of__0,axiom, % 185.61/186.53 ! [V_v_2] : % 185.61/186.53 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of2,axiom, % 185.61/186.53 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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H_2,V_v_2] : % 185.61/186.53 ( 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))) % 185.61/186.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H_2,V_v_2] : % 185.61/186.53 ( 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))) % 185.61/186.53 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__special_I1_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__special_I3_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__special_I3_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__special_I1_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__0__number__of,axiom, % 185.61/186.53 ! [V_v_2] : % 185.61/186.53 ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__nat__number__of,axiom, % 185.61/186.53 ! [V_v_H,V_v] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.61/186.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 185.61/186.53 => 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) ) % 185.61/186.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 185.61/186.53 => 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)) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__pred,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__special_I4_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( class_Int_Onumber__ring(T_b) % 185.61/186.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 185.61/186.53 <=> 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))))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__special_I2_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( class_Int_Onumber__ring(T_b) % 185.61/186.53 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.61/186.53 <=> 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__special_I2_J,axiom, % 185.61/186.53 ! [V_v,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__special_I1_J,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__div__eq__add3__div,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I51_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 185.61/186.53 <=> V_k_2 = V_l_2 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I34_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__eq__int__code_I16_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I17_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__int__code_I16_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I39_J,axiom, % 185.61/186.53 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I46_J,axiom, % 185.61/186.53 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_Bit1__Min,axiom, % 185.61/186.53 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I43_J,axiom, % 185.61/186.53 ! [V_l_2] : % 185.61/186.53 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 185.61/186.53 <=> c_Int_OMin = V_l_2 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I47_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 185.61/186.53 <=> V_k_2 = c_Int_OMin ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_bin__less__0__simps_I4_J,axiom, % 185.61/186.53 ! [V_w_2] : % 185.61/186.53 ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I22_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I12_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Bit1__def,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I26_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I30_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I9_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I13_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__number__of__Bit1,axiom, % 185.61/186.53 ! [V_w_2] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 185.61/186.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__Bit1,axiom, % 185.61/186.53 ! [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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_iszero__number__of__Bit1,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_a) % 185.61/186.53 & class_Int_Oring__char__0(T_a) ) % 185.61/186.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__Pls,axiom, % 185.61/186.53 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__Bit1,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__numeral__1__right,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__numeral__1,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_numeral__1__eq__1,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_semiring__norm_I110_J,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I29_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I5_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__is__num__one,axiom, % 185.61/186.53 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Numeral1__eq1__nat,axiom, % 185.61/186.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__numeral__1__eq__1,axiom, % 185.61/186.53 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I4_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__Min,axiom, % 185.61/186.53 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__iszero__Numeral1,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_numeral__1__eq__Suc__0,axiom, % 185.61/186.53 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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_numeral__3__eq__3,axiom, % 185.61/186.53 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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power3__eq__cube,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 185.61/186.53 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))))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc3__eq__add__3,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 185.61/186.53 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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 185.61/186.53 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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__special_I4_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_le__special_I2_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__special_I4_J,axiom, % 185.61/186.53 ! [V_x_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__special_I2_J,axiom, % 185.61/186.53 ! [V_y_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Rings_Olinordered__idom(T_b) ) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__special_I2_J,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__special_I3_J,axiom, % 185.61/186.53 ! [V_v,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__diff__eq__diff__pred,axiom, % 185.61/186.53 ! [V_m,V_n] : % 185.61/186.53 ( 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)) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mod__Suc__eq__mod__add3,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__mod__eq__add3__mod,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div__Suc__eq__div__add3,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zmod__number__of__Bit1,axiom, % 185.61/186.53 ! [V_v,V_w] : % 185.61/186.53 ( ( 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))) % 185.61/186.53 => 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)) ) % 185.61/186.53 & ( ~ 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))) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__zmod__mult__2,axiom, % 185.61/186.53 ! [V_b,V_a] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pos__zdiv__mult__2,axiom, % 185.61/186.53 ! [V_b,V_a] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__zdiv__mult__2,axiom, % 185.61/186.53 ! [V_b,V_a] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pos__zmod__mult__2,axiom, % 185.61/186.53 ! [V_b,V_a] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_of__nat__double,axiom, % 185.61/186.53 ! [V_x,T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I48_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 185.61/186.53 <=> V_k_2 = V_l_2 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__eq__int__code_I13_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I31_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__int__code_I13_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I14_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I44_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 185.61/186.53 <=> V_k_2 = c_Int_OPls ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I38_J,axiom, % 185.61/186.53 ! [V_l_2] : % 185.61/186.53 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 185.61/186.53 <=> c_Int_OPls = V_l_2 ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Bit0__Pls,axiom, % 185.61/186.53 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I50_J,axiom, % 185.61/186.53 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I49_J,axiom, % 185.61/186.53 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Bit0__def,axiom, % 185.61/186.53 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Bit0__Bit0,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__Bit0,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I7_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__Bit0,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I45_J,axiom, % 185.61/186.53 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I42_J,axiom, % 185.61/186.53 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 185.61/186.53 % 185.61/186.53 fof(fact_bin__less__0__simps_I3_J,axiom, % 185.61/186.53 ! [V_w_2] : % 185.61/186.53 ( 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))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I27_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I21_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__eq__int__code_I14_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I32_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I10_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I4_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__int__code_I15_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I16_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Bit1__Bit0,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Bit0__Bit1,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I3_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I10_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I9_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I28_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I8_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zdiv__number__of__Bit0,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_neg__number__of__Bit0,axiom, % 185.61/186.53 ! [V_w_2] : % 185.61/186.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 185.61/186.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pred__Bit1,axiom, % 185.61/186.53 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pred__Bit0,axiom, % 185.61/186.53 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_pred__Min,axiom, % 185.61/186.53 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 185.61/186.53 % 185.61/186.53 fof(fact_iszero__number__of__Bit0,axiom, % 185.61/186.53 ! [V_w_2,T_b] : % 185.61/186.53 ( ( class_Int_Onumber__ring(T_b) % 185.61/186.53 & class_Int_Oring__char__0(T_b) ) % 185.61/186.53 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 185.61/186.53 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__Bit0,axiom, % 185.61/186.53 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 185.61/186.53 % 185.61/186.53 fof(fact_succ__Bit1,axiom, % 185.61/186.53 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of__Bit0,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I15_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__int__code_I14_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I33_J,axiom, % 185.61/186.53 ! [V_l_2,V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__eq__int__code_I15_J,axiom, % 185.61/186.53 ! [V_k2_2,V_k1_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__Bit1,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I25_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_rel__simps_I11_J,axiom, % 185.61/186.53 ! [V_k_2] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I6_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I5_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__bin__simps_I8_J,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__Bit1__Bit1,axiom, % 185.61/186.53 ! [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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_double__number__of__Bit0,axiom, % 185.61/186.53 ! [V_w,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_number__of1,axiom, % 185.61/186.53 ! [V_n] : % 185.61/186.53 ( 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))) % 185.61/186.53 => ( 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)))) % 185.61/186.53 & 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)))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__2,axiom, % 185.61/186.53 ! [V_z,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__2__right,axiom, % 185.61/186.53 ! [V_z,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__add__one__is__two,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__power2,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__eq__power2,axiom, % 185.61/186.53 ! [V_a_2,T_b] : % 185.61/186.53 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.61/186.53 => ( 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) % 185.61/186.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_numeral__2__eq__2,axiom, % 185.61/186.53 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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_semiring__norm_I115_J,axiom, % 185.61/186.53 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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__eq__square,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 185.61/186.53 ! [V_x,T_a] : % 185.61/186.53 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 185.61/186.53 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))))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__2__eq__Suc,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__2__eq__Suc_H,axiom, % 185.61/186.53 ! [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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__power2,axiom, % 185.61/186.53 ! [T_a] : % 185.61/186.53 ( class_Rings_Osemiring__1(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__minus,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Oring__1(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__mult__2__right,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__mult__2,axiom, % 185.61/186.53 ! [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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__even__eq,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 185.61/186.53 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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 185.61/186.53 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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__abs,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_abs__power2,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__1__add__1,axiom, % 185.61/186.53 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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mod2__Suc__Suc,axiom, % 185.61/186.53 ! [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)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div2__Suc__Suc,axiom, % 185.61/186.53 ! [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))))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zmod__number__of__Bit0,axiom, % 185.61/186.53 ! [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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__self__div__2,axiom, % 185.61/186.53 ! [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 ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__le__power2,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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)))))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__le__imp__le,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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)))))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__eq__imp__eq,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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)))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.53 => V_x = V_y ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__less__power2,axiom, % 185.61/186.53 ! [V_a_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.53 => ( 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)))))) % 185.61/186.53 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__less__0,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => ~ 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_sum__power2__eq__zero__iff,axiom, % 185.61/186.53 ! [V_y_2,V_x_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.53 => ( 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) % 185.61/186.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__eq__square__number__of,axiom, % 185.61/186.53 ! [V_w,T_b] : % 185.61/186.53 ( ( class_Groups_Omonoid__mult(T_b) % 185.61/186.53 & class_Int_Onumber(T_b) ) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_less__2__cases,axiom, % 185.61/186.53 ! [V_n] : % 185.61/186.53 ( 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))))) % 185.61/186.53 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.53 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__2,axiom, % 185.61/186.53 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))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__eq__1__iff,axiom, % 185.61/186.53 ! [V_a_2,T_b] : % 185.61/186.53 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.61/186.53 => ( 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) % 185.61/186.53 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 185.61/186.53 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 185.61/186.53 ! [V_n,V_x,T_a] : % 185.61/186.53 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__minus__even,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Oring__1(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__less__imp__less,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__semidom(T_a) % 185.61/186.53 => ( 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)))))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_sum__power2__le__zero__iff,axiom, % 185.61/186.53 ! [V_y_2,V_x_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.53 => ( 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))) % 185.61/186.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_sum__power2__ge__zero,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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))))))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_not__sum__power2__lt__zero,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => ~ 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_sum__power2__gt__zero__iff,axiom, % 185.61/186.53 ! [V_y_2,V_x_2,T_b] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.53 => ( 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))))))) % 185.61/186.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__sum,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__le__even__power_H,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => 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)))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__odd__eq,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Groups_Omonoid__mult(T_a) % 185.61/186.53 => 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))))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 185.61/186.53 ! [V_n,V_x,T_a] : % 185.61/186.53 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.53 => 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))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__minus1__even,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( class_Rings_Oring__1(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zdiv__number__of__Bit1,axiom, % 185.61/186.53 ! [V_v,V_w] : % 185.61/186.53 ( ( 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))) % 185.61/186.53 => 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)) ) % 185.61/186.53 & ( ~ 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))) % 185.61/186.53 => 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)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mod2__gr__0,axiom, % 185.61/186.53 ! [V_m_2] : % 185.61/186.53 ( 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)))))) % 185.61/186.53 <=> 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_div__2__gt__zero,axiom, % 185.61/186.53 ! [V_n] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 185.61/186.53 => 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)))))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power2__diff,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_odd__0__le__power__imp__0__le,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => ( 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))))) % 185.61/186.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_odd__power__less__zero,axiom, % 185.61/186.53 ! [V_n,V_a,T_a] : % 185.61/186.53 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => 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))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__minus1__odd,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( class_Rings_Oring__1(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__m1__even,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__m1__odd,axiom, % 185.61/186.53 ! [V_n,T_a] : % 185.61/186.53 ( class_Int_Onumber__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Suc__n__div__2__gt__zero,axiom, % 185.61/186.53 ! [V_n] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.53 => 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)))))) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_int__of__code,axiom, % 185.61/186.53 ! [V_k] : % 185.61/186.53 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.53 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.53 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.53 => ( ( 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) % 185.61/186.53 => 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)))))) ) % 185.61/186.53 & ( 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) % 185.61/186.53 => 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)) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_one__code__numeral__code,axiom, % 185.61/186.53 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)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_half__gt__zero,axiom, % 185.61/186.53 ! [V_r,T_a] : % 185.61/186.53 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.53 & class_Int_Onumber__ring(T_a) ) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 185.61/186.53 => 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)))))) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_half__gt__zero__iff,axiom, % 185.61/186.53 ! [V_r_2,T_b] : % 185.61/186.53 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.53 & class_Int_Onumber__ring(T_b) ) % 185.61/186.53 => ( 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)))))) % 185.61/186.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 185.61/186.53 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nat__intermed__int__val,axiom, % 185.61/186.53 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 185.61/186.53 ( ! [B_i] : % 185.61/186.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 185.61/186.53 => 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))) ) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.61/186.53 => ? [B_i] : % 185.61/186.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.61/186.53 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_code__numeral__zero__minus__one,axiom, % 185.61/186.53 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) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__zero,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__zero__left,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_add__divide__distrib,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_times__divide__times__eq,axiom, % 185.61/186.53 ! [V_w,V_z,V_y,V_x,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_times__divide__eq__right,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_diff__divide__distrib,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__1,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__divide__divide,axiom, % 185.61/186.53 ! [V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__divide__right,axiom, % 185.61/186.53 ! [V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_minus__divide__left,axiom, % 185.61/186.53 ! [V_b,V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => 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) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_power__divide,axiom, % 185.61/186.53 ! [V_n,V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_abs__divide,axiom, % 185.61/186.53 ! [V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.53 => 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)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 185.61/186.53 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 185.61/186.53 ! [V_y,V_x] : % 185.61/186.53 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.53 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.61/186.53 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 185.61/186.53 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 185.61/186.53 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 185.61/186.53 ! [V_y,V_x] : % 185.61/186.53 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.53 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.61/186.53 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 185.61/186.53 ! [V_y,V_x] : % 185.61/186.53 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.53 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.61/186.53 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 185.61/186.53 ! [V_y,V_x] : % 185.61/186.53 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.53 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.61/186.53 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 185.61/186.53 ! [V_n,V_x] : % 185.61/186.53 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.53 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__le__divide__iff,axiom, % 185.61/186.53 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.53 => ( 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_ba_2))) % 185.61/186.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.61/186.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__le__0__iff,axiom, % 185.61/186.53 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.61/186.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__right__mono,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__right__mono__neg,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__strict__right__mono__neg,axiom, % 185.61/186.53 ! [V_c,V_a,V_b,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__strict__right__mono,axiom, % 185.61/186.53 ! [V_c,V_b,V_a,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__neg__neg,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__neg__pos,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__pos__neg,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__pos__pos,axiom, % 185.61/186.53 ! [V_y,V_x,T_a] : % 185.61/186.53 ( class_Fields_Olinordered__field(T_a) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.53 => 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))) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__less__0__iff,axiom, % 185.61/186.53 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.61/186.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_zero__less__divide__iff,axiom, % 185.61/186.53 ! [V_ba_2,V_a_2,T_b] : % 185.61/186.53 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.53 => ( 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_ba_2))) % 185.61/186.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.61/186.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__divide__eq,axiom, % 185.61/186.53 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.53 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.61/186.53 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) % 185.61/186.53 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__eq__eq,axiom, % 185.61/186.53 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.53 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 185.61/186.53 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) % 185.61/186.53 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__divide__mult__cancel__right,axiom, % 185.61/186.53 ! [V_b,V_a,V_c,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_mult__divide__mult__cancel__left,axiom, % 185.61/186.53 ! [V_b,V_a,V_c,T_a] : % 185.61/186.53 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_frac__eq__eq,axiom, % 185.61/186.53 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 185.61/186.53 ( class_Fields_Ofield(T_b) % 185.61/186.53 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => ( 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) % 185.61/186.53 <=> 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) ) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_eq__divide__imp,axiom, % 185.61/186.53 ! [V_b,V_a,V_c,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 185.61/186.53 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__eq__imp,axiom, % 185.61/186.53 ! [V_a,V_b,V_c,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 185.61/186.53 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nonzero__divide__eq__eq,axiom, % 185.61/186.53 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_b) % 185.61/186.53 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 185.61/186.53 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nonzero__eq__divide__eq,axiom, % 185.61/186.53 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_b) % 185.61/186.53 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.61/186.53 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_right__inverse__eq,axiom, % 185.61/186.53 ! [V_a_2,V_ba_2,T_b] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_b) % 185.61/186.53 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.53 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2) = c_Groups_Oone__class_Oone(T_b) % 185.61/186.53 <=> V_a_2 = V_ba_2 ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__self,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_divide__self__if,axiom, % 185.61/186.53 ! [V_a,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 185.61/186.53 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 185.61/186.53 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nonzero__minus__divide__divide,axiom, % 185.61/186.53 ! [V_a,V_b,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.53 => 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) ) ) ). % 185.61/186.53 % 185.61/186.53 fof(fact_nonzero__minus__divide__right,axiom, % 185.61/186.53 ! [V_a,V_b,T_a] : % 185.61/186.53 ( class_Rings_Odivision__ring(T_a) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nonzero__power__divide,axiom, % 185.61/186.54 ! [V_n,V_a,V_b,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nonzero__abs__divide,axiom, % 185.61/186.54 ! [V_a,V_b,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__one__over,axiom, % 185.61/186.54 ! [V_n,V_a,T_a] : % 185.61/186.54 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 185.61/186.54 ! [V_y,V_x] : % 185.61/186.54 ( c_Nat__Transfer_Ois__nat(V_x) % 185.61/186.54 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.61/186.54 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__nonpos__neg,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__nonpos__pos,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_frac__le,axiom, % 185.61/186.54 ! [V_z,V_w,V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 185.61/186.54 => 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))) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_frac__less,axiom, % 185.61/186.54 ! [V_z,V_w,V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 185.61/186.54 => 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))) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_frac__less2,axiom, % 185.61/186.54 ! [V_z,V_w,V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 185.61/186.54 => 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))) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__nonneg__neg,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__nonneg__pos,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__strict__left__mono__neg,axiom, % 185.61/186.54 ! [V_c,V_b,V_a,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__strict__left__mono,axiom, % 185.61/186.54 ! [V_c,V_a,V_b,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_neg__divide__less__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_neg__less__divide__eq,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mult__imp__less__div__pos,axiom, % 185.61/186.54 ! [V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => ( 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)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mult__imp__div__pos__less,axiom, % 185.61/186.54 ! [V_z,V_x,V_y,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pos__divide__less__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pos__less__divide__eq,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__less__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__divide__eq,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_is__nat__def,axiom, % 185.61/186.54 ! [V_x_2] : % 185.61/186.54 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_add__num__frac,axiom, % 185.61/186.54 ! [V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_add__divide__eq__iff,axiom, % 185.61/186.54 ! [V_y,V_x,V_z,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_add__frac__num,axiom, % 185.61/186.54 ! [V_z,V_x,V_y,T_a] : % 185.61/186.54 ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__add__eq__iff,axiom, % 185.61/186.54 ! [V_y,V_x,V_z,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_add__frac__eq,axiom, % 185.61/186.54 ! [V_w,V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_diff__frac__eq,axiom, % 185.61/186.54 ! [V_w,V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__diff__eq__iff,axiom, % 185.61/186.54 ! [V_y,V_x,V_z,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_diff__divide__eq__iff,axiom, % 185.61/186.54 ! [V_y,V_x,V_z,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__eq__eq__number__of1,axiom, % 185.61/186.54 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 % 185.61/186.54 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => V_ba_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)) ) % 185.61/186.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__eq__eq__number__of,axiom, % 185.61/186.54 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 185.61/186.54 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) ) % 185.61/186.54 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_eq__divide__eq__number__of,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.61/186.54 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_ba_2 ) % 185.61/186.54 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_eq__divide__eq__number__of1,axiom, % 185.61/186.54 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) % 185.61/186.54 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => 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_ba_2 ) % 185.61/186.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.61/186.54 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_gt__half__sum,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__half__sum,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.61/186.54 => 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))))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__Numeral0,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 & class_Int_Onumber__ring(T_a) ) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_abs__div__pos,axiom, % 185.61/186.54 ! [V_x,V_y,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__numeral__1,axiom, % 185.61/186.54 ! [V_a,T_a] : % 185.61/186.54 ( ( class_Fields_Ofield(T_a) % 185.61/186.54 & class_Int_Onumber__ring(T_a) ) % 185.61/186.54 => 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 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__Numeral1,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( ( class_Fields_Ofield(T_a) % 185.61/186.54 & class_Int_Onumber__ring(T_a) ) % 185.61/186.54 => 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 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__minus1,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 & class_Int_Onumber__ring(T_a) ) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zero__code__numeral__code,axiom, % 185.61/186.54 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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__divide__eq,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__le__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pos__le__divide__eq,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pos__divide__le__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mult__imp__div__pos__le,axiom, % 185.61/186.54 ! [V_z,V_x,V_y,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mult__imp__le__div__pos,axiom, % 185.61/186.54 ! [V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.61/186.54 => ( 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)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_neg__le__divide__eq,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_neg__divide__le__eq,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__left__mono,axiom, % 185.61/186.54 ! [V_c,V_a,V_b,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__left__mono__neg,axiom, % 185.61/186.54 ! [V_c,V_b,V_a,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => 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))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__divide__eq__number__of1,axiom, % 185.61/186.54 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 185.61/186.54 <=> ( ( 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))) % 185.61/186.54 => 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_ba_2)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_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)))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__divide__eq__number__of,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( 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_ba_2),V_ca_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => 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))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__less__eq__number__of,axiom, % 185.61/186.54 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => 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))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__less__eq__number__of1,axiom, % 185.61/186.54 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 185.61/186.54 <=> ( ( 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_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)))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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_ba_2)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__diff,axiom, % 185.61/186.54 ! [V_m,V_n,V_a,T_a] : % 185.61/186.54 ( class_Fields_Ofield(T_a) % 185.61/186.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus1__divide,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.61/186.54 & class_Int_Onumber__ring(T_a) ) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 185.61/186.54 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__le__eq__number__of1,axiom, % 185.61/186.54 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 185.61/186.54 <=> ( ( 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_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)))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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_ba_2)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divide__le__eq__number__of,axiom, % 185.61/186.54 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => 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))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__divide__eq__number__of,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( 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_ba_2),V_ca_2))) % 185.61/186.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.61/186.54 => 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))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__divide__eq__number__of1,axiom, % 185.61/186.54 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.61/186.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.61/186.54 & class_Int_Onumber(T_b) ) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 185.61/186.54 <=> ( ( 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))) % 185.61/186.54 => 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_ba_2)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_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)))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__aux__code,axiom, % 185.61/186.54 ! [V_n,V_i] : % 185.61/186.54 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.54 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 185.61/186.54 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osize_I1_J,axiom, % 185.61/186.54 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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osize_I3_J,axiom, % 185.61/186.54 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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osimps_I4_J,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_log_Osimps,axiom, % 185.61/186.54 ! [V_i,V_b] : % 185.61/186.54 ( ( ( 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))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 185.61/186.54 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 185.61/186.54 & ( ~ ( 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))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_field__le__epsilon,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Fields_Olinordered__field(T_a) % 185.61/186.54 => ( ! [B_e] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 185.61/186.54 => 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))) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus__shift__def,axiom, % 185.61/186.54 ! [V_r,V_l,V_k] : % 185.61/186.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_inc__shift__def,axiom, % 185.61/186.54 ! [V_k,V_v] : % 185.61/186.54 ( ( V_v = V_k % 185.61/186.54 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 185.61/186.54 & ( V_v != V_k % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osize_I4_J,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osize_I2_J,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus__code__numeral__code,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subtract__code__numeral__def,axiom, % 185.61/186.54 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Oinject,axiom, % 185.61/186.54 ! [V_code__numeral_H_2,V_code__numeral_2] : % 185.61/186.54 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 185.61/186.54 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osimps_I2_J,axiom, % 185.61/186.54 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osimps_I3_J,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Osimps_I5_J,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Suc__code__numeral__minus__one,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( 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)))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ 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)))) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_diff__nat__number__of,axiom, % 185.61/186.54 ! [V_v_2,V_v_H_2] : % 185.61/186.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Orecs_I2_J,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__step,axiom, % 185.61/186.54 ! [V_m,V_n] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral__not__eq__zero,axiom, % 185.61/186.54 ! [V_i_2] : % 185.61/186.54 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.61/186.54 <=> 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_beyond__def,axiom, % 185.61/186.54 ! [V_l,V_k] : % 185.61/186.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.61/186.54 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.61/186.54 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__zero,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 185.61/186.54 <=> V_n_2 = V_m_2 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 185.61/186.54 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fun__Compl__def,axiom, % 185.61/186.54 ! [V_x_2,V_A_2,T_c,T_b] : % 185.61/186.54 ( class_Groups_Ouminus(T_b) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fun__diff__def,axiom, % 185.61/186.54 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.61/186.54 ( class_Groups_Ominus(T_b) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 185.61/186.54 ! [V_n_2,V_m_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 185.61/186.54 <=> 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__base,axiom, % 185.61/186.54 ! [V_n,V_m] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__eq__Suc__le__raw,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_diff__Suc,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__number__of__Bit0,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_times__code__numeral__code,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__div__mod,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__number__of__even,axiom, % 185.61/186.54 ! [V_w_2,V_z_2,T_b] : % 185.61/186.54 ( class_Int_Onumber__ring(T_b) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zpower__number__of__even,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_beyond__zero,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__number__of__even__number__of,axiom, % 185.61/186.54 ! [V_w_2,V_v_2,T_b] : % 185.61/186.54 ( class_Int_Onumber__ring(T_b) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_diff__nat__eq__if,axiom, % 185.61/186.54 ! [V_z_2,V_z_H_2] : % 185.61/186.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__div__mod,axiom, % 185.61/186.54 ! [V_l,V_k] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__minus1,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 185.61/186.54 ! [V_n_2,T_b] : % 185.61/186.54 ( class_Rings_Osemiring__1(T_b) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_adjust__eq,axiom, % 185.61/186.54 ! [V_r_2,V_q_2,V_ba_2] : hAPP(c_Divides_Oadjust(V_ba_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_ba_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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zero__code__numeral__def,axiom, % 185.61/186.54 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_one__code__numeral__def,axiom, % 185.61/186.54 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__code__numeral__code,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Suc__eq__number__of,axiom, % 185.61/186.54 ! [V_v_2,V_n_2] : % 185.61/186.54 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 185.61/186.54 <=> 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_eq__number__of__Suc,axiom, % 185.61/186.54 ! [V_n_2,V_v_2] : % 185.61/186.54 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 185.61/186.54 <=> 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__case__number__of,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__rec__number__of,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_plus__code__numeral__code,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__eq__code__numeral__code,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__number__of__Bit1,axiom, % 185.61/186.54 ! [V_w_2] : % 185.61/186.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 185.61/186.54 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__Suc__number__of,axiom, % 185.61/186.54 ! [V_v_2,V_n_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__number__of__Suc,axiom, % 185.61/186.54 ! [V_n_2,V_v_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__Suc__number__of,axiom, % 185.61/186.54 ! [V_v_2,V_n_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__number__of__Suc,axiom, % 185.61/186.54 ! [V_n_2,V_v_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subtract__code__numeral__code,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__case__add__eq__if,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__rec__add__eq__if,axiom, % 185.61/186.54 ! [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))))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__number__of__odd,axiom, % 185.61/186.54 ! [V_z_2,V_w_2,T_b] : % 185.61/186.54 ( class_Int_Onumber__ring(T_b) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zpower__number__of__odd,axiom, % 185.61/186.54 ! [V_z_2,V_w_2] : % 185.61/186.54 ( ( 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))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg_Osimps,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( ( ( 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))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( ~ ( 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))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_power__number__of__odd__number__of,axiom, % 185.61/186.54 ! [V_v_2,V_w_2,T_b] : % 185.61/186.54 ( class_Int_Onumber__ring(T_b) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Orecs_I1_J,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__eqn,axiom, % 185.61/186.54 ! [V_a,V_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__eqn__number__of,axiom, % 185.61/186.54 ! [V_w,V_v] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( 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)))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ 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)))) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_norm__frac_Osimps,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2] : % 185.61/186.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) ) % 185.61/186.54 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg_Osimps,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_adjust__def,axiom, % 185.61/186.54 ! [V_ba_2] : c_Divides_Oadjust(V_ba_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_ba_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_ba_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))))))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__eqn__number__of,axiom, % 185.61/186.54 ! [V_w,V_v] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__eqn,axiom, % 185.61/186.54 ! [V_a,V_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__0,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__div__mod,axiom, % 185.61/186.54 ! [V_l,V_k] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_of__int__num,axiom, % 185.61/186.54 ! [V_k_2,T_b] : % 185.61/186.54 ( class_Rings_Oring__1(T_b) % 185.61/186.54 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 185.61/186.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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))) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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))))) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_MGT__def,axiom, % 185.61/186.54 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 185.61/186.54 ! [V_a,V_r,V_q,V_c,V_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 185.61/186.54 ! [V_c,V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg_Opsimps,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2] : % 185.61/186.54 ( 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_ba_2))) % 185.61/186.54 => ( ( ( 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_ba_2))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => c_Divides_OnegDivAlg(V_a_2,V_ba_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_ba_2)) ) % 185.61/186.54 & ( ~ ( 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_ba_2))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => c_Divides_OnegDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_accp__downward,axiom, % 185.61/186.54 ! [V_a_2,V_ba_2,V_r_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_ba_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.61/186.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_accp_Oequations,axiom, % 185.61/186.54 ! [V_a_2,V_r_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 185.61/186.54 <=> ! [B_x] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 185.61/186.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_accp_Osimps,axiom, % 185.61/186.54 ! [V_a_2,V_r_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 185.61/186.54 <=> ! [B_x] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 185.61/186.54 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__unique,axiom, % 185.61/186.54 ! [V_qr_H,V_qr,V_n,V_m] : % 185.61/186.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 185.61/186.54 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 185.61/186.54 => V_qr = V_qr_H ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_accp__subset,axiom, % 185.61/186.54 ! [V_R2_2,V_R1_2,T_b] : % 185.61/186.54 ( 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)) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__eq,axiom, % 185.61/186.54 ! [V_qr,V_n,V_m] : % 185.61/186.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 185.61/186.54 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 185.61/186.54 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__eq,axiom, % 185.61/186.54 ! [V_r,V_q,V_n,V_m] : % 185.61/186.54 ( 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))) % 185.61/186.54 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__eq,axiom, % 185.61/186.54 ! [V_r,V_q,V_n,V_m] : % 185.61/186.54 ( 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))) % 185.61/186.54 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__mod__div,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__add1__eq,axiom, % 185.61/186.54 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg_Opsimps,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2] : % 185.61/186.54 ( 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_ba_2))) % 185.61/186.54 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 185.61/186.54 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_norm__frac_Opsimps,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2] : % 185.61/186.54 ( 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_ba_2))) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) ) % 185.61/186.54 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.61/186.54 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nitpick_OFrac__def,axiom, % 185.61/186.54 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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__def,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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))) ) ) ) ) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => 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))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg_Opinduct,axiom, % 185.61/186.54 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ! [B_a,B_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( ~ ( 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))) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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))) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negateSnd__eq,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_splitI,axiom, % 185.61/186.54 ! [T_c,T_b,V_ba_2,V_a_2,V_f_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) % 185.61/186.54 => 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_ba_2))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod__caseI,axiom, % 185.61/186.54 ! [T_c,T_b,V_ba_2,V_a_2,V_f1_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_ba_2)) % 185.61/186.54 => 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_ba_2))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg_Opinduct,axiom, % 185.61/186.54 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ! [B_a,B_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.61/186.54 => 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))) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__gcd_Opsimps,axiom, % 185.61/186.54 ! [V_y_2,V_x_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 185.61/186.54 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__pdivmod,axiom, % 185.61/186.54 ! [V_l_2,V_k_2] : % 185.61/186.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apsnd__conv,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__paired__All,axiom, % 185.61/186.54 ! [T_c,T_b,V_Pa_2] : % 185.61/186.54 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.61/186.54 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Pair__eq,axiom, % 185.61/186.54 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 185.61/186.54 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) % 185.61/186.54 <=> ( V_a_2 = V_a_H_2 % 185.61/186.54 & V_ba_2 = V_b_H_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Pair__inject,axiom, % 185.61/186.54 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 185.61/186.54 ( 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) % 185.61/186.54 => ~ ( V_a = V_a_H % 185.61/186.54 => V_b != V_b_H ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negateSnd__def,axiom, % 185.61/186.54 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__weak__cong,axiom, % 185.61/186.54 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 185.61/186.54 ( V_p_2 = V_q_2 % 185.61/186.54 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod_Osimps_I2_J,axiom, % 185.61/186.54 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__conv,axiom, % 185.61/186.54 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f_2,V_a_2),V_ba_2) ). % 185.61/186.54 % 185.61/186.54 fof(fact_splitD,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 185.61/186.54 ( 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_ba_2))) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__eta,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__twice,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pdivmod__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pdivmod__posDivAlg,axiom, % 185.61/186.54 ! [V_k,V_l] : % 185.61/186.54 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__code,axiom, % 185.61/186.54 ! [V_l_2,V_k_2] : % 185.61/186.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)) ) % 185.61/186.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__mod__code__numeral__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zmult2__lemma,axiom, % 185.61/186.54 ! [V_c,V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__pos__neg__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__def,axiom, % 185.61/186.54 ! [V_ba_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_ba_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_ba_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_ba_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_ba_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_ba_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_ba_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))))))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_norm__frac_Opinduct,axiom, % 185.61/186.54 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ! [B_a,B_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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))) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_splitD_H,axiom, % 185.61/186.54 ! [V_ca_2,V_ba_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 185.61/186.54 ( 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_ba_2)),V_ca_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_ba_2),V_ca_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_snd__conv,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_snd__eqD,axiom, % 185.61/186.54 ! [V_a,V_y,V_x,T_a,T_b] : % 185.61/186.54 ( 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 % 185.61/186.54 => V_y = V_a ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apsnd__eq__conv,axiom, % 185.61/186.54 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 185.61/186.54 ( 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) % 185.61/186.54 <=> 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_snd__apsnd,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_snd__def,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__int__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__0,axiom, % 185.61/186.54 ! [V_b] : % 185.61/186.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_self__remainder,axiom, % 185.61/186.54 ! [V_r,V_q,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_unique__quotient,axiom, % 185.61/186.54 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => V_q = V_q_H ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_unique__remainder,axiom, % 185.61/186.54 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => V_r = V_r_H ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__neg,axiom, % 185.61/186.54 ! [V_qr,V_b,V_a] : % 185.61/186.54 ( 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)) % 185.61/186.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__correct,axiom, % 185.61/186.54 ! [V_a,V_b] : % 185.61/186.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_self__quotient,axiom, % 185.61/186.54 ! [V_r,V_q,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__mod,axiom, % 185.61/186.54 ! [V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__div,axiom, % 185.61/186.54 ! [V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_negDivAlg__correct,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__neg__pos,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__rel__div__mod,axiom, % 185.61/186.54 ! [V_a,V_b] : % 185.61/186.54 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_posDivAlg__correct,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__pos__pos,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__pos__pos__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zadd1__lemma,axiom, % 185.61/186.54 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( 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))) % 185.61/186.54 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zminus1__lemma,axiom, % 185.61/186.54 ! [V_r_2,V_q_2,V_ba_2,V_a_2] : % 185.61/186.54 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_ba_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 185.61/186.54 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_ba_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_ba_2),V_r_2))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__pos__neg,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__if,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__int__relI,axiom, % 185.61/186.54 ! [V_r,V_q,V_b,V_a] : % 185.61/186.54 ( 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) % 185.61/186.54 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__neg__neg,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_zmult1__lemma,axiom, % 185.61/186.54 ! [V_a,V_r,V_q,V_c,V_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_equalityI,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.61/186.54 => V_A_2 = V_B_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__pos__neg__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => 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))))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__gcd_Opinduct,axiom, % 185.61/186.54 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ! [B_x,B_y] : % 185.61/186.54 ( 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))) % 185.61/186.54 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 185.61/186.54 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__neg__neg,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__number__of__Suc,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__0L,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__0R,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__Suc__Suc,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__le__iff__disj,axiom, % 185.61/186.54 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__le1,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__le2,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__iff__inf,axiom, % 185.61/186.54 ! [V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.54 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__inf__iff,axiom, % 185.61/186.54 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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))) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__infI1,axiom, % 185.61/186.54 ! [V_b,V_x,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__infI2,axiom, % 185.61/186.54 ! [V_a,V_x,V_b,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__absorb1,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__absorb2,axiom, % 185.61/186.54 ! [V_x,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__infI,axiom, % 185.61/186.54 ! [V_b,V_a,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__greatest,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__mono,axiom, % 185.61/186.54 ! [V_d,V_b,V_c,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__infE,axiom, % 185.61/186.54 ! [V_b,V_a,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( 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))) % 185.61/186.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.61/186.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__diff__distrib__left,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Oordered__ab__group__add(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oless__infI1,axiom, % 185.61/186.54 ! [V_b,V_x,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oless__infI2,axiom, % 185.61/186.54 ! [V_a,V_x,V_b,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__less__iff__disj,axiom, % 185.61/186.54 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__less__iff__conj,axiom, % 185.61/186.54 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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))) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__add__distrib__left,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__assoc,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf_Oassoc,axiom, % 185.61/186.54 ! [V_c,V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__left__commute,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 185.61/186.54 ! [V_c,V_a,V_b,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__left__idem,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__commute,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf_Ocommute,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf_Oidem,axiom, % 185.61/186.54 ! [V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__diff,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fst__eqD,axiom, % 185.61/186.54 ! [V_a,V_y,V_x,T_b,T_a] : % 185.61/186.54 ( 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 % 185.61/186.54 => V_x = V_a ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fst__conv,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod__eqI,axiom, % 185.61/186.54 ! [V_q,V_p,T_b,T_a] : % 185.61/186.54 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 185.61/186.54 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 185.61/186.54 => V_p = V_q ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Pair__fst__snd__eq,axiom, % 185.61/186.54 ! [T_c,T_b,V_t_2,V_s_2] : % 185.61/186.54 ( V_s_2 = V_t_2 % 185.61/186.54 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 185.61/186.54 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fst__apsnd,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fst__def,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__number__of,axiom, % 185.61/186.54 ! [V_v,V_u,T_b] : % 185.61/186.54 ( ( class_Int_Onumber(T_b) % 185.61/186.54 & class_Orderings_Oord(T_b) ) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_surjective__pairing,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pair__collapse,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod__case__beta,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__int__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__nat__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__beta,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__comp__eq,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_split__def,axiom, % 185.61/186.54 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_double__diff,axiom, % 185.61/186.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.61/186.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Diff__mono,axiom, % 185.61/186.54 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Diff__subset,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Compl__anti__mono,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Compl__subset__Compl__iff,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( 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))) % 185.61/186.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_equalityE,axiom, % 185.61/186.54 ! [T_b,V_B_2,V_A_2] : % 185.61/186.54 ( V_A_2 = V_B_2 % 185.61/186.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subset__trans,axiom, % 185.61/186.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_equalityD2,axiom, % 185.61/186.54 ! [T_b,V_B_2,V_A_2] : % 185.61/186.54 ( V_A_2 = V_B_2 % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_equalityD1,axiom, % 185.61/186.54 ! [T_b,V_B_2,V_A_2] : % 185.61/186.54 ( V_A_2 = V_B_2 % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_set__eq__subset,axiom, % 185.61/186.54 ! [T_b,V_B_2,V_A_2] : % 185.61/186.54 ( V_A_2 = V_B_2 % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subset__refl,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subset__psubset__trans,axiom, % 185.61/186.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_psubset__subset__trans,axiom, % 185.61/186.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_psubset__imp__subset,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_subset__iff__psubset__eq,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 | V_A_2 = V_B_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_psubset__eq,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 & V_A_2 != V_B_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__Suc1,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__Suc2,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__neg__pos,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__pos__pos,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__pos__pos__1__number__of,axiom, % 185.61/186.54 ! [V_w] : % 185.61/186.54 ( 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))) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__pos__neg,axiom, % 185.61/186.54 ! [V_b,V_a] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.61/186.54 => 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)))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__Suc__number__of,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod__size__simp,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_conjI__realizer,axiom, % 185.61/186.54 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] : % 185.61/186.54 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 185.61/186.54 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 185.61/186.54 => ( 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)))) % 185.61/186.54 & hBOOL(hAPP(V_Q_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)))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_exI__realizer,axiom, % 185.61/186.54 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 185.61/186.54 => 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__ord__min,axiom, % 185.61/186.54 ! [T_b] : % 185.61/186.54 ( class_Orderings_Oord(T_b) % 185.61/186.54 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_prod_Orecs,axiom, % 185.61/186.54 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Compl__eq__Compl__iff,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : % 185.61/186.54 ( 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) % 185.61/186.54 <=> V_A_2 = V_B_2 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_double__complement,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_Diff__idemp,axiom, % 185.61/186.54 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.61/186.54 % 185.61/186.54 fof(fact_psubset__trans,axiom, % 185.61/186.54 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.61/186.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__nat__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_divmod__nat__rel__def,axiom, % 185.61/186.54 ! [V_qr_2,V_n_2,V_m_2] : % 185.61/186.54 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 185.61/186.54 <=> ( 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)) % 185.61/186.54 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.61/186.54 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.61/186.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.61/186.54 => ( 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))) % 185.61/186.54 & 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)) ) ) % 185.61/186.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.61/186.54 => ( 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))) % 185.61/186.54 & 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))) ) ) ) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_range,axiom, % 185.61/186.54 ! [V_s,V_k] : % 185.61/186.54 ( 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)) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__number__of__Suc,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__Suc__number__of,axiom, % 185.61/186.54 ! [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)))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apsnd__apfst,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__diff__distrib__left,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Oordered__ab__group__add(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__max__iff__disj,axiom, % 185.61/186.54 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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))) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__less__iff__conj,axiom, % 185.61/186.54 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oless__supI2,axiom, % 185.61/186.54 ! [V_a,V_b,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oless__supI1,axiom, % 185.61/186.54 ! [V_b,V_a,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__inf__absorb,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__sup__absorb,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__inf__distrib1,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__inf__distrib2,axiom, % 185.61/186.54 ! [V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 185.61/186.54 ! [V_x,V_z,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__0L,axiom, % 185.61/186.54 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__0R,axiom, % 185.61/186.54 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__Suc__Suc,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__max__iff__disj,axiom, % 185.61/186.54 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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))) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 185.61/186.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__maxI1,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_le__maxI2,axiom, % 185.61/186.54 ! [V_x,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__iff__sup,axiom, % 185.61/186.54 ! [V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.61/186.54 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__sup__iff,axiom, % 185.61/186.54 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => ( 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)) % 185.61/186.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.61/186.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__supI1,axiom, % 185.61/186.54 ! [V_b,V_a,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__supI2,axiom, % 185.61/186.54 ! [V_a,V_b,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.61/186.54 => 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))) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__absorb2,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__absorb1,axiom, % 185.61/186.54 ! [V_x,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__supI,axiom, % 185.61/186.54 ! [V_b,V_x,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__least,axiom, % 185.61/186.54 ! [V_z,V_x,V_y,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 185.61/186.54 => 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)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__mono,axiom, % 185.61/186.54 ! [V_d,V_b,V_c,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.61/186.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.61/186.54 => 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))) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Ole__supE,axiom, % 185.61/186.54 ! [V_x,V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => ( 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)) % 185.61/186.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.61/186.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__add__distrib__left,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__assoc,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup_Oassoc,axiom, % 185.61/186.54 ! [V_c,V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__left__commute,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup_Oleft__commute,axiom, % 185.61/186.54 ! [V_c,V_a,V_b,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__left__idem,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup_Oleft__idem,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup__commute,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup_Ocommute,axiom, % 185.61/186.54 ! [V_b,V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Osup_Oidem,axiom, % 185.61/186.54 ! [V_a,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apfst__conv,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apfst__eq__conv,axiom, % 185.61/186.54 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 185.61/186.54 ( 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) % 185.61/186.54 <=> 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_fst__apfst,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_snd__apfst,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__number__of,axiom, % 185.61/186.54 ! [V_v,V_u,T_b] : % 185.61/186.54 ( ( class_Int_Onumber(T_b) % 185.61/186.54 & class_Orderings_Oord(T_b) ) % 185.61/186.54 => ( ( 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))) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( ~ 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))) % 185.61/186.54 => 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) ) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Odistrib__inf__le,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_min__max_Odistrib__sup__le,axiom, % 185.61/186.54 ! [V_z,V_y,V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => 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)))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus__max__eq__min,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus__min__eq__max,axiom, % 185.61/186.54 ! [V_y,V_x,T_a] : % 185.61/186.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 185.61/186.54 => 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)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__minus__add__max,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apsnd__apfst__commute,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__Suc1,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__Suc2,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_apfst__apsnd,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_dual__min,axiom, % 185.61/186.54 ! [T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_max__ord__max,axiom, % 185.61/186.54 ! [T_b] : % 185.61/186.54 ( class_Orderings_Oord(T_b) % 185.61/186.54 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral__decr,axiom, % 185.61/186.54 ! [V_k] : % 185.61/186.54 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.61/186.54 => 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nitpick_Ozero__frac__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_pos__not__random__dseq__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 185.61/186.54 ! [V_l_2,V_k_2] : % 185.61/186.54 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 185.61/186.54 <=> V_k_2 = V_l_2 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_code__numeral_Onat__of__inject,axiom, % 185.61/186.54 ! [V_y_2,V_x_2] : % 185.61/186.54 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 185.61/186.54 <=> V_x_2 = V_y_2 ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__of__nat,axiom, % 185.61/186.54 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 185.61/186.54 % 185.61/186.54 fof(fact_of__nat__nat__of,axiom, % 185.61/186.54 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__inverse,axiom, % 185.61/186.54 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__code__numeral__def,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 185.61/186.54 <=> 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__number,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_less__eq__code__numeral__def,axiom, % 185.61/186.54 ! [V_m_2,V_n_2] : % 185.61/186.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 185.61/186.54 <=> 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))) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__code,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_nat__of__aux__def,axiom, % 185.61/186.54 ! [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) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Min_Oidem,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Max_Oidem,axiom, % 185.61/186.54 ! [V_x,T_a] : % 185.61/186.54 ( class_Orderings_Olinorder(T_a) % 185.61/186.54 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_dual__max,axiom, % 185.61/186.54 ! [T_b] : % 185.61/186.54 ( class_Orderings_Olinorder(T_b) % 185.61/186.54 => 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) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Suc__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_minus__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_plus__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_div__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_times__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_mod__code__numeral__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nitpick_Oone__frac__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 185.61/186.54 ! [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))) ). % 185.61/186.54 % 185.61/186.54 fof(fact_Nitpick_Ofrac__def,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_surjective__sum,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_iterate_Osimps,axiom, % 185.61/186.54 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 185.61/186.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.54 => 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) ) % 185.61/186.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.54 => 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)) ) ) ). % 185.61/186.54 % 185.61/186.54 fof(fact_sum__case__KK,axiom, % 185.61/186.54 ! [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 ). % 185.61/186.54 % 185.61/186.54 fof(fact_scomp__scomp,axiom, % 185.61/186.54 ! [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)) ). % 185.61/186.54 % 185.61/186.54 fof(fact_sum__case__inject,axiom, % 185.61/186.55 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] : % 185.61/186.55 ( 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) % 185.61/186.55 => ~ ( V_f1_2 = V_g1_2 % 185.61/186.55 => V_f2_2 != V_g2_2 ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_sum__case__weak__cong,axiom, % 185.61/186.55 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] : % 185.61/186.55 ( V_s_2 = V_t_2 % 185.61/186.55 => 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) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_scomp__Pair,axiom, % 185.61/186.55 ! [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 ). % 185.61/186.55 % 185.61/186.55 fof(fact_Pair__scomp,axiom, % 185.61/186.55 ! [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) ). % 185.61/186.55 % 185.61/186.55 fof(fact_scomp__apply,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_sum_Osimps_I6_J,axiom, % 185.61/186.55 ! [V_ba_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_ba_2)) = hAPP(V_f2_2,V_ba_2) ). % 185.61/186.55 % 185.61/186.55 fof(fact_sum_Osimps_I5_J,axiom, % 185.61/186.55 ! [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) ). % 185.61/186.55 % 185.61/186.55 fof(fact_scomp__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_scomp__unfold,axiom, % 185.61/186.55 ! [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))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Oplus__frac__def,axiom, % 185.61/186.55 ! [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))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_internal__split__def,axiom, % 185.61/186.55 ! [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) ). % 185.61/186.55 % 185.61/186.55 fof(fact_transfer__morphism__int__nat,axiom, % 185.61/186.55 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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 185.61/186.55 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 185.61/186.55 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.55 => 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) ) % 185.61/186.55 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.55 => 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)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 185.61/186.55 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 185.61/186.55 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.55 => 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) ) % 185.61/186.55 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.61/186.55 => 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)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_internal__split__conv,axiom, % 185.61/186.55 ! [V_ba_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_ba_2) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Otimes__frac__def,axiom, % 185.61/186.55 ! [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))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Oof__frac__def,axiom, % 185.61/186.55 ! [V_q,T_a,T_b] : % 185.61/186.55 ( ( class_Rings_Oinverse(T_b) % 185.61/186.55 & class_Rings_Oring__1(T_b) ) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 185.61/186.55 ! [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))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Oless__frac__def,axiom, % 185.61/186.55 ! [V_r_2,V_q_2,T_b] : % 185.61/186.55 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 185.61/186.55 <=> 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 185.61/186.55 ! [V_r_2,V_q_2,T_b] : % 185.61/186.55 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 185.61/186.55 <=> 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__DSequence_Opos__empty__def,axiom, % 185.61/186.55 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 185.61/186.55 % 185.61/186.55 fof(fact_pos__empty__def,axiom, % 185.61/186.55 ! [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) ). % 185.61/186.55 % 185.61/186.55 fof(fact_neg__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_New__DSequence_Opos__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_predicate2D,axiom, % 185.61/186.55 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.61/186.55 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_rev__predicate2D,axiom, % 185.61/186.55 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2)) % 185.61/186.55 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_predicate1D,axiom, % 185.61/186.55 ! [V_x_2,V_Q_2,V_Pa_2,T_b] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 185.61/186.55 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.61/186.55 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_rev__predicate1D,axiom, % 185.61/186.55 ! [V_Q_2,T_b,V_x_2,V_Pa_2] : % 185.61/186.55 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 185.61/186.55 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_pos__bind__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_The__split,axiom, % 185.61/186.55 ! [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))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Random_Osimps,axiom, % 185.61/186.55 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 185.61/186.55 ( ( 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))) % 185.61/186.55 => 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)) ) % 185.61/186.55 & ( ~ 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))) % 185.61/186.55 => 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))))))) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_exE__realizer,axiom, % 185.61/186.55 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] : % 185.61/186.55 ( 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))) % 185.61/186.55 => ( ! [B_x,B_y] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 185.61/186.55 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 185.61/186.55 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_curry__def,axiom, % 185.61/186.55 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_curryI,axiom, % 185.61/186.55 ! [V_ba_2,V_a_2,T_c,T_b,V_f_2] : % 185.61/186.55 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_curryD,axiom, % 185.61/186.55 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 185.61/186.55 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_curryE,axiom, % 185.61/186.55 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 185.61/186.55 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_curry__conv,axiom, % 185.61/186.55 ! [V_ba_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_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_split__curry,axiom, % 185.61/186.55 ! [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 ). % 185.61/186.55 % 185.61/186.55 fof(fact_curry__split,axiom, % 185.61/186.55 ! [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 ). % 185.61/186.55 % 185.61/186.55 fof(fact_split__paired__The,axiom, % 185.61/186.55 ! [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)))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_The__split__eq,axiom, % 185.61/186.55 ! [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) ). % 185.61/186.55 % 185.61/186.55 fof(fact_divmod__nat__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Random__Sequence_Oempty__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Random__Sequence_Osingle__def,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_the__eq__trivial,axiom, % 185.61/186.55 ! [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 ). % 185.61/186.55 % 185.61/186.55 fof(fact_the__sym__eq__trivial,axiom, % 185.61/186.55 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 185.61/186.55 % 185.61/186.55 fof(fact_Powp__def,axiom, % 185.61/186.55 ! [V_B_2,V_A_2,T_b] : % 185.61/186.55 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 185.61/186.55 <=> ! [B_x] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.61/186.55 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_Powp__mono,axiom, % 185.61/186.55 ! [V_B_2,V_A_2,T_b] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_power__dvd__imp__le,axiom, % 185.61/186.55 ! [V_n,V_m,V_i] : % 185.61/186.55 ( 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))) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult__cancel2,axiom, % 185.61/186.55 ! [V_n_2,V_m_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.61/186.55 => ( 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)) % 185.61/186.55 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult__cancel1,axiom, % 185.61/186.55 ! [V_n_2,V_m_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.61/186.55 => ( 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)) % 185.61/186.55 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_zdvd__mult__cancel1,axiom, % 185.61/186.55 ! [V_n_2,V_m_2] : % 185.61/186.55 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.61/186.55 => ( 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)) % 185.61/186.55 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_arith__series__int,axiom, % 185.61/186.55 ! [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)))) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oorder__refl,axiom, % 185.61/186.55 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__0__right,axiom, % 185.61/186.55 ! [V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__1__left,axiom, % 185.61/186.55 ! [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)) ). % 185.61/186.55 % 185.61/186.55 fof(fact_setsum__abs,axiom, % 185.61/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.61/186.55 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_setsum__abs__ge__zero,axiom, % 185.61/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.61/186.55 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_zdvd__antisym__abs,axiom, % 185.61/186.55 ! [V_b,V_a] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a)) % 185.61/186.55 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_nat__dvd__1__iff__1,axiom, % 185.61/186.55 ! [V_m_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 185.61/186.55 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__if__abs__eq,axiom, % 185.61/186.55 ! [V_k,V_l,T_a] : % 185.61/186.55 ( class_Rings_Olinordered__idom(T_a) % 185.61/186.55 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_abs__dvd__iff,axiom, % 185.61/186.55 ! [V_k_2,V_m_2,T_b] : % 185.61/186.55 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) % 185.61/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__abs__iff,axiom, % 185.61/186.55 ! [V_k_2,V_m_2,T_b] : % 185.61/186.55 ( class_Rings_Olinordered__idom(T_b) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) % 185.61/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__power__same,axiom, % 185.61/186.55 ! [V_n,V_y,V_x,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 185.61/186.55 => 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))) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_one__dvd,axiom, % 185.61/186.55 ! [V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__0__left,axiom, % 185.61/186.55 ! [V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.61/186.55 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__add,axiom, % 185.61/186.55 ! [V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 185.61/186.55 => 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))) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_lessThan__eq__iff,axiom, % 185.61/186.55 ! [V_y_2,V_x_2,T_b] : % 185.61/186.55 ( class_Orderings_Olinorder(T_b) % 185.61/186.55 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 185.61/186.55 <=> V_x_2 = V_y_2 ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oeq__iff,axiom, % 185.61/186.55 ! [V_y_2,V_x_2] : % 185.61/186.55 ( V_x_2 = V_y_2 % 185.61/186.55 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Ole__less,axiom, % 185.61/186.55 ! [V_y_2,V_x_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 185.61/186.55 | V_x_2 = V_y_2 ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__le,axiom, % 185.61/186.55 ! [V_y_2,V_x_2] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 185.61/186.55 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 & V_x_2 != V_y_2 ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oneq__le__trans,axiom, % 185.61/186.55 ! [V_b,V_a] : % 185.61/186.55 ( V_a != V_b % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oeq__refl,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( V_x = V_y % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oantisym__conv,axiom, % 185.61/186.55 ! [V_x_2,V_y_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 <=> V_x_2 = V_y_2 ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Ole__imp__less__or__eq,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 | V_x = V_y ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Ole__neq__trans,axiom, % 185.61/186.55 ! [V_b,V_a] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 => ( V_a != V_b % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oord__eq__le__trans,axiom, % 185.61/186.55 ! [V_c,V_b,V_a] : % 185.61/186.55 ( V_a = V_b % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oord__le__eq__trans,axiom, % 185.61/186.55 ! [V_c,V_b,V_a] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 => ( V_b = V_c % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__antisym,axiom, % 185.61/186.55 ! [V_n,V_m] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) % 185.61/186.55 => V_m = V_n ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oantisym,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 185.61/186.55 => V_x = V_y ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oorder__trans,axiom, % 185.61/186.55 ! [V_z,V_y,V_x] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oord__eq__less__trans,axiom, % 185.61/186.55 ! [V_c,V_b,V_a] : % 185.61/186.55 ( V_a = V_b % 185.61/186.55 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) ) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Ole__less__trans,axiom, % 185.61/186.55 ! [V_z,V_y,V_x] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__imp__neq,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => V_x != V_y ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__not__sym,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__imp__le,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__imp__not__less,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__imp__not__eq,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => V_x != V_y ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__imp__not__eq2,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => V_y != V_x ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oord__less__eq__trans,axiom, % 185.61/186.55 ! [V_c,V_b,V_a] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 185.61/186.55 => ( V_b = V_c % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__le__trans,axiom, % 185.61/186.55 ! [V_z,V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__asym_H,axiom, % 185.61/186.55 ! [V_b,V_a] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 185.61/186.55 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__trans,axiom, % 185.61/186.55 ! [V_z,V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd_Oless__asym,axiom, % 185.61/186.55 ! [V_y,V_x] : % 185.61/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 185.61/186.55 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 185.61/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__refl,axiom, % 185.61/186.55 ! [V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__trans,axiom, % 185.61/186.55 ! [V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mod__imp__dvd,axiom, % 185.61/186.55 ! [V_n,V_m,V_k,T_a] : % 185.61/186.55 ( class_Divides_Osemiring__div(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mod,axiom, % 185.61/186.55 ! [V_n,V_m,V_k,T_a] : % 185.61/186.55 ( class_Divides_Osemiring__div(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_mod__mod__cancel,axiom, % 185.61/186.55 ! [V_a,V_b,V_c,T_a] : % 185.61/186.55 ( class_Divides_Osemiring__div(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 185.61/186.55 => 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) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mod__iff,axiom, % 185.61/186.55 ! [V_m_2,V_n_2,V_k_2,T_b] : % 185.61/186.55 ( class_Divides_Osemiring__div(T_b) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) % 185.61/186.55 => ( 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))) % 185.61/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_transfer__int__nat__relations_I4_J,axiom, % 185.61/186.55 ! [V_y_2,V_x_2] : % 185.61/186.55 ( 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))) % 185.61/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_zdvd__int,axiom, % 185.61/186.55 ! [V_y_2,V_x_2] : % 185.61/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.61/186.55 <=> 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__triv__left,axiom, % 185.61/186.55 ! [V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__triv__right,axiom, % 185.61/186.55 ! [V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => 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))) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult2,axiom, % 185.61/186.55 ! [V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.61/186.55 => 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))) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult,axiom, % 185.61/186.55 ! [V_b,V_c,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 185.61/186.55 => 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))) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_mult__dvd__mono,axiom, % 185.61/186.55 ! [V_d,V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 185.61/186.55 => 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))) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvdI,axiom, % 185.61/186.55 ! [V_k,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Odvd(T_a) % 185.61/186.55 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult__left,axiom, % 185.61/186.55 ! [V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( 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)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_dvd__mult__right,axiom, % 185.61/186.55 ! [V_c,V_b,V_a,T_a] : % 185.61/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.61/186.55 => ( 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)) % 185.61/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_div__dvd__div,axiom, % 185.61/186.55 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.61/186.55 ( class_Divides_Osemiring__div(T_b) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2)) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ca_2),V_a_2))) % 185.61/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ba_2),V_ca_2)) ) ) ) ) ). % 185.61/186.55 % 185.61/186.55 fof(fact_zdvd__zmod__imp__zdvd,axiom, % 185.61/186.55 ! [V_n,V_m,V_k] : % 185.61/186.55 ( 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))) % 185.61/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__zmod,axiom, % 185.95/186.55 ! [V_n,V_m,V_f] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_uminus__dvd__conv_I2_J,axiom, % 185.95/186.55 ! [V_t_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 185.95/186.55 <=> 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_uminus__dvd__conv_I1_J,axiom, % 185.95/186.55 ! [V_t_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 185.95/186.55 <=> 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__zdiffD,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__reduce,axiom, % 185.95/186.55 ! [V_n_2,V_k_2] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_of__nat__setsum,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Rings_Osemiring__1(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__minus__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Rings_Ocomm__ring__1(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_minus__dvd__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Rings_Ocomm__ring__1(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__diff,axiom, % 185.95/186.55 ! [V_z,V_y,V_x,T_a] : % 185.95/186.55 ( class_Rings_Ocomm__ring__1(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__lessThan__Suc,axiom, % 185.95/186.55 ! [V_n_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_of__int__setsum,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Rings_Oring__1(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__diff__nat,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__commute,axiom, % 185.95/186.55 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__0,axiom, % 185.95/186.55 ! [V_A_2,T_c,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__addf,axiom, % 185.95/186.55 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__right__distrib,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 185.95/186.55 ( class_Rings_Osemiring__0(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__left__distrib,axiom, % 185.95/186.55 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Rings_Osemiring__0(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__product,axiom, % 185.95/186.55 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Rings_Osemiring__0(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__subtractf,axiom, % 185.95/186.55 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Groups_Oab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__negf,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Groups_Oab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__divide__distrib,axiom, % 185.95/186.55 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Fields_Ofield(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_abs__setsum__abs,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__relations_I4_J,axiom, % 185.95/186.55 ! [V_y_2,V_x_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_int__dvd__iff,axiom, % 185.95/186.55 ! [V_z_2,V_m_2] : % 185.95/186.55 ( 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)) % 185.95/186.55 <=> 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)))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__int__iff,axiom, % 185.95/186.55 ! [V_m_2,V_z_2] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_lessThan__subset__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__mult__cancel__left,axiom, % 185.95/186.55 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.95/186.55 ( class_Rings_Oidom(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.95/186.55 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__mult__cancel__right,axiom, % 185.95/186.55 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.95/186.55 ( class_Rings_Oidom(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2))) % 185.95/186.55 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__imp__mod__0,axiom, % 185.95/186.55 ! [V_b,V_a,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.95/186.55 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__eq__mod__eq__0,axiom, % 185.95/186.55 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 185.95/186.55 <=> c_Divides_Odiv__class_Omod(T_b,V_ba_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_lessThan__strict__subset__iff,axiom, % 185.95/186.55 ! [V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_div__add,axiom, % 185.95/186.55 ! [V_y,V_x,V_z,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__mult__div__cancel,axiom, % 185.95/186.55 ! [V_b,V_a,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.95/186.55 => 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 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_div__mult__swap,axiom, % 185.95/186.55 ! [V_a,V_b,V_c,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 185.95/186.55 => 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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__div__mult__self,axiom, % 185.95/186.55 ! [V_b,V_a,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.95/186.55 => 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 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__div__mult,axiom, % 185.95/186.55 ! [V_c,V_b,V_a,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 185.95/186.55 => 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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_div__mult__div__if__dvd,axiom, % 185.95/186.55 ! [V_w,V_z,V_x,V_y,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__div__neg,axiom, % 185.95/186.55 ! [V_x,V_y,T_a] : % 185.95/186.55 ( class_Divides_Oring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__neg__div,axiom, % 185.95/186.55 ! [V_x,V_y,T_a] : % 185.95/186.55 ( class_Divides_Oring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_power__le__dvd,axiom, % 185.95/186.55 ! [V_m,V_b,V_n,V_a,T_a] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.95/186.55 => ( 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)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__power__le,axiom, % 185.95/186.55 ! [V_m,V_n,V_y,V_x,T_a] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__imp__power__dvd,axiom, % 185.95/186.55 ! [V_a,V_n,V_m,T_a] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_div__power,axiom, % 185.95/186.55 ! [V_n,V_x,V_y,T_a] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__antisym__nonneg,axiom, % 185.95/186.55 ! [V_n,V_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 185.95/186.55 => V_m = V_n ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__not__zless,axiom, % 185.95/186.55 ! [V_n,V_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n)) % 185.95/186.55 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__mono,axiom, % 185.95/186.55 ! [V_t_2,V_m_2,V_k_2] : % 185.95/186.55 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) % 185.95/186.55 <=> 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__mult__cancel,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__reduce,axiom, % 185.95/186.55 ! [V_m_2,V_n_2,V_k_2] : % 185.95/186.55 ( 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)))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__period,axiom, % 185.95/186.55 ! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> 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_ca_2),V_d_2))),V_t_2))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__1__iff__1,axiom, % 185.95/186.55 ! [V_m_2] : % 185.95/186.55 ( 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)))) % 185.95/186.55 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_nat__dvd__not__less,axiom, % 185.95/186.55 ! [V_n,V_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.95/186.55 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 185.95/186.55 ! [V_n_2,V_m_2,V_k_2] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.55 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__mult__div__cancel,axiom, % 185.95/186.55 ! [V_m,V_n] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 185.95/186.55 => 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 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zmod__eq__dvd__iff,axiom, % 185.95/186.55 ! [V_y_2,V_n_2,V_x_2] : % 185.95/186.55 ( 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) % 185.95/186.55 <=> 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__diffD1,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__diffD,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd1__eq,axiom, % 185.95/186.55 ! [V_x_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 185.95/186.55 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_abs__div,axiom, % 185.95/186.55 ! [V_x,V_y] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x)) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_nat__dvd__iff,axiom, % 185.95/186.55 ! [V_m_2,V_z_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) % 185.95/186.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.95/186.55 => 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))) ) % 185.95/186.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.95/186.55 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_arith__series__general,axiom, % 185.95/186.55 ! [V_n_2,V_d_2,V_a_2,T_b] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_b) % 185.95/186.55 => 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)))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_unity__coeff__ex,axiom, % 185.95/186.55 ! [V_l_2,V_Pa_2,T_b] : % 185.95/186.55 ( ( class_Rings_Odvd(T_b) % 185.95/186.55 & class_Rings_Osemiring__0(T_b) ) % 185.95/186.55 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 185.95/186.55 <=> ? [B_x] : % 185.95/186.55 ( 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)))) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__period_I3_J,axiom, % 185.95/186.55 ! [V_t_2,V_D_2,V_d_2,T_b] : % 185.95/186.55 ( ( class_Rings_Ocomm__ring(T_b) % 185.95/186.55 & class_Rings_Odvd(T_b) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x,B_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__period_I4_J,axiom, % 185.95/186.55 ! [V_t_2,V_D_2,V_d_2,T_b] : % 185.95/186.55 ( ( class_Rings_Ocomm__ring(T_b) % 185.95/186.55 & class_Rings_Odvd(T_b) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x,B_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__eq__mod__eq__0__number__of,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( ( class_Divides_Osemiring__div(T_b) % 185.95/186.55 & class_Int_Onumber(T_b) ) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> 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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__div__div__eq__mult,axiom, % 185.95/186.55 ! [V_d_2,V_ba_2,V_ca_2,V_a_2,T_b] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_b) % 185.95/186.55 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2)) % 185.95/186.55 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2) % 185.95/186.55 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__div__eq__mult,axiom, % 185.95/186.55 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Divides_Osemiring__div(T_b) % 185.95/186.55 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 185.95/186.55 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = V_ca_2 % 185.95/186.55 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__imp__le,axiom, % 185.95/186.55 ! [V_n,V_z] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom, % 185.95/186.55 ! [V_y_2,V_x_2] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__imp__le,axiom, % 185.95/186.55 ! [V_n,V_k] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__mult__cancel,axiom, % 185.95/186.55 ! [V_n,V_m,V_k] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_nat__mult__dvd__cancel1,axiom, % 185.95/186.55 ! [V_n_2,V_m_2,V_k_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__imp__le__int,axiom, % 185.95/186.55 ! [V_d,V_i] : % 185.95/186.55 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd__power,axiom, % 185.95/186.55 ! [V_x,V_n,T_a] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_a) % 185.95/186.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.95/186.55 | V_x = c_Groups_Oone__class_Oone(T_a) ) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd_Ostrict__monoD,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,V_f_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( 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) % 185.95/186.55 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.95/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_arith__series__nat,axiom, % 185.95/186.55 ! [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)))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd_OmonoD,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,V_f_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__natinterval__difff,axiom, % 185.95/186.55 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Oab__group__add(T_b) % 185.95/186.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => 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)))) ) % 185.95/186.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => 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) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_gauss__sum,axiom, % 185.95/186.55 ! [V_n_2,T_b] : % 185.95/186.55 ( class_Rings_Ocomm__semiring__1(T_b) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 185.95/186.55 ! [V_k_2,V_f_2] : % 185.95/186.55 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd_Ostrict__mono__mono,axiom, % 185.95/186.55 ! [V_f_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( 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) % 185.95/186.55 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastatMost__subset__iff,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 185.95/186.55 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.95/186.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.95/186.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 185.95/186.55 ! [V_n_2,V_m_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 185.95/186.55 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_int__setsum,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastatMost__psubset__iff,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 185.95/186.55 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.95/186.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.95/186.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) % 185.95/186.55 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) % 185.95/186.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_d_2)) ) ) ) % 185.95/186.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__head__Suc,axiom, % 185.95/186.55 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__cl__ivl__Suc,axiom, % 185.95/186.55 ! [V_f_2,V_m_2,V_n_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 185.95/186.55 => 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) ) % 185.95/186.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__ub__add__nat,axiom, % 185.95/186.55 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( 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)))) % 185.95/186.55 => 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)))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_all__nat__less,axiom, % 185.95/186.55 ! [V_Pa_2,V_n_2] : % 185.95/186.55 ( ! [B_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.95/186.55 <=> ! [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ex__nat__less,axiom, % 185.95/186.55 ! [V_Pa_2,V_n_2] : % 185.95/186.55 ( ? [B_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.95/186.55 <=> ? [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sum__diff__distrib,axiom, % 185.95/186.55 ! [V_n_2,V_Pa_2,V_Q_2] : % 185.95/186.55 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x))) % 185.95/186.55 => 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_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_geometric__sum,axiom, % 185.95/186.55 ! [V_n_2,V_x_2,T_b] : % 185.95/186.55 ( class_Fields_Ofield(T_b) % 185.95/186.55 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ex__nat__less__eq,axiom, % 185.95/186.55 ! [V_Pa_2,V_n_2] : % 185.95/186.55 ( ? [B_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.95/186.55 <=> ? [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_all__nat__less__eq,axiom, % 185.95/186.55 ! [V_Pa_2,V_n_2] : % 185.95/186.55 ( ! [B_m] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.95/186.55 <=> ! [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.95/186.55 => V_ba_2 = V_d_2 ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.95/186.55 => V_a_2 = V_ca_2 ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThan__eq__iff,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.95/186.55 <=> ( V_a_2 = V_ca_2 % 185.95/186.55 & V_ba_2 = V_d_2 ) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeast0LessThan,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThan__subset__iff,axiom, % 185.95/186.55 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2))) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 185.95/186.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.95/186.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 185.95/186.55 ! [V_n_2,V_m_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 185.95/186.55 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__diff,axiom, % 185.95/186.55 ! [V_m_2,V_n_2,V_i_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 185.95/186.55 => 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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__add__nat__ivl,axiom, % 185.95/186.55 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__diff__nat__ivl,axiom, % 185.95/186.55 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Oab__group__add(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 185.95/186.55 ! [V_k_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__head__upt__Suc,axiom, % 185.95/186.55 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__op__ivl__Suc,axiom, % 185.95/186.55 ! [V_f_2,V_m_2,V_n_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.95/186.55 => 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) ) % 185.95/186.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_bset_I6_J,axiom, % 185.95/186.55 ! [V_t_2,V_B_2,V_D_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_aset_I8_J,axiom, % 185.95/186.55 ! [V_t_2,V_A_2,V_D_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_periodic__finite__ex,axiom, % 185.95/186.55 ! [V_Pa_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.95/186.55 => ( ! [B_x,B_k] : % 185.95/186.55 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.95/186.55 <=> 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)))) ) % 185.95/186.55 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.95/186.55 <=> ? [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_aset_I7_J,axiom, % 185.95/186.55 ! [V_t_2,V_A_2,V_D_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_bset_I5_J,axiom, % 185.95/186.55 ! [V_t_2,V_B_2,V_D_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 185.95/186.55 => 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)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_aset_I10_J,axiom, % 185.95/186.55 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( ~ 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))) % 185.95/186.55 => ~ 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_bset_I10_J,axiom, % 185.95/186.55 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( ~ 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))) % 185.95/186.55 => ~ 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_aset_I9_J,axiom, % 185.95/186.55 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( 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))) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_bset_I9_J,axiom, % 185.95/186.55 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 185.95/186.55 => ! [B_x] : % 185.95/186.55 ( ! [B_xa] : % 185.95/186.55 ( 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))) % 185.95/186.55 => ! [B_xb] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.55 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.55 => ( 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))) % 185.95/186.55 => 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__atLeastZeroLessThan__int,axiom, % 185.95/186.55 ! [V_u_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__head,axiom, % 185.95/186.55 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_dvd_Ostrict__monoI,axiom, % 185.95/186.55 ! [V_f_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( ! [B_x,B_y] : % 185.95/186.55 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 185.95/186.55 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) ) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 185.95/186.55 => 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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__atLeastLessThan,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__greaterThanAtMost,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_subset__image__iff,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 185.95/186.55 ( 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))) % 185.95/186.55 <=> ? [B_AA] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 185.95/186.55 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__mono,axiom, % 185.95/186.55 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 <=> 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__image,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 <=> 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( V_A_2 = V_B_2 % 185.95/186.55 <=> 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__diff__subset,axiom, % 185.95/186.55 ! [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)))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__atLeastAtMost,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 185.95/186.55 ! [V_A_2,V_f_2,T_b] : % 185.95/186.55 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 185.95/186.55 ! [V_n_2,V_m_2] : % 185.95/186.55 ( c_Nat__Transfer_Ois__nat(V_m_2) % 185.95/186.55 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__SucD,axiom, % 185.95/186.55 ! [V_n_2,V_A_2,V_f_2,T_b] : % 185.95/186.55 ( 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) % 185.95/186.55 => ? [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.55 & 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__ivl__cong,axiom, % 185.95/186.55 ! [V_g_2,V_f_2,V_d_2,V_ba_2,V_ca_2,V_a_2,T_b,T_c] : % 185.95/186.55 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.55 & class_Orderings_Oord(T_b) ) % 185.95/186.55 => ( V_a_2 = V_ca_2 % 185.95/186.55 => ( V_ba_2 = V_d_2 % 185.95/186.55 => ( ! [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 185.95/186.55 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 185.95/186.55 => 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_ba_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atLeastAtMost__int,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__lessThan,axiom, % 185.95/186.55 ! [V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__greaterThanAtMost__int,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_greaterThan__eq__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 185.95/186.55 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__Suc__atLeastLessThan,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__Suc__atLeastAtMost,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__add__atLeastLessThan,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__add__atLeastAtMost,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__eq__setsum,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__int__nat__set__return__embed,axiom, % 185.95/186.55 ! [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 ). % 185.95/186.55 % 185.95/186.55 fof(fact_greaterThan__subset__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__constant,axiom, % 185.95/186.55 ! [V_A_2,V_y_2,T_c,T_b] : % 185.95/186.55 ( class_Rings_Osemiring__1(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atLeastZeroLessThan__int,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atLeastLessThan__int,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__add__int__atLeastLessThan,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__greaterThan,axiom, % 185.95/186.55 ! [V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__greaterThanLessThan__int,axiom, % 185.95/186.55 ! [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)))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 185.95/186.55 ! [V_f_2,V_A_2,T_b] : % 185.95/186.55 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 <=> 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 <=> 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))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 185.95/186.55 ! [V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__lessThan,axiom, % 185.95/186.55 ! [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 ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => ( V_A_2 = V_B_2 % 185.95/186.55 <=> 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) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atLeastLessThan,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__greaterThanAtMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_nat__set__def,axiom, % 185.95/186.55 ! [V_S_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_S_2) % 185.95/186.55 <=> ! [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__greaterThanLessThan,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 185.95/186.55 ! [V_y_2,V_x_2] : % 185.95/186.55 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.95/186.55 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atLeastAtMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_subset__card__intvl__is__intvl,axiom, % 185.95/186.55 ! [V_k_2,V_A_2] : % 185.95/186.55 ( 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))))) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 185.95/186.55 ! [V_y_2,V_x_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.95/186.55 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__set__return__embed,axiom, % 185.95/186.55 ! [V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => 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 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 185.95/186.55 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.55 => ( V_A_2 = V_B_2 % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => ( ! [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.95/186.55 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 185.95/186.55 => 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) ) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I19_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I18_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup1E,axiom, % 185.95/186.55 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( 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)) % 185.95/186.55 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 185.95/186.55 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup1CI,axiom, % 185.95/186.55 ! [T_b,V_A_2,V_x_2,V_B_2] : % 185.95/186.55 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 185.95/186.55 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I9_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__Un,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup1I1,axiom, % 185.95/186.55 ! [V_B_2,T_b,V_x_2,V_A_2] : % 185.95/186.55 ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup1I2,axiom, % 185.95/186.55 ! [V_A_2,T_b,V_x_2,V_B_2] : % 185.95/186.55 ( hBOOL(hAPP(V_B_2,V_x_2)) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__absorb,axiom, % 185.95/186.55 ! [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 ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__commute,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__left__absorb,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__left__commute,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__assoc,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_bex__Un,axiom, % 185.95/186.55 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( ? [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.95/186.55 <=> ( ? [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.95/186.55 | ? [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.95/186.55 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ball__Un,axiom, % 185.95/186.55 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( ! [B_x] : % 185.95/186.55 ( 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))) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.95/186.55 <=> ( ! [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.95/186.55 & ! [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.95/186.55 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup_Oidem,axiom, % 185.95/186.55 ! [V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__idem,axiom, % 185.95/186.55 ! [V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup_Ocommute,axiom, % 185.95/186.55 ! [V_b,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__aci_I5_J,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__commute,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup_Oleft__idem,axiom, % 185.95/186.55 ! [V_b,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__aci_I8_J,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__left__idem,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup_Oleft__commute,axiom, % 185.95/186.55 ! [V_c,V_a,V_b,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__aci_I7_J,axiom, % 185.95/186.55 ! [V_z,V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__left__commute,axiom, % 185.95/186.55 ! [V_z,V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup_Oassoc,axiom, % 185.95/186.55 ! [V_c,V_b,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__aci_I6_J,axiom, % 185.95/186.55 ! [V_z,V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__assoc,axiom, % 185.95/186.55 ! [V_z,V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__apply,axiom, % 185.95/186.55 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Lattices_Olattice(T_b) % 185.95/186.55 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__fun__def,axiom, % 185.95/186.55 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.55 ( class_Lattices_Olattice(T_b) % 185.95/186.55 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__Diff__cancel,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__Diff__cancel2,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__Diff,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Sup__fin_Oidem,axiom, % 185.95/186.55 ! [V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__max,axiom, % 185.95/186.55 ! [T_b] : % 185.95/186.55 ( ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.55 & class_Orderings_Olinorder(T_b) ) % 185.95/186.55 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atMost__eq__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 185.95/186.55 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__supE,axiom, % 185.95/186.55 ! [V_x,V_b,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 185.95/186.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.95/186.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__mono,axiom, % 185.95/186.55 ! [V_d,V_b,V_c,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__least,axiom, % 185.95/186.55 ! [V_z,V_x,V_y,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__supI,axiom, % 185.95/186.55 ! [V_b,V_x,V_a,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__absorb1,axiom, % 185.95/186.55 ! [V_x,V_y,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__absorb2,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__supI2,axiom, % 185.95/186.55 ! [V_a,V_b,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__supI1,axiom, % 185.95/186.55 ! [V_b,V_a,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__sup__iff,axiom, % 185.95/186.55 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) % 185.95/186.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.95/186.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_le__iff__sup,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.95/186.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__ge2,axiom, % 185.95/186.55 ! [V_x,V_y,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__ord_I4_J,axiom, % 185.95/186.55 ! [V_x,V_y,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__ge1,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_inf__sup__ord_I3_J,axiom, % 185.95/186.55 ! [V_y,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Olattice(T_a) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__upper1,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__upper2,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_subset__Un__eq,axiom, % 185.95/186.55 ! [V_B_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__absorb1,axiom, % 185.95/186.55 ! [V_B_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__absorb2,axiom, % 185.95/186.55 ! [V_A_2,V_B_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__least,axiom, % 185.95/186.55 ! [V_B_2,V_C_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.95/186.55 => 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)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Un__mono,axiom, % 185.95/186.55 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_less__supI2,axiom, % 185.95/186.55 ! [V_a,V_b,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_less__supI1,axiom, % 185.95/186.55 ! [V_b,V_a,V_x,T_a] : % 185.95/186.55 ( class_Lattices_Osemilattice__sup(T_a) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.95/186.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__atMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I10_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I7_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I17_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Diff__partition,axiom, % 185.95/186.55 ! [V_B_2,V_A_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.55 => 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 ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Diff__subset__conv,axiom, % 185.95/186.55 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.95/186.55 ( 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)) % 185.95/186.55 <=> 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I20_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Compl__Diff__eq,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 185.95/186.55 ! [V_B_2,V_A_2] : % 185.95/186.55 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.55 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.55 => 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))) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeast0AtMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_card__greaterThanLessThan,axiom, % 185.95/186.55 ! [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)) ). % 185.95/186.55 % 185.95/186.55 fof(fact_lessThan__Suc__atMost,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atMost__subset__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I21_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeastLessThan__add__Un,axiom, % 185.95/186.55 ! [V_k_2,V_j_2,V_i_2] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I8_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),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) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I22_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I11_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Compl__atMost,axiom, % 185.95/186.55 ! [V_k_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Compl__greaterThan,axiom, % 185.95/186.55 ! [V_k_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I15_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I16_J,axiom, % 185.95/186.55 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_setsum__atMost__Suc,axiom, % 185.95/186.55 ! [V_n_2,V_f_2,T_b] : % 185.95/186.55 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.55 => 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))) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I12_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I13_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_hoare__derivs_OBody,axiom, % 185.95/186.55 ! [V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Q_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_Q_2)),V_Procs_2)) % 185.95/186.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_UN__le__eq__Un0,axiom, % 185.95/186.55 ! [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))) ). % 185.95/186.55 % 185.95/186.55 fof(fact_sup__nat__def,axiom, % 185.95/186.55 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 185.95/186.55 % 185.95/186.55 fof(fact_asm,axiom, % 185.95/186.55 ! [V_Ga_2,V_ts_2,T_b] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 185.95/186.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_weaken,axiom, % 185.95/186.55 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] : % 185.95/186.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) % 185.95/186.55 => ( 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)) % 185.95/186.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_thin,axiom, % 185.95/186.55 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 185.95/186.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) % 185.95/186.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeast__eq__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 185.95/186.55 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_cut,axiom, % 185.95/186.55 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 185.95/186.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 185.95/186.55 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) % 185.95/186.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_SUP1__iff,axiom, % 185.95/186.55 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.55 ( 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_ba_2)) % 185.95/186.55 <=> ? [B_x] : % 185.95/186.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.55 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeast__Suc__greaterThan,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_atLeast__subset__iff,axiom, % 185.95/186.55 ! [V_y_2,V_x_2,T_b] : % 185.95/186.55 ( class_Orderings_Oorder(T_b) % 185.95/186.55 => ( 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))) % 185.95/186.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Compl__atLeast,axiom, % 185.95/186.55 ! [V_k_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_Compl__lessThan,axiom, % 185.95/186.55 ! [V_k_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => 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) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_UN__le__add__shift,axiom, % 185.95/186.55 ! [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) ). % 185.95/186.55 % 185.95/186.55 fof(fact_ivl__disj__un_I14_J,axiom, % 185.95/186.55 ! [V_u_2,V_l_2,T_b] : % 185.95/186.55 ( class_Orderings_Olinorder(T_b) % 185.95/186.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__atLeast,axiom, % 185.95/186.55 ! [V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.55 fof(fact_image__uminus__atMost,axiom, % 185.95/186.55 ! [V_x_2,T_b] : % 185.95/186.55 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.55 => 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)) ) ). % 185.95/186.55 % 185.95/186.56 fof(fact_SUP__subset,axiom, % 185.95/186.56 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I6_J,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I6_J,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUPR__apply,axiom, % 185.95/186.56 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ball__UN,axiom, % 185.95/186.56 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.56 ( ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 => ! [B_xa] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 185.95/186.56 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP__commute,axiom, % 185.95/186.56 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__UN__flatten,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I9_J,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I9_J,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP__le__iff,axiom, % 185.95/186.56 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.56 => ( 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)) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_less__SUP__iff,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 185.95/186.56 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.56 & class_Orderings_Olinorder(T_b) ) % 185.95/186.56 => ( 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))) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__subset__iff,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I10_J,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__UN,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I10_J,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__Un__distrib,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__Un,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThan__0,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom, % 185.95/186.56 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] : % 185.95/186.56 ( 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_ba_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2))) % 185.95/186.56 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.56 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) % 185.95/186.56 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ca_2)) ) % 185.95/186.56 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_ba_2)) ) ) ) ) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_d_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OmonoI,axiom, % 185.95/186.56 ! [V_f_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( ! [B_x,B_y] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 185.95/186.56 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_upto_Opinduct,axiom, % 185.95/186.56 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ( ! [B_i,B_j] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 185.95/186.56 => 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)) ) % 185.95/186.56 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 185.95/186.56 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_top1I,axiom, % 185.95/186.56 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__UNIV__left,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__UNIV__right,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__UNIV,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_top__apply,axiom, % 185.95/186.56 ! [V_x_2,T_c,T_b] : % 185.95/186.56 ( class_Orderings_Otop(T_b) % 185.95/186.56 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_range__composition,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_top__greatest,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Orderings_Otop(T_a) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__top__right,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Obounded__lattice__top(T_a) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__top__left,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Obounded__lattice__top(T_a) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__lessThan__UNIV,axiom, % 185.95/186.56 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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__atMost__UNIV,axiom, % 185.95/186.56 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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__atLeast__UNIV,axiom, % 185.95/186.56 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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__partition2,axiom, % 185.95/186.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__partition,axiom, % 185.95/186.56 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__eq__Diff__UNIV,axiom, % 185.95/186.56 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeast__0,axiom, % 185.95/186.56 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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_compl__sup__top,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__compl__top,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__UN__finite__eq,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastatMost__subset__iff,axiom, % 185.95/186.56 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] : % 185.95/186.56 ( 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_ba_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2))) % 185.95/186.56 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.56 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_surj__Compl__image__subset,axiom, % 185.95/186.56 ! [V_A_2,V_f_2,T_b,T_c] : % 185.95/186.56 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__finite2__subset,axiom, % 185.95/186.56 ! [V_B_2,V_k_2,V_A_2,T_b] : % 185.95/186.56 ( ! [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))) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__finite2__eq,axiom, % 185.95/186.56 ! [V_B_2,V_k_2,V_A_2,T_b] : % 185.95/186.56 ( ! [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) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__finite__subset,axiom, % 185.95/186.56 ! [V_C_2,V_A_2,T_b] : % 185.95/186.56 ( ! [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)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__UNIV__bool,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__ident,axiom, % 185.95/186.56 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition__code__numeral,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff__nat,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff,axiom, % 185.95/186.56 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Oab__group__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atLeastLessThan,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atLeastAtMost__int,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atLeastAtMost,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__lessThan,axiom, % 185.95/186.56 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atMost,axiom, % 185.95/186.56 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atLeastLessThan__int,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__greaterThanAtMost,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__greaterThanAtMost__int,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__greaterThanLessThan__int,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__greaterThanLessThan,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__insert__right,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__insert__left,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__insertI,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__insertI2,axiom, % 185.95/186.56 ! [V_ba_2,V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => 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_ba_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__mono,axiom, % 185.95/186.56 ! [V_a_2,V_D_2,V_C_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 185.95/186.56 ! [V_N_2] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 185.95/186.56 <=> ? [B_m] : % 185.95/186.56 ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__nat__set__iff__bounded,axiom, % 185.95/186.56 ! [V_N_2] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 185.95/186.56 <=> ? [B_m] : % 185.95/186.56 ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__code,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_y_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 185.95/186.56 <=> ( V_y_2 = V_x_2 % 185.95/186.56 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__commute,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__absorb2,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 185.95/186.56 ! [V_A_2] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__insert,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 185.95/186.56 ! [V_A_2] : % 185.95/186.56 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 185.95/186.56 <=> 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Oinfinite,axiom, % 185.95/186.56 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__infinite,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_lessThan__Suc,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atMost__Suc,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__eq__0__iff,axiom, % 185.95/186.56 ! [V_f_2,V_F_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.56 => ( 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) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 185.95/186.56 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__insert,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Odistrib,axiom, % 185.95/186.56 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastAtMostSuc__conv,axiom, % 185.95/186.56 ! [V_n_2,V_m_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__eq__Suc0__iff,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( 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)) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.95/186.56 & ! [B_xa] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.95/186.56 => ( B_x != B_xa % 185.95/186.56 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__eq__1__iff,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( 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) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.95/186.56 & ! [B_xa] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.95/186.56 => ( B_x != B_xa % 185.95/186.56 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__psubset,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( 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))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_diff__card__le__card__Diff,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => 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)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff__subset,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Diff,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite_OinsertI,axiom, % 185.95/186.56 ! [V_a_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__imageI,axiom, % 185.95/186.56 ! [V_h_2,T_c,V_F_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_infinite__UNIV__int,axiom, % 185.95/186.56 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UNIV__option__conv,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__code,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( class_Finite__Set_Ofinite(T_b) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( class_Finite__Set_Ofinite(T_b) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__UNIV__unit,axiom, % 185.95/186.56 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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_infinite__UNIV__nat,axiom, % 185.95/186.56 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__insert,axiom, % 185.95/186.56 ! [V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 185.95/186.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_rev__finite__subset,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__subset,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Prod__UNIV,axiom, % 185.95/186.56 ! [T_c,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__fun__UNIVD2,axiom, % 185.95/186.56 ! [T_c,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Plus__UNIV__iff,axiom, % 185.95/186.56 ! [T_c,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) % 185.95/186.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__option__UNIV,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) % 185.95/186.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__UNIV,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( class_Finite__Set_Ofinite(T_b) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Un,axiom, % 185.95/186.56 ! [V_Ga_2,V_F_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 185.95/186.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__UnI,axiom, % 185.95/186.56 ! [V_Ga_2,V_F_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Diff2,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__UN,axiom, % 185.95/186.56 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__surj,axiom, % 185.95/186.56 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__Diff__insert,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) % 185.95/186.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__infinite,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 => ( 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))) % 185.95/186.56 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__compl,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.95/186.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__range__imageI,axiom, % 185.95/186.56 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 185.95/186.56 ( 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))))) % 185.95/186.56 => 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))))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__ge__0__finite,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__insert__le,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__mono,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__seteq,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( 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))) % 185.95/186.56 => V_A_2 = V_B_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__image__le,axiom, % 185.95/186.56 ! [V_f_2,T_c,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_psubset__card__mono,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__UNIV__card__ge__0,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 => 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))))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__fun__UNIVD1,axiom, % 185.95/186.56 ! [T_c,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 185.95/186.56 => ( 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)) % 185.95/186.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_OAbs__image,axiom, % 185.95/186.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_ORep__range,axiom, % 185.95/186.56 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 185.95/186.56 ! [V_x_2,V_y_2,V_ca_2] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 185.95/186.56 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.95/186.56 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.95/186.56 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite_OemptyI,axiom, % 185.95/186.56 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty__subsetI,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite_Oequations_I1_J,axiom, % 185.95/186.56 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_singleton__inject,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.56 => V_a_2 = V_ba_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_doubleton__eq__iff,axiom, % 185.95/186.56 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 <=> ( ( V_a_2 = V_ca_2 % 185.95/186.56 & V_ba_2 = V_d_2 ) % 185.95/186.56 | ( V_a_2 = V_d_2 % 185.95/186.56 & V_ba_2 = V_ca_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__not__empty,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty__not__insert,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__empty__left,axiom, % 185.95/186.56 ! [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 ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__empty__right,axiom, % 185.95/186.56 ! [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 ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__empty,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__empty,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( 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)))) % 185.95/186.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_not__psubset__empty,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__fun__def,axiom, % 185.95/186.56 ! [V_x_2,T_c,T_b] : % 185.95/186.56 ( class_Orderings_Obot(T_b) % 185.95/186.56 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__apply,axiom, % 185.95/186.56 ! [V_x_2,T_c,T_b] : % 185.95/186.56 ( class_Orderings_Obot(T_b) % 185.95/186.56 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__cancel,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__empty,axiom, % 185.95/186.56 ! [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 ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty__Diff,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ball__empty,axiom, % 185.95/186.56 ! [V_Pa_2,T_b,B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.56 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__is__empty,axiom, % 185.95/186.56 ! [V_A_2,V_f_2,T_b,T_c] : % 185.95/186.56 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__empty,axiom, % 185.95/186.56 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty__is__image,axiom, % 185.95/186.56 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.56 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) % 185.95/186.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UNIV__not__empty,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__least,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Orderings_Obot(T_a) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP__const,axiom, % 185.95/186.56 ! [V_M_2,T_b,V_A_2,T_c] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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 ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UNION__empty__conv_I2_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__constant,axiom, % 185.95/186.56 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.95/186.56 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.95/186.56 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__empty2,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UNION__empty__conv_I1_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.56 ( 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) % 185.95/186.56 <=> ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__eq__bot__iff,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,T_b] : % 185.95/186.56 ( class_Lattices_Obounded__lattice__bot(T_b) % 185.95/186.56 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 185.95/186.56 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 185.95/186.56 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__bot__right,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__bot__left,axiom, % 185.95/186.56 ! [V_x,T_a] : % 185.95/186.56 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Oempty,axiom, % 185.95/186.56 ! [V_g_2,T_c,T_b] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__empty,axiom, % 185.95/186.56 ! [V_f_2,T_c,T_b] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__singletonD,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( 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))))) % 185.95/186.56 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 | 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__is__Un,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastatMost__empty__iff,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastatMost__empty__iff2,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastatMost__empty,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) % 185.95/186.56 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__Diff__single,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__insert2,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__insert,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThan__empty,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 185.95/186.56 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card_Oempty,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThan__empty__iff,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThan__empty__iff2,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__UNIV,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastAtMost__singleton,axiom, % 185.95/186.56 ! [V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastAtMost__singleton__iff,axiom, % 185.95/186.56 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.56 <=> ( V_a_2 = V_ba_2 % 185.95/186.56 & V_ba_2 = V_ca_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastAtMost__singleton_H,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( V_a_2 = V_ba_2 % 185.95/186.56 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__Compl__self__eq,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.95/186.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__UNIV__eq,axiom, % 185.95/186.56 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__empty__eq,axiom, % 185.95/186.56 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThan0,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThanAtMost__empty,axiom, % 185.95/186.56 ! [V_k_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThanAtMost__empty__iff,axiom, % 185.95/186.56 ! [V_l_2,V_k_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( 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)) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 185.95/186.56 ! [V_l_2,V_k_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( 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) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThanLessThan__empty,axiom, % 185.95/186.56 ! [V_k_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_lessThan__0,axiom, % 185.95/186.56 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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__constant__conv,axiom, % 185.95/186.56 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.95/186.56 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.95/186.56 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I1_J,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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))) ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__singleton,axiom, % 185.95/186.56 ! [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 ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I1_J,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2] : % 185.95/186.56 ( 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_ba_2) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2] : % 185.95/186.56 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastatMost__empty,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) % 185.95/186.56 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I2_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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 ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__extend__simps_I3_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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 ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I2_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__simps_I3_J,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.56 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_compl__bot__eq,axiom, % 185.95/186.56 ! [T_a] : % 185.95/186.56 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.56 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_compl__top__eq,axiom, % 185.95/186.56 ! [T_a] : % 185.95/186.56 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.56 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__eq__0__iff,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.56 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_single__Diff__lessThan,axiom, % 185.95/186.56 ! [V_k_2,T_b] : % 185.95/186.56 ( class_Orderings_Oorder(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__eq__UN,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThan__singleton,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atMost__0,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_ORep__inverse,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_ORep__inject,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 185.95/186.56 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2] : % 185.95/186.56 ( V_a_2 = V_ba_2 % 185.95/186.56 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 185.95/186.56 ! [V_ca_2,V_ba_2,V_a_2] : % 185.95/186.56 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) % 185.95/186.56 <=> ( V_a_2 = V_ba_2 % 185.95/186.56 & V_ba_2 = V_ca_2 ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeast__Suc,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThan__Suc,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__gt__0__iff,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I2_J,axiom, % 185.95/186.56 ! [V_u_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeastLessThanSuc,axiom, % 185.95/186.56 ! [V_n_2,V_m_2] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I1_J,axiom, % 185.95/186.56 ! [V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Oinsert__remove,axiom, % 185.95/186.56 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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)))))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__insert,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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)))))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff1__le,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I6_J,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I5_J,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I3_J,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ivl__disj__un_I4_J,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,T_b] : % 185.95/186.56 ( class_Orderings_Olinorder(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card_Oinsert__remove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => 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)))))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_the__elem__def,axiom, % 185.95/186.56 ! [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))))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 185.95/186.56 ! [V_k_2,V_l_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_the__elem__eq,axiom, % 185.95/186.56 ! [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 ). % 185.95/186.56 % 185.95/186.56 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_derivs__insertD,axiom, % 185.95/186.56 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) % 185.95/186.56 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_hoare__derivs_Oinsert,axiom, % 185.95/186.56 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 185.95/186.56 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty,axiom, % 185.95/186.56 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__nat__def,axiom, % 185.95/186.56 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Comp,axiom, % 185.95/186.56 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_hoare__derivs_OSkip,axiom, % 185.95/186.56 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 185.95/186.56 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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_LoopF,axiom, % 185.95/186.56 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_ba_2))),c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_simp__from__to,axiom, % 185.95/186.56 ! [V_i_2,V_j_2] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ass,axiom, % 185.95/186.56 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_set__empty__eq,axiom, % 185.95/186.56 ! [V_xo_2,T_b] : % 185.95/186.56 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_weak__Body,axiom, % 185.95/186.56 ! [V_Q_2,V_pn_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_BodyN,axiom, % 185.95/186.56 ! [V_Ga_2,V_Q_2,V_pn_2,V_Pa_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,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_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Body1,axiom, % 185.95/186.56 ! [V_pn_2,V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_Pa_2)),c_Com_Ocom_OBODY)),V_Q_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_Q_2)),V_Procs_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_Pa_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_nat__def,axiom, % 185.95/186.56 ! [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)))))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__mono3,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.95/186.56 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( ! [B_x] : % 185.95/186.56 ( 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))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 185.95/186.56 => 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))) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff__singleton,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_equalityCE,axiom, % 185.95/186.56 ! [V_ca_2,T_b,V_B_2,V_A_2] : % 185.95/186.56 ( V_A_2 = V_B_2 % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) % 185.95/186.56 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP2__I,axiom, % 185.95/186.56 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 185.95/186.56 => 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_ba_2),V_ca_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_emptyE,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insertE,axiom, % 185.95/186.56 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 185.95/186.56 => ( V_a_2 != V_ba_2 % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insertCI,axiom, % 185.95/186.56 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 185.95/186.56 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.95/186.56 => V_a_2 = V_ba_2 ) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subsetD,axiom, % 185.95/186.56 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UNIV__I,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__eqI,axiom, % 185.95/186.56 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_ba_2] : % 185.95/186.56 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UnE,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UnCI,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 185.95/186.56 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_DiffI,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_DiffE,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ComplI,axiom, % 185.95/186.56 ! [V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP1__I,axiom, % 185.95/186.56 ! [T_c,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 185.95/186.56 => 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_ba_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__I,axiom, % 185.95/186.56 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_mem__splitI,axiom, % 185.95/186.56 ! [T_d,T_c,V_ba_2,V_a_2,V_ca_2,V_z_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_ba_2))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_pair__imageI,axiom, % 185.95/186.56 ! [V_f_2,T_d,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.56 ( 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_ba_2)),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_ba_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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__empty__eq2,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> 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)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_equals0D,axiom, % 185.95/186.56 ! [V_a_2,T_b,V_A_2] : % 185.95/186.56 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_empty__iff,axiom, % 185.95/186.56 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ex__in__conv,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_all__not__in__conv,axiom, % 185.95/186.56 ! [V_A_2,T_b] : % 185.95/186.56 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__iff,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_DiffD1,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_DiffD2,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot__empty__eq,axiom, % 185.95/186.56 ! [V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OatLeastAtMost__iff,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_pred__equals__eq2,axiom, % 185.95/186.56 ! [V_S_2,V_R_2,T_c,T_b] : % 185.95/186.56 ( 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) % 185.95/186.56 <=> V_R_2 = V_S_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__Un__eq2,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_pred__subset__eq,axiom, % 185.95/186.56 ! [V_S_2,V_R_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Un__iff,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UnI1,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UnI2,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_in__mono,axiom, % 185.95/186.56 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_set__rev__mp,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_set__mp,axiom, % 185.95/186.56 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_psubsetD,axiom, % 185.95/186.56 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Rep__Integ__inject,axiom, % 185.95/186.56 ! [V_y_2,V_x_2] : % 185.95/186.56 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 185.95/186.56 <=> V_x_2 = V_y_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_eq__mem__trans,axiom, % 185.95/186.56 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 185.95/186.56 ( V_a_2 = V_ba_2 % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_eqelem__imp__iff,axiom, % 185.95/186.56 ! [V_A_2,T_b,V_y_2,V_x_2] : % 185.95/186.56 ( V_x_2 = V_y_2 % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_eqset__imp__iff,axiom, % 185.95/186.56 ! [V_x_2,T_b,V_B_2,V_A_2] : % 185.95/186.56 ( V_A_2 = V_B_2 % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_mem__def,axiom, % 185.95/186.56 ! [V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_eq__mem,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 185.95/186.56 <=> V_x_2 = V_y_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_pred__equals__eq,axiom, % 185.95/186.56 ! [V_S_2,V_R_2,T_b] : % 185.95/186.56 ( 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) % 185.95/186.56 <=> V_R_2 = V_S_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ComplE,axiom, % 185.95/186.56 ! [V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.95/186.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ComplD,axiom, % 185.95/186.56 ! [V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.95/186.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Compl__iff,axiom, % 185.95/186.56 ! [V_A_2,V_ca_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.95/186.56 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_ORep,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_OAbs__inverse,axiom, % 185.95/186.56 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 185.95/186.56 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_type__definition_OAbs__inject,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.95/186.56 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 185.95/186.56 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 185.95/186.56 <=> V_x_2 = V_y_2 ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__iff,axiom, % 185.95/186.56 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_imageI,axiom, % 185.95/186.56 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_rev__image__eqI,axiom, % 185.95/186.56 ! [T_c,V_f_2,V_ba_2,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 185.95/186.56 ! [V_A_2,V_x_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insertI1,axiom, % 185.95/186.56 ! [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))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__iff,axiom, % 185.95/186.56 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 185.95/186.56 <=> ( V_a_2 = V_ba_2 % 185.95/186.56 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__ident,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => ( 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) % 185.95/186.56 <=> V_A_2 = V_B_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insertI2,axiom, % 185.95/186.56 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__absorb,axiom, % 185.95/186.56 ! [V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup__Un__eq,axiom, % 185.95/186.56 ! [V_x_2,V_S_2,V_R_2,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__iff,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_singletonE,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.95/186.56 => V_ba_2 = V_a_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_singleton__iff,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.95/186.56 <=> V_ba_2 = V_a_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__subset,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__insert,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( 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))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__image,axiom, % 185.95/186.56 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_range__eqI,axiom, % 185.95/186.56 ! [T_c,T_b,V_x_2,V_f_2,V_ba_2] : % 185.95/186.56 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_rangeI,axiom, % 185.95/186.56 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__Diff1,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__Diff__if,axiom, % 185.95/186.56 ! [V_A_2,V_B_2,V_x_2,T_b] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => 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) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_lessThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2,T_b] : % 185.95/186.56 ( class_Orderings_Oord(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 185.95/186.56 ! [V_A_2,V_x_2] : % 185.95/186.56 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.95/186.56 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.95/186.56 <=> 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))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atMost__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2,T_b] : % 185.95/186.56 ( class_Orderings_Oord(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_atLeast__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2,T_b] : % 185.95/186.56 ( class_Orderings_Oord(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_greaterThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2,T_b] : % 185.95/186.56 ( class_Orderings_Oord(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_code__numeral_Oof__nat__inject,axiom, % 185.95/186.56 ! [V_y_2,V_x_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.95/186.56 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 185.95/186.56 <=> V_x_2 = V_y_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_le__SUPI,axiom, % 185.95/186.56 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 185.95/186.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_nat__of,axiom, % 185.95/186.56 ! [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)))) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 185.95/186.56 ! [V_x_2,V_A_2] : % 185.95/186.56 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.95/186.56 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP__UN__eq2,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__insert__distrib,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__upper,axiom, % 185.95/186.56 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP__UN__eq,axiom, % 185.95/186.56 ! [V_x_2,V_r_2,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_UN__absorb,axiom, % 185.95/186.56 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 185.95/186.56 => 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) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_elem__set,axiom, % 185.95/186.56 ! [V_xo_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2))) % 185.95/186.56 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_pred__subset__eq2,axiom, % 185.95/186.56 ! [V_S_2,V_R_2,T_c,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_insert__Diff,axiom, % 185.95/186.56 ! [V_A_2,V_a_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Diff__insert__absorb,axiom, % 185.95/186.56 ! [V_A_2,V_x_2,T_b] : % 185.95/186.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 185.95/186.56 ! [V_x_2,V_A_2] : % 185.95/186.56 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__delta_H,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.56 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.56 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__delta,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.56 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.56 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_image__constant,axiom, % 185.95/186.56 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_of__nat__inverse,axiom, % 185.95/186.56 ! [V_y_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.95/186.56 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Oinsert,axiom, % 185.95/186.56 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__insert,axiom, % 185.95/186.56 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_diff__single__insert,axiom, % 185.95/186.56 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_subset__insert__iff,axiom, % 185.95/186.56 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__insert__if,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__insert__disjoint,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card_Oinsert,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_psubset__insert__iff,axiom, % 185.95/186.56 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff1__nat,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,V_a_2,T_b] : % 185.95/186.56 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum_Oremove,axiom, % 185.95/186.56 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)))))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff1_H,axiom, % 185.95/186.56 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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)))))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff1,axiom, % 185.95/186.56 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Oab__group__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__diff1__ring,axiom, % 185.95/186.56 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( class_Rings_Oring(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Suc__Diff1,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff2__less,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.56 => 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))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff1__less,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff__insert,axiom, % 185.95/186.56 ! [V_B_2,V_a_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.95/186.56 => 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)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card_Oremove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)))))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Diff__singleton__if,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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)) ) % 185.95/186.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => 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) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_in__rel__def,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 185.95/186.56 <=> 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_finite__pointwise,axiom, % 185.95/186.56 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2)) % 185.95/186.56 => ( ! [B_p] : % 185.95/186.56 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) % 185.95/186.56 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 185.95/186.56 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_Pa_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,T_b] : % 185.95/186.56 ( ! [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bset_I8_J,axiom, % 185.95/186.56 ! [V_B_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( 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)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 185.95/186.56 => 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))) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup2CI,axiom, % 185.95/186.56 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 185.95/186.56 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup2E,axiom, % 185.95/186.56 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.56 ( 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)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bot2E,axiom, % 185.95/186.56 ! [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)) ). % 185.95/186.56 % 185.95/186.56 fof(fact_less__by__empty,axiom, % 185.95/186.56 ! [V_B_2,T_b,V_A_2] : % 185.95/186.56 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_SUP2__iff,axiom, % 185.95/186.56 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.56 ( 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_ba_2),V_ca_2)) % 185.95/186.56 <=> ? [B_x] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup2I2,axiom, % 185.95/186.56 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_sup2I1,axiom, % 185.95/186.56 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nitpick_Orefl_H__def,axiom, % 185.95/186.56 ! [V_r_2,T_b] : % 185.95/186.56 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 185.95/186.56 <=> ! [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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_aset_I6_J,axiom, % 185.95/186.56 ! [V_A_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( 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)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 185.95/186.56 => 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)) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OgreaterThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OgreaterThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_less_2,V_i_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OlessThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_aset_I4_J,axiom, % 185.95/186.56 ! [V_A_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( B_x != V_t_2 % 185.95/186.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bset_I4_J,axiom, % 185.95/186.56 ! [V_B_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( B_x != V_t_2 % 185.95/186.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OlessThan__iff,axiom, % 185.95/186.56 ! [V_k_2,V_less_2,V_i_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bset_I3_J,axiom, % 185.95/186.56 ! [V_B_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( 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)) % 185.95/186.56 => ( ! [B_x] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xa] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 185.95/186.56 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 185.95/186.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_aset_I3_J,axiom, % 185.95/186.56 ! [V_A_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( 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)) % 185.95/186.56 => ( ! [B_x] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xa] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 185.95/186.56 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 185.95/186.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_aset_I5_J,axiom, % 185.95/186.56 ! [V_A_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 185.95/186.56 => 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)) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_bset_I7_J,axiom, % 185.95/186.56 ! [V_B_2,V_t_2,V_D_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 185.95/186.56 => ! [B_x] : % 185.95/186.56 ( ! [B_xa] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ! [B_xb] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.95/186.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 185.95/186.56 => 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))) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_in__measure,axiom, % 185.95/186.56 ! [V_f_2,V_y_2,V_x_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatMost__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OatMost__iff,axiom, % 185.95/186.56 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeast__iff,axiom, % 185.95/186.56 ! [V_k_2,V_i_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__image__simple_Oremove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.95/186.56 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__one_Oremove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 185.95/186.56 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__image__simple_Oempty,axiom, % 185.95/186.56 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.56 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__one_Osingleton,axiom, % 185.95/186.56 ! [V_x_2,V_F_2,V_f_2,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__image__simple_Oinsert,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__one_Oinsert,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_folding__one_Oinsert__remove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.95/186.56 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OatLeast__iff,axiom, % 185.95/186.56 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 185.95/186.56 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( 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) % 185.95/186.56 => 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)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__mono2,axiom, % 185.95/186.56 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.95/186.56 ( class_Groups_Oordered__comm__monoid__add(T_c) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.56 => ( ! [B_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 185.95/186.56 => 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))) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_flat__lub__def,axiom, % 185.95/186.56 ! [V_ba_2,V_A_2,T_b] : % 185.95/186.56 ( ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.95/186.56 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = V_ba_2 ) % 185.95/186.56 & ( ~ 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.95/186.56 => c_Partial__Function_Oflat__lub(T_b,V_ba_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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 185.95/186.56 ! [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) ). % 185.95/186.56 % 185.95/186.56 fof(fact_mlex__leq,axiom, % 185.95/186.56 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 => ( 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)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_mlex__less,axiom, % 185.95/186.56 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 185.95/186.56 ( 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))) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_setsum__bounded,axiom, % 185.95/186.56 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.56 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 185.95/186.56 & class_Rings_Osemiring__1(T_c) ) % 185.95/186.56 => ( ! [B_i] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_card__Suc__eq,axiom, % 185.95/186.56 ! [V_k_2,V_A_2,T_b] : % 185.95/186.56 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 185.95/186.56 <=> ? [B_b,B_B] : % 185.95/186.56 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 185.95/186.56 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 185.95/186.56 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.56 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_ord_OatLeastLessThan__iff,axiom, % 185.95/186.56 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 185.95/186.56 ( 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))) % 185.95/186.56 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 185.95/186.56 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 185.95/186.56 ! [V_k_2,V_l_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 185.95/186.56 => 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)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 185.95/186.56 ! [V_a_2,V_ba_2] : % 185.95/186.56 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 185.95/186.56 => 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_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 185.95/186.56 ! [V_l_2,V_k_2] : % 185.95/186.56 ( 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)) % 185.95/186.56 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2] : % 185.95/186.56 ( 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_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 185.95/186.56 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 185.95/186.56 ! [V_l_2,V_k_2] : % 185.95/186.56 ( 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) % 185.95/186.56 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2] : % 185.95/186.56 ( 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_ba_2) % 185.95/186.56 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.56 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nats__number__of,axiom, % 185.95/186.56 ! [V_w_2,T_b] : % 185.95/186.56 ( class_Int_Onumber__ring(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__odd__less__0,axiom, % 185.95/186.56 ! [V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Olinordered__idom(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => ( 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))) % 185.95/186.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Oremove,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 185.95/186.56 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Osingleton,axiom, % 185.95/186.56 ! [V_x_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__0,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__add,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__mult,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__diff,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__number__of,axiom, % 185.95/186.56 ! [V_w_2,T_b] : % 185.95/186.56 ( class_Int_Onumber__ring(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__1,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__minus,axiom, % 185.95/186.56 ! [V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__of__nat,axiom, % 185.95/186.56 ! [V_n_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__power,axiom, % 185.95/186.56 ! [V_n_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => 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))) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__of__int,axiom, % 185.95/186.56 ! [V_z_2,T_b] : % 185.95/186.56 ( class_Rings_Oring__1(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Oin__idem,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nats__0,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( class_Rings_Osemiring__1(T_b) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nats__add,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Osemiring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nats__mult,axiom, % 185.95/186.56 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.56 ( class_Rings_Osemiring__1(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Nats__1,axiom, % 185.95/186.56 ! [T_b] : % 185.95/186.56 ( class_Rings_Osemiring__1(T_b) % 185.95/186.56 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_of__nat__in__Nats,axiom, % 185.95/186.56 ! [V_n_2,T_b] : % 185.95/186.56 ( class_Rings_Osemiring__1(T_b) % 185.95/186.56 => 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))) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__double__eq__0__iff,axiom, % 185.95/186.56 ! [V_a_2,T_b] : % 185.95/186.56 ( class_Int_Oring__char__0(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.95/186.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Oinsert__idem,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Osubset__idem,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.56 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Ounion__idem,axiom, % 185.95/186.56 ! [V_B_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.56 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Ints__odd__nonzero,axiom, % 185.95/186.56 ! [V_a_2,T_b] : % 185.95/186.56 ( class_Int_Oring__char__0(T_b) % 185.95/186.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.95/186.56 => 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) ) ) ). % 185.95/186.56 % 185.95/186.56 fof(fact_Sup__fin_Oinsert,axiom, % 185.95/186.56 ! [V_x_2,V_A_2,T_b] : % 185.95/186.56 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Sup__fin_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => 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 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_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)))))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Sup__fin_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Oremove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Oremove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_minus__Max__eq__Min,axiom, % 185.95/186.57 ! [V_S_2,T_b] : % 185.95/186.57 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_minus__Min__eq__Max,axiom, % 185.95/186.57 ! [V_S_2,T_b] : % 185.95/186.57 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Osingleton,axiom, % 185.95/186.57 ! [V_x_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Osingleton,axiom, % 185.95/186.57 ! [V_x_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max__ge,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min__le,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max__in,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min__in,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Oin__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Oin__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min__antimono,axiom, % 185.95/186.57 ! [V_N_2,V_M_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 185.95/186.57 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => 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))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max__mono,axiom, % 185.95/186.57 ! [V_N_2,V_M_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 185.95/186.57 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => 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))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min__insert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max__insert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Osubset__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Osubset__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min__Un,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max__Un,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Oinsert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Oinsert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_iso__tuple__UNIV__I,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 185.95/186.57 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 185.95/186.57 | ? [B_x,B_y] : % 185.95/186.57 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 185.95/186.57 & 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_in__lex__prod,axiom, % 185.95/186.57 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.57 ( 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_ba_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))) % 185.95/186.57 <=> ( 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)) % 185.95/186.57 | ( V_a_2 = V_a_H_2 % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card__Plus__conv__if,axiom, % 185.95/186.57 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.57 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 185.95/186.57 => 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)) ) % 185.95/186.57 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_InrI,axiom, % 185.95/186.57 ! [V_A_2,T_c,V_B_2,V_ba_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_ba_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_InlI,axiom, % 185.95/186.57 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Plus__eq__empty__conv,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Plus__def,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__Plus__iff,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__Plus,axiom, % 185.95/186.57 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__PlusD_I1_J,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__PlusD_I2_J,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UNIV__Plus__UNIV,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card__Plus,axiom, % 185.95/186.57 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_same__fstI,axiom, % 185.95/186.57 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 185.95/186.57 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.95/186.57 => ( 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))) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_in__finite__psubset,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oremove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 185.95/186.57 ! [V_x_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 185.95/186.57 ! [V_a_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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 ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => 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 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__le__Sup,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oremove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 185.95/186.57 ! [V_x_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_Osup__Inf__absorb,axiom, % 185.95/186.57 ! [V_a_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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 ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ( hAPP(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)) % 185.95/186.57 => 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 ) % 185.95/186.57 & ( hAPP(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)) % 185.95/186.57 => 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)))))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one_Oclosed,axiom, % 185.95/186.57 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [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)))))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__image,axiom, % 185.95/186.57 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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)))))) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__triv,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__idem,axiom, % 185.95/186.57 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 185.95/186.57 ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.95/186.57 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__other,axiom, % 185.95/186.57 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 185.95/186.57 ( V_z_2 != V_x_2 % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__twist,axiom, % 185.95/186.57 ! [V_d_2,V_ba_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] : % 185.95/186.57 ( V_a_2 != V_ca_2 % 185.95/186.57 => 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_ba_2)),V_ca_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_ca_2),V_d_2)),V_a_2),V_ba_2) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__apply,axiom, % 185.95/186.57 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 185.95/186.57 ( ( V_z_2 = V_x_2 % 185.95/186.57 => 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 ) % 185.95/186.57 & ( V_z_2 != V_x_2 % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__same,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__upd,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__idem__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2 % 185.95/186.57 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__def,axiom, % 185.95/186.57 ! [V_ba_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 185.95/186.57 ( ( V_x_2 = V_a_2 % 185.95/186.57 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_ba_2),V_x_2) = V_ba_2 ) % 185.95/186.57 & ( V_x_2 != V_a_2 % 185.95/186.57 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__range__updI,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( 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))))) % 185.95/186.57 => 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_ba_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_image__map__upd,axiom, % 185.95/186.57 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_map__upd__nonempty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_map__upd__Some__unfold,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_ba_2,V_a_2,V_m_2,T_b,T_c] : % 185.95/186.57 ( 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_ba_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 185.95/186.57 <=> ( ( V_x_2 = V_a_2 % 185.95/186.57 & V_ba_2 = V_y_2 ) % 185.95/186.57 | ( V_x_2 != V_a_2 % 185.95/186.57 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_map__upd__triv,axiom, % 185.95/186.57 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] : % 185.95/186.57 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_map__upd__eqD1,axiom, % 185.95/186.57 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => V_x_2 = V_y_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_empty__upd__none,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ran__map__upd,axiom, % 185.95/186.57 ! [V_ba_2,T_c,T_b,V_a_2,V_m_2] : % 185.95/186.57 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.57 => 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_ba_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__None__restrict,axiom, % 185.95/186.57 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 185.95/186.57 => 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))))) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__gen__delta,axiom, % 185.95/186.57 ! [V_ca_2,V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_ba_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__in,axiom, % 185.95/186.57 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__1,axiom, % 185.95/186.57 ! [V_A_2,T_c,T_b] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_of__int__setprod,axiom, % 185.95/186.57 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 & class_Rings_Oring__1(T_b) ) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_of__nat__setprod,axiom, % 185.95/186.57 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 & class_Rings_Osemiring__1(T_b) ) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_int__setprod,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__timesf,axiom, % 185.95/186.57 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_abs__setprod,axiom, % 185.95/186.57 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( class_Fields_Olinordered__field(T_b) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 185.95/186.57 ! [V_A_2,V_f_2,T_b] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.57 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__zero,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Rings_Ocomm__semiring__1(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ? [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__zero__iff,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( ( class_Rings_Ocomm__semiring__1(T_c) % 185.95/186.57 & class_Rings_Ono__zero__divisors(T_c) ) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( 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) % 185.95/186.57 <=> ? [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__empty,axiom, % 185.95/186.57 ! [V_f_2,T_c,T_b] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Oempty,axiom, % 185.95/186.57 ! [V_g_2,T_c,T_b] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__infinite,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Oinfinite,axiom, % 185.95/186.57 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__eq__1__iff,axiom, % 185.95/186.57 ! [V_f_2,V_F_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.57 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.95/186.57 <=> ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 185.95/186.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__map__empty,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,T_b] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.57 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.57 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Odistrib,axiom, % 185.95/186.57 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__dividef,axiom, % 185.95/186.57 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Fields_Ofield__inverse__zero(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__out,axiom, % 185.95/186.57 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_dvd__setprod,axiom, % 185.95/186.57 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Rings_Ocomm__semiring__1(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__pos__nat__iff,axiom, % 185.95/186.57 ! [V_f_2,V_S_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( 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))) % 185.95/186.57 <=> ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__dvd__setprod__subset,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 & class_Rings_Odvd(T_c) ) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__map__insert,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__delta,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__delta_H,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.95/186.57 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__map__def,axiom, % 185.95/186.57 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__map__to__empty,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__constant,axiom, % 185.95/186.57 ! [V_y_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Oinsert,axiom, % 185.95/186.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__insert,axiom, % 185.95/186.57 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ranI,axiom, % 185.95/186.57 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] : % 185.95/186.57 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__restrict,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ran__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Oremove,axiom, % 185.95/186.57 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__diff1,axiom, % 185.95/186.57 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Fields_Ofield(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 185.95/186.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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)) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__restrict__conv,axiom, % 185.95/186.57 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__fun__upd,axiom, % 185.95/186.57 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 185.95/186.57 => 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) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__complement__singleton__eq,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__upd__same,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__nonneg__leq__bound,axiom, % 185.95/186.57 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Oordered__ab__group__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.95/186.57 => ( ! [B_i] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 185.95/186.57 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__nonneg__0,axiom, % 185.95/186.57 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Oordered__ab__group__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.95/186.57 => ( ! [B_i] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 185.95/186.57 => ( 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) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 185.95/186.57 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_pair__lessI2,axiom, % 185.95/186.57 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 185.95/186.57 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_pair__lessI1,axiom, % 185.95/186.57 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.57 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_pair__leqI2,axiom, % 185.95/186.57 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 185.95/186.57 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_smax__insertI,axiom, % 185.95/186.57 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_smin__insertI,axiom, % 185.95/186.57 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_smin__emptyI,axiom, % 185.95/186.57 ! [V_X_2] : % 185.95/186.57 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_smax__emptyI,axiom, % 185.95/186.57 ! [V_Y_2] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 185.95/186.57 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_pair__leqI1,axiom, % 185.95/186.57 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.95/186.57 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_wmin__insertI,axiom, % 185.95/186.57 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_wmax__insertI,axiom, % 185.95/186.57 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 185.95/186.57 ! [V_f_2,V_A_2,T_b] : % 185.95/186.57 ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_wmax__emptyI,axiom, % 185.95/186.57 ! [V_X_2] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_wmin__emptyI,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__weak__def,axiom, % 185.95/186.57 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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_max__weak__def,axiom, % 185.95/186.57 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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__rpair__set,axiom, % 185.95/186.57 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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_max__strict__def,axiom, % 185.95/186.57 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.95/186.57 % 185.95/186.57 fof(fact_max__ext__additive,axiom, % 185.95/186.57 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 => ( 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))) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__strict__def,axiom, % 185.95/186.57 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.95/186.57 % 185.95/186.57 fof(fact_max__rpair__set,axiom, % 185.95/186.57 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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_max__extp__max__ext__eq,axiom, % 185.95/186.57 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 185.95/186.57 ( 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) % 185.95/186.57 <=> 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_less__than__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_intrel__iff,axiom, % 185.95/186.57 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_pair__less__def,axiom, % 185.95/186.57 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 185.95/186.57 % 185.95/186.57 fof(fact_mlex__prod__def,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_rp__inv__image__rp,axiom, % 185.95/186.57 ! [V_f_2,T_c,V_Pa_2,T_b] : % 185.95/186.57 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.95/186.57 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 185.95/186.57 ! [V_N_2,V_h_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( ! [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)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_rp__inv__image__def,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_in__inv__image,axiom, % 185.95/186.57 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 <=> 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 185.95/186.57 ! [V_N_2,V_h_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( ! [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)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Max_Ohom__commute,axiom, % 185.95/186.57 ! [V_N_2,V_h_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( ! [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)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_measure__def,axiom, % 185.95/186.57 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 185.95/186.57 % 185.95/186.57 fof(fact_irrefl__def,axiom, % 185.95/186.57 ! [V_r_2,T_b] : % 185.95/186.57 ( c_Relation_Oirrefl(T_b,V_r_2) % 185.95/186.57 <=> ! [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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Field__insert,axiom, % 185.95/186.57 ! [V_r_2,V_ba_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_ba_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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__on__def,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__on__def_H,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__on__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Field__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_mono__Field,axiom, % 185.95/186.57 ! [V_s_2,V_r_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Field__Un,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__Field,axiom, % 185.95/186.57 ! [V_r_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.95/186.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__on__eqI,axiom, % 185.95/186.57 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 185.95/186.57 ( V_a_2 = V_ba_2 % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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_ba_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__on__iff,axiom, % 185.95/186.57 ! [V_A_2,V_y_2,V_x_2,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 <=> ( V_x_2 = V_y_2 % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Id__onE,axiom, % 185.95/186.57 ! [V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) % 185.95/186.57 => ~ ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Min_Ohom__commute,axiom, % 185.95/186.57 ! [V_N_2,V_h_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => ( ! [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)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Sup__fin_Ohom__commute,axiom, % 185.95/186.57 ! [V_N_2,V_h_2,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => ( ! [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)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__mono__one__left,axiom, % 185.95/186.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.95/186.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__mono__one__right,axiom, % 185.95/186.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.95/186.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.57 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__mono__zero__right,axiom, % 185.95/186.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.95/186.57 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__mono__zero__left,axiom, % 185.95/186.57 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.95/186.57 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.57 => 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) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_escape,axiom, % 185.95/186.57 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] : % 185.95/186.57 ( ! [B_Z,B_s] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.95/186.57 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 185.95/186.57 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card__Pow,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_PowI,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__insert,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__empty,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__bottom,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__not__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__top,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_PowD,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__iff,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 185.95/186.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Cantors__paradox,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ~ ? [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_image__Pow__surj,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 185.95/186.57 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__UNIV,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__Pow__iff,axiom, % 185.95/186.57 ! [V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 185.95/186.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__mono,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.57 => 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Pow__subset,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__Pow__subset,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Powp__Pow__eq,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_image__Pow__mono,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__empty__induct,axiom, % 185.95/186.57 ! [V_Pa_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 185.95/186.57 => ( ! [B_a,B_A] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 185.95/186.57 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 185.95/186.57 => 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)))))) ) ) ) % 185.95/186.57 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one__idem_Ounion__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__subset__induct,axiom, % 185.95/186.57 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.57 => ( ! [B_a,B_F] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 185.95/186.57 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 185.95/186.57 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 185.95/186.57 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one__idem_Oidem,axiom, % 185.95/186.57 ! [V_x_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.57 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one__idem_Oin__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__one__idem_Osubset__idem,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__strict__mono,axiom, % 185.95/186.57 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.57 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__intrel__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2] : % 185.95/186.57 ( 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)))) % 185.95/186.57 <=> 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__Plus,axiom, % 185.95/186.57 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__Un,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__UN,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_image__compose,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_K__record__comp,axiom, % 185.95/186.57 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__eq__dest__lhs,axiom, % 185.95/186.57 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.95/186.57 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = V_ca_2 % 185.95/186.57 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_apfst__compose,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_apsnd__compose,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_comp__cong,axiom, % 185.95/186.57 ! [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] : % 185.95/186.57 ( 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)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__def,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__assoc,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__apply,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__eq__dest,axiom, % 185.95/186.57 ! [V_v_2,V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.95/186.57 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 185.95/186.57 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_o__eq__elim,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.95/186.57 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 185.95/186.57 => ! [B_v] : hAPP(V_a_2,hAPP(V_ba_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_fun__upd__comp,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_comp__surj,axiom, % 185.95/186.57 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 185.95/186.57 ( 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)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__mono,axiom, % 185.95/186.57 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Image,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__iff,axiom, % 185.95/186.57 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 185.95/186.57 <=> ? [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_rev__ImageI,axiom, % 185.95/186.57 ! [V_r_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => ( 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_ba_2)),V_r_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__eq__UN,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__singleton__iff,axiom, % 185.95/186.57 ! [V_a_2,V_r_2,T_c,V_ba_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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)))))) % 185.95/186.57 <=> 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_ba_2)),V_r_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_of__int,axiom, % 185.95/186.57 ! [V_j_2,V_i_2,T_b] : % 185.95/186.57 ( class_Rings_Oring__1(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_One__int__def,axiom, % 185.95/186.57 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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_mult,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__o,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Rep__Integ__inverse,axiom, % 185.95/186.57 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 185.95/186.57 % 185.95/186.57 fof(fact_split__comp,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_number__of__code__numeral__def,axiom, % 185.95/186.57 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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_int__of__def,axiom, % 185.95/186.57 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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_minus,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Zero__int__def,axiom, % 185.95/186.57 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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_int__def,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_add,axiom, % 185.95/186.57 ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_nat,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_minus__int__def,axiom, % 185.95/186.57 ! [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))))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_less,axiom, % 185.95/186.57 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.95/186.57 ( 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))))))) % 185.95/186.57 <=> 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le,axiom, % 185.95/186.57 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.95/186.57 ( 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))))))) % 185.95/186.57 <=> 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_hoare__derivs_OIf,axiom, % 185.95/186.57 ! [V_d_2,V_Q_2,V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.57 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.57 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_ba_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.57 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_ba_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Loop,axiom, % 185.95/186.57 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.57 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.57 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_ba_2,V_ca_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_ba_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Nitpick_Odenom__def,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_peek__and__def,axiom, % 185.95/186.57 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 185.95/186.57 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 185.95/186.57 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Nitpick_Onum__def,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Oremove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_eq__Abs__Integ,axiom, % 185.95/186.57 ! [V_z_2] : % 185.95/186.57 ~ ! [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))))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Oinsert__remove,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 185.95/186.57 ! [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] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__comp,axiom, % 185.95/186.57 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__left__comp,axiom, % 185.95/186.57 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 185.95/186.57 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__comp_H_H,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__left__comp_H,axiom, % 185.95/186.57 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ocommute__comp_H,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Oinsert,axiom, % 185.95/186.57 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__reindex__nonzero,axiom, % 185.95/186.57 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.57 => ( ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.57 => ! [B_y] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 185.95/186.57 => ( B_x != B_y % 185.95/186.57 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 185.95/186.57 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Random__Sequence_Omap__def,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__def,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__is__empty,axiom, % 185.95/186.57 ! [V_r_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__is__empty2,axiom, % 185.95/186.57 ! [V_r_2,V_A_2,T_b] : % 185.95/186.57 ( 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) % 185.95/186.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__empty,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotientI,axiom, % 185.95/186.57 ! [V_r_2,V_A_2,V_x_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_singleton__quotient,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_subset__equiv__class,axiom, % 185.95/186.57 ! [V_a_2,V_ba_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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_ba_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)))))) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.95/186.57 => 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_ba_2)),V_r_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotientE,axiom, % 185.95/186.57 ! [V_r_2,V_A_2,V_X_2,T_b] : % 185.95/186.57 ( 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))) % 185.95/186.57 => ~ ! [B_x] : % 185.95/186.57 ( 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)))) % 185.95/186.57 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_eq__equiv__class__iff2,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.57 => ( 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) % 185.95/186.57 <=> 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__intrel,axiom, % 185.95/186.57 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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__class__self,axiom, % 185.95/186.57 ! [V_a_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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)))))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__class__eq,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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_ba_2)),V_r_2)) % 185.95/186.57 => 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__eq__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 185.95/186.57 => ( V_X_2 = V_Y_2 % 185.95/186.57 <=> 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)) ) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__eqI,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 185.95/186.57 => ( 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)) % 185.95/186.57 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_eq__equiv__class__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.57 => ( 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)))) % 185.95/186.57 <=> 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_eq__equiv__class,axiom, % 185.95/186.57 ! [V_A_2,V_ba_2,V_a_2,V_r_2,T_b] : % 185.95/186.57 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.57 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.95/186.57 => 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_ba_2)),V_r_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__class__eq__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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)) % 185.95/186.57 <=> ( 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)))) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__class__subset,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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_ba_2)),V_r_2)) % 185.95/186.57 => 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__equiv__class2,axiom, % 185.95/186.57 ! [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] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.95/186.57 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.95/186.57 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 185.95/186.57 => 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) ) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__equiv__class,axiom, % 185.95/186.57 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_equiv__class__nondisjoint,axiom, % 185.95/186.57 ! [V_ba_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) % 185.95/186.57 => 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_ba_2)),V_r_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf1I,axiom, % 185.95/186.57 ! [T_b,V_B_2,V_x_2,V_A_2] : % 185.95/186.57 ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.95/186.57 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf1E,axiom, % 185.95/186.57 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.95/186.57 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_IntE,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.57 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.57 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_IntI,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_finite__Int,axiom, % 185.95/186.57 ! [V_Ga_2,V_F_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.57 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 185.95/186.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__eq__top__iff,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,T_b] : % 185.95/186.57 ( class_Lattices_Obounded__lattice__top(T_b) % 185.95/186.57 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 185.95/186.57 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 185.95/186.57 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__top__right,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Obounded__lattice__top(T_a) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__top__left,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Obounded__lattice__top(T_a) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__UNIV__right,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__UNIV__left,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_IntD2,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_IntD1,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__iff,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.57 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__Int__eq,axiom, % 185.95/186.57 ! [V_x_2,V_S_2,V_R_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_sup__inf__distrib2,axiom, % 185.95/186.57 ! [V_x,V_z,V_y,T_a] : % 185.95/186.57 ( class_Lattices_Odistrib__lattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__distrib2,axiom, % 185.95/186.57 ! [V_x,V_z,V_y,T_a] : % 185.95/186.57 ( class_Lattices_Odistrib__lattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_sup__inf__distrib1,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Odistrib__lattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__distrib1,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Odistrib__lattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_sup__inf__absorb,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__absorb,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Int__crazy,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Int__distrib2,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__Un__distrib2,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Int__distrib,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__Un__distrib,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__empty__left,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__empty__right,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_disjoint__iff__not__equal,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 <=> ! [B_x] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.57 => ! [B_xa] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 185.95/186.57 => B_x != B_xa ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__bot__left,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__bot__right,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_insert__inter__insert,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_restrict__restrict,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 185.95/186.57 ! [V_B_2,V_A_2] : % 185.95/186.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf1D1,axiom, % 185.95/186.57 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf1D2,axiom, % 185.95/186.57 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__absorb,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__commute,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__left__absorb,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__left__commute,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__assoc,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf_Oidem,axiom, % 185.95/186.57 ! [V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__idem,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf_Ocommute,axiom, % 185.95/186.57 ! [V_b,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__aci_I1_J,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__commute,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf_Oleft__idem,axiom, % 185.95/186.57 ! [V_b,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__aci_I4_J,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__left__idem,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf_Oleft__commute,axiom, % 185.95/186.57 ! [V_c,V_a,V_b,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__aci_I3_J,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__left__commute,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf_Oassoc,axiom, % 185.95/186.57 ! [V_c,V_b,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__aci_I2_J,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__assoc,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__apply,axiom, % 185.95/186.57 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__fun__def,axiom, % 185.95/186.57 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__min,axiom, % 185.95/186.57 ! [T_b] : % 185.95/186.57 ( ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.57 & class_Orderings_Olinorder(T_b) ) % 185.95/186.57 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Inf__fin_Oidem,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_less__infI2,axiom, % 185.95/186.57 ! [V_a,V_x,V_b,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_less__infI1,axiom, % 185.95/186.57 ! [V_b,V_x,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Int2,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Int__distrib2,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__Diff,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Int__distrib,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__infE,axiom, % 185.95/186.57 ! [V_b,V_a,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.95/186.57 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__mono,axiom, % 185.95/186.57 ! [V_d,V_b,V_c,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__greatest,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__infI,axiom, % 185.95/186.57 ! [V_b,V_a,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.95/186.57 => 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))) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__absorb2,axiom, % 185.95/186.57 ! [V_x,V_y,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__absorb1,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__infI2,axiom, % 185.95/186.57 ! [V_a,V_x,V_b,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__infI1,axiom, % 185.95/186.57 ! [V_b,V_x,V_a,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.95/186.57 => 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)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__inf__iff,axiom, % 185.95/186.57 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.57 => ( 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))) % 185.95/186.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.95/186.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_le__iff__inf,axiom, % 185.95/186.57 ! [V_y_2,V_x_2,T_b] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.95/186.57 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__le2,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__ord_I2_J,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__le1,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Osemilattice__inf(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__sup__ord_I1_J,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__lower1,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__lower2,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__absorb2,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__absorb1,axiom, % 185.95/186.57 ! [V_A_2,V_B_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__greatest,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_C_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__mono,axiom, % 185.95/186.57 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Pow__Int__eq,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__UN__distrib2,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__extend__simps_I4_J,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__UN__distrib,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__extend__simps_I5_J,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__simps_I4_J,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_UN__simps_I5_J,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_distrib__sup__le,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_distrib__inf__le,axiom, % 185.95/186.57 ! [V_z,V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Olattice(T_a) % 185.95/186.57 => 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)))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__compl__bot,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_compl__inf__bot,axiom, % 185.95/186.57 ! [V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_diff__eq,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_compl__inf,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_compl__sup,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__left__if1,axiom, % 185.95/186.57 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__right__if1,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__left__if0,axiom, % 185.95/186.57 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.95/186.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__right__if0,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.95/186.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__left,axiom, % 185.95/186.57 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.95/186.57 => 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)) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__insert__right,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.95/186.57 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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)) ) % 185.95/186.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_image__Int__subset,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__disjoint,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__triv,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Int__assoc__eq,axiom, % 185.95/186.57 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.95/186.57 ( 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)) % 185.95/186.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Int,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Un,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Un__Diff__Int,axiom, % 185.95/186.57 ! [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 ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I11_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 185.95/186.57 ! [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))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Compl__disjoint,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Compl__disjoint2,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__Int__subset,axiom, % 185.95/186.57 ! [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)))) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Compl__Int,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Compl__Un,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__eq,axiom, % 185.95/186.57 ! [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)) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Diff__Compl,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I14_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Image__Id__on,axiom, % 185.95/186.57 ! [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) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 185.95/186.57 ! [V_B_2,V_A_2] : % 185.95/186.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.95/186.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.57 => 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))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_congruent2__implies__congruent,axiom, % 185.95/186.57 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 185.95/186.57 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_inf__Sup__absorb,axiom, % 185.95/186.57 ! [V_a_2,V_A_2,T_b] : % 185.95/186.57 ( class_Lattices_Olattice(T_b) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.57 => 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 ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_disjoint__eq__subset__Compl,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.57 <=> 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))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I15_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastAtMost,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastLessThan,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I4_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I2_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I16_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I12_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I13_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__greaterThanAtMost,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I9_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__greaterThanLessThan,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastAtMostL1,axiom, % 185.95/186.57 ! [V_d_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_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_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastAtMostR1,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_ba_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I8_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I7_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastAtMostL2,axiom, % 185.95/186.57 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_ba_2) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_Int__atLeastAtMostR2,axiom, % 185.95/186.57 ! [V_d_2,V_ca_2,V_a_2,T_b] : % 185.95/186.57 ( class_Orderings_Olinorder(T_b) % 185.95/186.57 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I3_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I10_J,axiom, % 185.95/186.57 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I1_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I6_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_ivl__disj__int_I5_J,axiom, % 185.95/186.57 ! [V_u_2,V_l_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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)) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding__image__simple_Ounion__inter,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_compl__unique,axiom, % 185.95/186.57 ! [V_y,V_x,T_a] : % 185.95/186.57 ( class_Lattices_Oboolean__algebra(T_a) % 185.95/186.57 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 185.95/186.57 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 185.95/186.57 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__Un__Int,axiom, % 185.95/186.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod_Ounion__inter,axiom, % 185.95/186.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setprod__Un__Int,axiom, % 185.95/186.57 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card__Un__Int,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card_Ounion__inter,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_card__Diff__subset__Int,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,T_b] : % 185.95/186.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.57 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_setsum__restrict__set,axiom, % 185.95/186.57 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.57 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => 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) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_folding_Ounion__inter,axiom, % 185.95/186.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.57 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.57 => 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)) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_quotient__disj,axiom, % 185.95/186.57 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.95/186.57 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( 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))) % 185.95/186.57 => ( V_X_2 = V_Y_2 % 185.95/186.57 | 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)) ) ) ) ) ). % 185.95/186.57 % 185.95/186.57 fof(fact_atMost__Int__atLeast,axiom, % 185.95/186.57 ! [V_n_2,T_b] : % 185.95/186.57 ( class_Orderings_Oorder(T_b) % 185.95/186.57 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__one_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__one_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_congruent__def,axiom, % 185.95/186.58 ! [V_f_2,V_r_2,T_c,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__Un__disjoint,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__Un,axiom, % 185.95/186.58 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Oab__group__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_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))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__Un__disjoint,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__Un__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sup__fin_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Min_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Min_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Max_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Max_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_congruent2D,axiom, % 185.95/186.58 ! [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] : % 185.95/186.58 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__Un__nat,axiom, % 185.95/186.58 ! [V_f_2,V_B_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding_Ounion,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_congruentD,axiom, % 185.95/186.58 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_congruent2__implies__congruent__UN,axiom, % 185.95/186.58 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.95/186.58 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.95/186.58 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UN__equiv__class__inject,axiom, % 185.95/186.58 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.95/186.58 => ( 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) % 185.95/186.58 => ( 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))) % 185.95/186.58 => ( 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))) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => ! [B_y] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.95/186.58 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 185.95/186.58 => 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)) ) ) ) % 185.95/186.58 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UN__equiv__class__type2,axiom, % 185.95/186.58 ! [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] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.95/186.58 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.95/186.58 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.95/186.58 => ( 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))) % 185.95/186.58 => ( 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))) % 185.95/186.58 => ( ! [B_x1] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 185.95/186.58 => ! [B_x2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UN__equiv__class__type,axiom, % 185.95/186.58 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.95/186.58 => ( 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))) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf__nat__def,axiom, % 185.95/186.58 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf__Int__eq2,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 <=> 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card_Ounion__inter__neutral,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.58 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.95/186.58 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__Un,axiom, % 185.95/186.58 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Fields_Ofield(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.58 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.58 => 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))) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Integ__def,axiom, % 185.95/186.58 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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf2I,axiom, % 185.95/186.58 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf2E,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.95/186.58 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf2D1,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inf2D2,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Rep__Integ,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_type__definition__Integ,axiom, % 185.95/186.58 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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod_Ounion__inter__neutral,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.58 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__Un__one,axiom, % 185.95/186.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 185.95/186.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum_Ounion__inter__neutral,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.95/186.58 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__Un__zero,axiom, % 185.95/186.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 185.95/186.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__def_H,axiom, % 185.95/186.58 ! [V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 <=> ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 185.95/186.58 => 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)) ) % 185.95/186.58 & ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oremove,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( ( hAPP(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)) % 185.95/186.58 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 185.95/186.58 & ( hAPP(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)) % 185.95/186.58 => 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)))))) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__Id__on,axiom, % 185.95/186.58 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Osingleton,axiom, % 185.95/186.58 ! [V_x_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__empty,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__Un,axiom, % 185.95/186.58 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__Int,axiom, % 185.95/186.58 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_sup__Inf__absorb,axiom, % 185.95/186.58 ! [V_a_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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 ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oin__idem,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__onD,axiom, % 185.95/186.58 ! [V_a_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__onD1,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__onD2,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oinsert__idem,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Osubset__idem,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.58 => 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) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Ounion__idem,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__le__Sup,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oinsert,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oinsert__remove,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ( hAPP(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)) % 185.95/186.58 => 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 ) % 185.95/186.58 & ( hAPP(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)) % 185.95/186.58 => 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)))))) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Ounion__inter,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Oclosed,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( ! [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)))))) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equiv__imp__dvd__card,axiom, % 185.95/186.58 ! [V_k_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( 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))) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) ) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Ounion__idem,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Oidem__left__comp,axiom, % 185.95/186.58 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Oidem__comp,axiom, % 185.95/186.58 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Oin__comp__idem,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Oinsert__idem,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equivp__equiv,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 185.95/186.58 <=> 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__quotient__disjoint,axiom, % 185.95/186.58 ! [V_r_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__Un__disjoint,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__empty,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__uminus,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Groups_Oordered__ab__group__add(T_b) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__strict__subset,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__contraD,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( V_x_2 != V_y_2 % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.58 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__iff,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.95/186.58 <=> V_x_2 = V_y_2 ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__onD,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.95/186.58 => V_x_2 = V_y_2 ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__Un__image__eq__iff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ( 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) % 185.95/186.58 <=> V_A_2 = V_B_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__comp,axiom, % 185.95/186.58 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__imageI,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 185.95/186.58 ( 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) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_comp__inj__on,axiom, % 185.95/186.58 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_comp__inj__on__iff,axiom, % 185.95/186.58 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 <=> 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__image,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__reindex,axiom, % 185.95/186.58 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_d) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__empty,axiom, % 185.95/186.58 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__id2,axiom, % 185.95/186.58 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__def,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => ! [B_xa] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.95/186.58 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 185.95/186.58 => B_x = B_xa ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__diff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_subset__inj__on,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__imageD,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.95/186.58 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__imageI2,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 185.95/186.58 ( 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) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_identity__equivp,axiom, % 185.95/186.58 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equivp__def,axiom, % 185.95/186.58 ! [V_R_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.95/186.58 <=> ! [B_x,B_y] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 185.95/186.58 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equivp__reflp,axiom, % 185.95/186.58 ! [V_x_2,V_R_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equivp__symp,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_R_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equivp__transp,axiom, % 185.95/186.58 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__image__eq__iff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( 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) % 185.95/186.58 <=> V_A_2 = V_B_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_injD,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.95/186.58 => V_x_2 = V_y_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__eq,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.95/186.58 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__fun,axiom, % 185.95/186.58 ! [T_d,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__Int,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__image__mem__iff,axiom, % 185.95/186.58 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( 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))) % 185.95/186.58 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_range__ex1__eq,axiom, % 185.95/186.58 ! [V_ba_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 185.95/186.58 <=> ? [B_x] : % 185.95/186.58 ( V_ba_2 = hAPP(V_f_2,B_x) % 185.95/186.58 & ! [B_y] : % 185.95/186.58 ( V_ba_2 = hAPP(V_f_2,B_y) % 185.95/186.58 => B_y = B_x ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 185.95/186.58 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__iff__surj,axiom, % 185.95/186.58 ! [V_A_H_2,T_c,T_b,V_A_2] : % 185.95/186.58 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( ? [B_f] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 185.95/186.58 & 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)) ) % 185.95/186.58 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_endo__inj__surj,axiom, % 185.95/186.58 ! [V_f_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 185.95/186.58 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__surj__inj,axiom, % 185.95/186.58 ! [V_f_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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))) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__UNIV__surj__inj,axiom, % 185.95/186.58 ! [V_f_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.58 => ( 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)) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__UNIV__inj__surj,axiom, % 185.95/186.58 ! [V_f_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__image__subset__iff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( 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))) % 185.95/186.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__image__Int,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__Int,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__iff__eq__card,axiom, % 185.95/186.58 ! [V_f_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 <=> 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_eq__card__imp__inj__on,axiom, % 185.95/186.58 ! [V_f_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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) % 185.95/186.58 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__image__set__diff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__set__diff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__reindex,axiom, % 185.95/186.58 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_pigeonhole,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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))) % 185.95/186.58 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__fun__updI,axiom, % 185.95/186.58 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__reindex,axiom, % 185.95/186.58 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__reindex__cong,axiom, % 185.95/186.58 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.95/186.58 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 185.95/186.58 => 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) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__singleton,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum_Oreindex,axiom, % 185.95/186.58 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__bij__eq,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod_Oreindex,axiom, % 185.95/186.58 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__distrib,axiom, % 185.95/186.58 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__image__Compl__subset,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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)))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__insert,axiom, % 185.95/186.58 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum_OF__eq,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum_Oeq__fold,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod_Oeq__fold,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod_OF__eq,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__insert,axiom, % 185.95/186.58 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 185.95/186.58 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 & ~ 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))))))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__Un,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.58 & 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__inj__on__le,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( 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)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => 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))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__iff__card__le,axiom, % 185.95/186.58 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => ( ? [B_f] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 185.95/186.58 & 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)) ) % 185.95/186.58 <=> 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))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_quotient__diff1,axiom, % 185.95/186.58 ! [V_a_2,V_A_2,V_r_2,T_b] : % 185.95/186.58 ( 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) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__Un__Int,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__eq__fold__image,axiom, % 185.95/186.58 ! [V_f_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card_Oeq__fold__g,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__def,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_comm__monoid__big_OF__eq,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.95/186.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image_Oreindex,axiom, % 185.95/186.58 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__Un__one,axiom, % 185.95/186.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) % 185.95/186.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.58 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__Inr,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__Suc,axiom, % 185.95/186.58 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__Some,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__Inl,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__add__nat,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__of__nat,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Nat_Osemiring__char__0(T_b) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__int,axiom, % 185.95/186.58 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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_swap__inj__on,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image_Odistrib,axiom, % 185.95/186.58 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image_Oeq__fold,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_comm__monoid__big_Oinfinite,axiom, % 185.95/186.58 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.95/186.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__comp,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 185.95/186.58 => ( 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)))) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__into,axiom, % 185.95/186.58 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__vimage__singleton,axiom, % 185.95/186.58 ! [V_a_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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))))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimageI,axiom, % 185.95/186.58 ! [T_c,V_B_2,T_b,V_ba_2,V_a_2,V_f_2] : % 185.95/186.58 ( hAPP(V_f_2,V_a_2) = V_ba_2 % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Diff,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__vimage__subset,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_surj__image__vimage__eq,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_b,T_c] : % 185.95/186.58 ( 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)) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__eq,axiom, % 185.95/186.58 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 185.95/186.58 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimageD,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimageI2,axiom, % 185.95/186.58 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Un,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__empty,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Compl,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__code,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 185.95/186.58 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__ident,axiom, % 185.95/186.58 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__mono,axiom, % 185.95/186.58 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__UN,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__compose,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__UNIV,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Int,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__singleton__eq,axiom, % 185.95/186.58 ! [V_ba_2,V_f_2,T_c,V_a_2,T_b] : % 185.95/186.58 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 185.95/186.58 <=> hAPP(V_f_2,V_a_2) = V_ba_2 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__insert,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__vimageD,axiom, % 185.95/186.58 ! [V_F_2,V_h_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 185.95/186.58 => ( 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)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__subsetD,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__vimage__eq,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__vimageI,axiom, % 185.95/186.58 ! [V_h_2,T_c,V_F_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.95/186.58 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__vimage__image__eq,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__const,axiom, % 185.95/186.58 ! [T_c,V_A_2,V_ca_2,T_b] : % 185.95/186.58 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__eq__UN,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__f__f,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => 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 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__f__eq,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__f__f,axiom, % 185.95/186.58 ! [V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__on__the__inv__into,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__onto,axiom, % 185.95/186.58 ! [V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__subsetI,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.58 => ( 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))) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_the__inv__into__def,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__if,axiom, % 185.95/186.58 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] : % 185.95/186.58 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.95/186.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.95/186.58 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_f__the__inv__into__f,axiom, % 185.95/186.58 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.58 => 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 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_Ohom__commute,axiom, % 185.95/186.58 ! [V_N_2,V_h_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( ! [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)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_ImageE,axiom, % 185.95/186.58 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 185.95/186.58 => ~ ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) % 185.95/186.58 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_strong__setprod__reindex__cong,axiom, % 185.95/186.58 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.95/186.58 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => 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) ) % 185.95/186.58 => 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) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 185.95/186.58 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.58 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.95/186.58 => ( V_A_2 = V_B_2 % 185.95/186.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.95/186.58 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 185.95/186.58 => 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) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__eq__singleton__conv,axiom, % 185.95/186.58 ! [V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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))) % 185.95/186.58 <=> ? [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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph__permute__diff,axiom, % 185.95/186.58 ! [V_a_2,V_x_2,V_A_2,V_ba_2,T_b] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_x_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.95/186.58 => 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_ba_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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph__imp__finite,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__dom__body,axiom, % 185.95/186.58 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph_Oequations_I1_J,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph_OemptyI,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_empty__fold__graphE,axiom, % 185.95/186.58 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => V_x_2 = V_z_2 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_domIff,axiom, % 185.95/186.58 ! [V_m_2,T_c,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2))) % 185.95/186.58 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_domI,axiom, % 185.95/186.58 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] : % 185.95/186.58 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__dom,axiom, % 185.95/186.58 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] : % 185.95/186.58 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__restrict,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph_OinsertI,axiom, % 185.95/186.58 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.95/186.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__empty,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__eq__empty__conv,axiom, % 185.95/186.58 ! [V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__const,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__minus,axiom, % 185.95/186.58 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] : % 185.95/186.58 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__graph__insert__swap,axiom, % 185.95/186.58 ! [V_z_2,V_y_2,V_A_2,V_ba_2,T_b] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_y_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.95/186.58 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Diff1__fold__graph,axiom, % 185.95/186.58 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__fun__upd,axiom, % 185.95/186.58 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] : % 185.95/186.58 ( ( V_y_2 = c_Option_Ooption_ONone(T_b) % 185.95/186.58 => 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)))) ) % 185.95/186.58 & ( V_y_2 != c_Option_Ooption_ONone(T_b) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1Set_Ointros,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_ran__restrictD,axiom, % 185.95/186.58 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 => ? [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.58 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_accp__acc__eq,axiom, % 185.95/186.58 ! [V_x_2,V_r_2,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_empty__fold1SetE,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1Set__nonempty,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,V_f_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 185.95/186.58 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_acc__subset,axiom, % 185.95/186.58 ! [V_R2_2,V_R1_2,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1Set__sing,axiom, % 185.95/186.58 ! [V_ba_2,V_a_2,V_f_2,T_b] : % 185.95/186.58 ( 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_ba_2)) % 185.95/186.58 <=> V_a_2 = V_ba_2 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_acc__downward,axiom, % 185.95/186.58 ! [V_a_2,V_r_2,V_ba_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.95/186.58 => ( 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_ba_2)),V_r_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_acc_Osimps,axiom, % 185.95/186.58 ! [V_r_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( 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)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_max__extp_Oequations,axiom, % 185.95/186.58 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 185.95/186.58 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 185.95/186.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 185.95/186.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 185.95/186.58 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 & ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 185.95/186.58 => ? [B_xa] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 185.95/186.58 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_max__ext_Ointros,axiom, % 185.95/186.58 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 185.95/186.58 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 185.95/186.58 => ? [B_xa] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 185.95/186.58 & 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)) ) ) % 185.95/186.58 => 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))) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_conseq2,axiom, % 185.95/186.58 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 185.95/186.58 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.58 => ( ! [B_Z,B_s] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 185.95/186.58 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_conseq1,axiom, % 185.95/186.58 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 185.95/186.58 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.95/186.58 => ( ! [B_Z,B_s] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 185.95/186.58 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1Set_Oequations,axiom, % 185.95/186.58 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 <=> ? [B_a,B_A] : % 185.95/186.58 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 185.95/186.58 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 185.95/186.58 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__fold1SetE,axiom, % 185.95/186.58 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ~ ! [B_a,B_A] : % 185.95/186.58 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_image__split__eq__Sigma,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__Un,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__antimono,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => 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))) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SigmaI,axiom, % 185.95/186.58 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.95/186.58 => 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Diff__distrib1,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__Diff__distrib1,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Diff__distrib2,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__eq__cancel2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 185.95/186.58 => ( 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)) % 185.95/186.58 <=> V_A_2 = V_B_2 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__empty1,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__cartesian__product,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__cartesian__product,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_b) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__empty,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)) % 185.95/186.58 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__empty2,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Compl__Times__UNIV2,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Compl__Times__UNIV1,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__cartesian__product,axiom, % 185.95/186.58 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.95/186.58 => 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Un__distrib1,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__Un__distrib1,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Un__distrib2,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_swap__product,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__singleton__def,axiom, % 185.95/186.58 ! [V_a_2,V_f_2,T_b,V_g_2] : % 185.95/186.58 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 185.95/186.58 => 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 ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__singleton,axiom, % 185.95/186.58 ! [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 ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__cartesian__product,axiom, % 185.95/186.58 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => 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)))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_equiv__type,axiom, % 185.95/186.58 ! [V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.58 => 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)))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Int__distrib2,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__Int__distrib1,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__Int__distrib1,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Id__on__subset__Times,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UNIV__Times__UNIV,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SigmaE2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.58 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.95/186.58 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SigmaD2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.58 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SigmaD1,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.58 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_mem__Sigma__iff,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.58 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.95/186.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 & hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__one_Oeq__fold,axiom, % 185.95/186.58 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__cartesian__product__singleton,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Times__subset__cancel2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 185.95/186.58 => ( 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)))) % 185.95/186.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Image__subset,axiom, % 185.95/186.58 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__cartesian__productD1,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__cartesian__productD2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fst__image__times,axiom, % 185.95/186.58 ! [V_A_2,T_c,T_b,V_B_2] : % 185.95/186.58 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) % 185.95/186.58 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_snd__image__times,axiom, % 185.95/186.58 ! [V_B_2,T_c,T_b,V_A_2] : % 185.95/186.58 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) % 185.95/186.58 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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 ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sup__fin_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Inf__fin_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Olattice(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Min_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Max_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__on__def,axiom, % 185.95/186.58 ! [V_r_2,V_A_2,T_b] : % 185.95/186.58 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.58 <=> ( 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)))) % 185.95/186.58 & ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__times__insert,axiom, % 185.95/186.58 ! [V_B_2,V_ba_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_ba_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_ba_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_ba_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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__equiv__class,axiom, % 185.95/186.58 ! [V_X_2,V_r_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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)))) % 185.95/186.58 => ( 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))) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UN__Times__distrib,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Sigma__def,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__belowI,axiom, % 185.95/186.58 ! [V_a_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__quotient,axiom, % 185.95/186.58 ! [V_r_2,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( 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)))) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_below__fold1__iff,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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))) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Ofold1__belowI,axiom, % 185.95/186.58 ! [V_a_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__insert__idem,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__below__iff,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 <=> ? [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Obelow__fold1__iff,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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))) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__Un2,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_strict__below__fold1__iff,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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))) % 185.95/186.58 <=> ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__strict__below__iff,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( 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)) % 185.95/186.58 <=> ? [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Times,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__insert,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_semilattice__big_OF__eq,axiom, % 185.95/186.58 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.58 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 185.95/186.58 ! [V_A_2,V_I_2,T_c,T_b] : % 185.95/186.58 ? [B_f] : % 185.95/186.58 ( 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)) % 185.95/186.58 & 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_refl__onI,axiom, % 185.95/186.58 ! [V_A_2,V_r_2,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => 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)) ) % 185.95/186.58 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__Sigma,axiom, % 185.95/186.58 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__Sigma,axiom, % 185.95/186.58 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold__image__Sigma,axiom, % 185.95/186.58 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__SigmaI,axiom, % 185.95/186.58 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fold1__in,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( ! [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)))))) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__SigmaI,axiom, % 185.95/186.58 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( ! [B_a] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_hom__fold1__commute,axiom, % 185.95/186.58 ! [V_N_2,V_h_2,T_b] : % 185.95/186.58 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.95/186.58 => ( ! [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)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SigmaE,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.95/186.58 => ~ ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.58 => ! [B_y] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 185.95/186.58 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__surj,axiom, % 185.95/186.58 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 185.95/186.58 ( 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)) % 185.95/186.58 => ( 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)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__inj__on,axiom, % 185.95/186.58 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.58 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 185.95/186.58 => 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))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__imageI,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.58 ( 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_ba_2)),V_R_2)) % 185.95/186.58 => 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_ba_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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fst__comp__map__pair,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_snd__comp__map__pair,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair_Ocompositionality,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__compose,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair_Ocomp,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_snd__prod__fun,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__ident,axiom, % 185.95/186.58 ! [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 ). % 185.95/186.58 % 185.95/186.58 fof(fact_fst__map__pair,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__simp,axiom, % 185.95/186.58 ! [V_ba_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_ba_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_ba_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_map__pair__surj__on,axiom, % 185.95/186.58 ! [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] : % 185.95/186.58 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 185.95/186.58 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_prod__fun__imageE,axiom, % 185.95/186.58 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) % 185.95/186.58 => ~ ! [B_x,B_y] : % 185.95/186.58 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 185.95/186.58 => ~ 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setprod__pos__nat,axiom, % 185.95/186.58 ! [V_f_2,V_S_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__one__idem_Ohom__commute,axiom, % 185.95/186.58 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.58 => ( ! [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)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Rep__Integ__induct,axiom, % 185.95/186.58 ! [V_Pa_2,V_y_2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 185.95/186.58 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 185.95/186.58 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Rep__Integ__cases,axiom, % 185.95/186.58 ! [V_y_2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 185.95/186.58 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( 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))) % 185.95/186.58 => hAPP(V_g_2,B_x) = V_z_2 ) % 185.95/186.58 => 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)) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem__remove,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__less__Suc,axiom, % 185.95/186.58 ! [V_i_2,V_M_2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.95/186.58 => 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))))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_CollectI,axiom, % 185.95/186.58 ! [T_b,V_a_2,V_Pa_2] : % 185.95/186.58 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.95/186.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__conjI,axiom, % 185.95/186.58 ! [V_Q_2,V_Pa_2,T_b] : % 185.95/186.58 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) % 185.95/186.58 => 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_Q_2)))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__less__nat,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__le__nat,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 185.95/186.58 ! [V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__split,axiom, % 185.95/186.58 ! [V_Q_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_Q_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_Q_2))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_SetCompr__Sigma__eq,axiom, % 185.95/186.58 ! [V_Q_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_Q_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_Q_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__Collect__eq,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__neg__eq,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__disjI,axiom, % 185.95/186.58 ! [V_Q_2,V_Pa_2,T_b] : % 185.95/186.58 ( 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_Q_2)))) % 185.95/186.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__mem__eq,axiom, % 185.95/186.58 ! [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 ). % 185.95/186.58 % 185.95/186.58 fof(fact_mem__Collect__eq,axiom, % 185.95/186.58 ! [V_Pa_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_CollectD,axiom, % 185.95/186.58 ! [V_Pa_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_CollectE,axiom, % 185.95/186.58 ! [V_Pa_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.95/186.58 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem__sup,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.58 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__disj__eq,axiom, % 185.95/186.58 ! [V_Q_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_Q_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_Q_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_empty__Collect__eq,axiom, % 185.95/186.58 ! [V_Pa_2,T_b] : % 185.95/186.58 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 185.95/186.58 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__empty__eq,axiom, % 185.95/186.58 ! [V_Pa_2,T_b] : % 185.95/186.58 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_empty__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__Collect,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__def,axiom, % 185.95/186.58 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 185.95/186.58 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.95/186.58 => 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)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 185.95/186.58 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.58 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem__insert,axiom, % 185.95/186.58 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_UNIV__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_fun__left__comm__idem__inf,axiom, % 185.95/186.58 ! [T_b] : % 185.95/186.58 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.58 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__conj__eq,axiom, % 185.95/186.58 ! [V_Q_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_Q_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_Q_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__compr,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__compr__raw,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Un__def,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Int__Collect,axiom, % 185.95/186.58 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 185.95/186.58 ( 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)))) % 185.95/186.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.58 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Int__def,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_singleton__conv2,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_singleton__conv,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__conv__if2,axiom, % 185.95/186.58 ! [T_b,V_a_2,V_Pa_2] : % 185.95/186.58 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.95/186.58 => 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))) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__conv__if,axiom, % 185.95/186.58 ! [T_b,V_a_2,V_Pa_2] : % 185.95/186.58 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.95/186.58 => 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))) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_set__diff__eq,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__not,axiom, % 185.95/186.58 ! [V_Pa_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 => ( 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)))) % 185.95/186.58 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_insert__def,axiom, % 185.95/186.58 ! [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) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Compl__eq,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_vimage__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Collect__imp__eq,axiom, % 185.95/186.58 ! [V_Q_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_Q_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_Q_2)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__M__bounded__by__nat,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__setsum__restrict,axiom, % 185.95/186.58 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 185.95/186.58 => 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) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_if__image__distrib,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__if,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_nat__seg__image__imp__finite,axiom, % 185.95/186.58 ! [V_n_2,V_f_2,T_b,V_A_2] : % 185.95/186.58 ( 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))) % 185.95/186.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__restrict__set_H,axiom, % 185.95/186.58 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__image__gen,axiom, % 185.95/186.58 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => 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)) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Image__singleton,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__cases,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 185.95/186.58 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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))))) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__less__Suc2,axiom, % 185.95/186.58 ! [V_i_2,V_M_2] : % 185.95/186.58 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.95/186.58 => 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))))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_card__less,axiom, % 185.95/186.58 ! [V_i_2,V_M_2] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_dom__override__on,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_setsum__multicount,axiom, % 185.95/186.58 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 185.95/186.58 => ( ! [B_x] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 185.95/186.58 => 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 ) % 185.95/186.58 => 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)) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__subsets,axiom, % 185.95/186.58 ! [V_A_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => 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)))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Pow__def,axiom, % 185.95/186.58 ! [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)) ). % 185.95/186.58 % 185.95/186.58 fof(fact_override__on__apply__in,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_override__on__apply__notin,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_override__on__emptyset,axiom, % 185.95/186.58 ! [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 ). % 185.95/186.58 % 185.95/186.58 fof(fact_inj__graph,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_override__on__def,axiom, % 185.95/186.58 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.58 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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) ) % 185.95/186.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.58 => 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) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__psubset__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_inv__image__def,axiom, % 185.95/186.58 ! [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))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Nitpick_Oprod__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_int__ge__less__than__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_int__ge__less__than2__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_reflp__def,axiom, % 185.95/186.58 ! [V_r_2,T_b] : % 185.95/186.58 ( c_Predicate_Oreflp(T_b,V_r_2) % 185.95/186.58 <=> 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))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_reflpE,axiom, % 185.95/186.58 ! [V_x_2,V_r_2,T_b] : % 185.95/186.58 ( c_Predicate_Oreflp(T_b,V_r_2) % 185.95/186.58 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 185.95/186.58 ! [V_B_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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))))))) ) ) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 185.95/186.58 ! [V_x_2,V_A_2,T_b] : % 185.95/186.58 ( class_Orderings_Olinorder(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.58 => 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))))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__Collect__bounded__ex,axiom, % 185.95/186.58 ! [V_Q_2,T_c,V_Pa_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 => ( 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_Q_2))))) % 185.95/186.58 <=> ! [B_y] : % 185.95/186.58 ( hBOOL(hAPP(V_Pa_2,B_y)) % 185.95/186.58 => 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_Q_2),B_y)))) ) ) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_finite__image__set,axiom, % 185.95/186.58 ! [V_f_2,T_c,V_Pa_2,T_b] : % 185.95/186.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.95/186.58 => 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))))) ) ). % 185.95/186.58 % 185.95/186.58 fof(fact_ran__def,axiom, % 185.95/186.58 ! [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)))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_Pow__Compl,axiom, % 185.95/186.58 ! [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))))) ). % 185.95/186.58 % 185.95/186.58 fof(fact_add__Max__commute,axiom, % 185.95/186.58 ! [V_k_2,V_N_2,T_b] : % 185.95/186.58 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 185.95/186.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_add__Min__commute,axiom, % 185.95/186.59 ! [V_k_2,V_N_2,T_b] : % 185.95/186.59 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.95/186.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sup__Inf2__distrib,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Odistrib__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))))) ) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sup__Inf1__distrib,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Odistrib__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inf__Sup1__distrib,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Odistrib__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inf__Sup2__distrib,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Odistrib__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))))) ) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))))) ) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setsum__mult__setsum__if__inj,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.59 ( class_Rings_Osemiring__0(T_d) % 185.95/186.59 => ( 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))) % 185.95/186.59 => 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))))))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setsum__multicount__gen,axiom, % 185.95/186.59 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 185.95/186.59 => 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) ) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inj__on__id,axiom, % 185.95/186.59 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 185.95/186.59 % 185.95/186.59 fof(fact_map__pair_Oid,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_map__pair_Oidentity,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_id__apply,axiom, % 185.95/186.59 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 185.95/186.59 % 185.95/186.59 fof(fact_id__def,axiom, % 185.95/186.59 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 185.95/186.59 % 185.95/186.59 fof(fact_apsnd__id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_apfst__id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_of__int__eq__id,axiom, % 185.95/186.59 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 185.95/186.59 % 185.95/186.59 fof(fact_vimage__id,axiom, % 185.95/186.59 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 185.95/186.59 % 185.95/186.59 fof(fact_o__id,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_id__o,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_o__eq__id__dest,axiom, % 185.95/186.59 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.95/186.59 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2) % 185.95/186.59 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_surj__id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_image__id,axiom, % 185.95/186.59 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 185.95/186.59 % 185.95/186.59 fof(fact_folding_Oempty,axiom, % 185.95/186.59 ! [V_F_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.59 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_apsnd__def,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_apfst__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_split__Pair,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setsum__reindex__id,axiom, % 185.95/186.59 ! [V_B_2,V_f_2,T_b,T_c] : % 185.95/186.59 ( class_Groups_Ocomm__monoid__add(T_c) % 185.95/186.59 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setprod__reindex__id,axiom, % 185.95/186.59 ! [V_B_2,V_f_2,T_b,T_c] : % 185.95/186.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.59 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__conv__nat__seg__image,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 <=> ? [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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__def,axiom, % 185.95/186.59 ! [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))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__compI,axiom, % 185.95/186.59 ! [V_s_2,V_ca_2,T_d,V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ba_2),V_ca_2)),V_s_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__UNION__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__UNION__distrib2,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__empty1,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__empty2,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__distrib2,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__mono,axiom, % 185.95/186.59 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_O__assoc,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_union__comp__emptyR,axiom, % 185.95/186.59 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_union__comp__emptyL,axiom, % 185.95/186.59 ! [V_B_2,V_C_2,V_A_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__comp__subset__Sigma,axiom, % 185.95/186.59 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)))) % 185.95/186.59 => ( 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)))) % 185.95/186.59 => 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)))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_max__ext__compat,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__ext__compat,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pred__comp__rel__comp__eq,axiom, % 185.95/186.59 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 185.95/186.59 ( 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) % 185.95/186.59 <=> 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_reduction__pairI,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__less__than,axiom, % 185.95/186.59 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pred__comp_Ointros,axiom, % 185.95/186.59 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_ba_2,V_a_2,V_r_2] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(V_s_2,V_ba_2),V_ca_2)) % 185.95/186.59 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__empty,axiom, % 185.95/186.59 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__inv__image,axiom, % 185.95/186.59 ! [V_f_2,T_c,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__lex__prod,axiom, % 185.95/186.59 ! [V_rb_2,T_c,V_ra_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_ra_2) % 185.95/186.59 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__measure,axiom, % 185.95/186.59 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__union__merge,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__no__loop,axiom, % 185.95/186.59 ! [V_R_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__comp__self,axiom, % 185.95/186.59 ! [V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__less,axiom, % 185.95/186.59 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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__int__ge__less__than,axiom, % 185.95/186.59 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__irrefl,axiom, % 185.95/186.59 ! [V_a_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ~ 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__asym,axiom, % 185.95/186.59 ! [V_x_2,V_a_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => ~ 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__not__sym,axiom, % 185.95/186.59 ! [V_x_2,V_a_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => ~ 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__not__refl,axiom, % 185.95/186.59 ! [V_a_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ~ 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__Int1,axiom, % 185.95/186.59 ! [V_r_H_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__Int2,axiom, % 185.95/186.59 ! [V_r_H_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_max__ext__wf,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__pair__less,axiom, % 185.95/186.59 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__subset,axiom, % 185.95/186.59 ! [V_p_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pred__comp_Oequations,axiom, % 185.95/186.59 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 185.95/186.59 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2) % 185.95/186.59 <=> ? [B_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 185.95/186.59 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__finite__psubset,axiom, % 185.95/186.59 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__ext__wf,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__mlex,axiom, % 185.95/186.59 ! [V_f_2,V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__acc__iff,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acc__wfD,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__int__ge__less__than2,axiom, % 185.95/186.59 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 <=> ~ ? [B_f] : % 185.95/186.59 ! [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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfE__pf,axiom, % 185.95/186.59 ! [V_A_2,V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 => ( 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))) % 185.95/186.59 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__union__compatible,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 => ( c_Wellfounded_Owf(T_b,V_S_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Orderings_Owellorder(T_b) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_reduction__pair__def,axiom, % 185.95/186.59 ! [V_Pa_2,T_b] : % 185.95/186.59 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.95/186.59 <=> ( 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)) % 185.95/186.59 & 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_reduction__pair__lemma,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 185.95/186.59 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.95/186.59 => ( 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))) % 185.95/186.59 => ( 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))) % 185.95/186.59 => ( c_Wellfounded_Owf(T_b,V_S_2) % 185.95/186.59 => 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)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__map__pair__image,axiom, % 185.95/186.59 ! [V_f_2,T_c,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__lenlex,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__if__measure,axiom, % 185.95/186.59 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 185.95/186.59 ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.95/186.59 => 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))) ) % 185.95/186.59 => 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))))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pred__nat__def,axiom, % 185.95/186.59 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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__lex,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__pred__nat,axiom, % 185.95/186.59 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 185.95/186.59 % 185.95/186.59 fof(fact_lex__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__lexn,axiom, % 185.95/186.59 ! [V_n_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_lexn_Osimps_I1_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__same__fst,axiom, % 185.95/186.59 ! [T_b,V_R_2,T_c,V_Pa_2] : % 185.95/186.59 ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.95/186.59 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 185.95/186.59 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Collect__split,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_RangeI,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Id__on,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__empty__iff,axiom, % 185.95/186.59 ! [V_r_2,T_b,T_c] : % 185.95/186.59 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Un__eq,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__Range,axiom, % 185.95/186.59 ! [V_r_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_snd__eq__Range,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__iff,axiom, % 185.95/186.59 ! [V_r_2,T_c,V_a_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 185.95/186.59 <=> ? [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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__insert,axiom, % 185.95/186.59 ! [V_r_2,V_ba_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_ba_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Int__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Diff__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_RangeP__Range__eq,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_RangeE,axiom, % 185.95/186.59 ! [V_r_2,T_c,V_ba_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 185.95/186.59 => ~ ! [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_ba_2)),V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_RangeP_Ointros,axiom, % 185.95/186.59 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.95/186.59 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_ba_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_RangeP_Oequations,axiom, % 185.95/186.59 ! [V_a2_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 185.95/186.59 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__Un,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ( c_Wellfounded_Owf(T_b,V_s_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__def,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.95/186.59 <=> 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__empty,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_DomainI,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Id__on,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__accp__iff,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.95/186.59 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_accp__wfPD,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.95/186.59 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__subset,axiom, % 185.95/186.59 ! [V_p_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__empty__iff,axiom, % 185.95/186.59 ! [V_r_2,T_c,T_b] : % 185.95/186.59 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__mono,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Un__eq,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__Domain,axiom, % 185.95/186.59 ! [V_r_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fst__eq__Domain,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__iff,axiom, % 185.95/186.59 ! [V_r_2,T_c,V_a_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 185.95/186.59 <=> ? [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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__insert,axiom, % 185.95/186.59 ! [V_r_2,V_ba_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_ba_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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Int__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Diff__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Field__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__in__rel,axiom, % 185.95/186.59 ! [V_R_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.95/186.59 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__wf__eq,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Collect__split,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_DomainP__Domain__eq,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_DomainE,axiom, % 185.95/186.59 ! [V_r_2,T_c,V_a_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 185.95/186.59 => ~ ! [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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_DomainP_Ointros,axiom, % 185.95/186.59 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.95/186.59 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_DomainP_Oequations,axiom, % 185.95/186.59 ! [V_a1_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 185.95/186.59 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__acyclicP,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_neg__map__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__acyclic,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acyclic__subset,axiom, % 185.95/186.59 ! [V_r_2,V_s_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__acyclic__wf,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.95/186.59 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__iff__acyclic__if__finite,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.95/186.59 => ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_neg__single__def,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pos__map__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_New__DSequence_Oneg__single__def,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pos__single__def,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_New__DSequence_Opos__single__def,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Nitpick_Owf_H__def,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Nitpick_Owf_H(T_b,V_r_2) % 185.95/186.59 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.95/186.59 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.95/186.59 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pigeonhole__infinite,axiom, % 185.95/186.59 ! [V_f_2,T_c,V_A_2,T_b] : % 185.95/186.59 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.95/186.59 => ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 & ~ 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)))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Abs__Integ__cases,axiom, % 185.95/186.59 ! [V_x_2] : % 185.95/186.59 ~ ! [B_y] : % 185.95/186.59 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 185.95/186.59 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Abs__Integ__induct,axiom, % 185.95/186.59 ! [V_x_2,V_Pa_2] : % 185.95/186.59 ( ! [B_y] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 185.95/186.59 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 185.95/186.59 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__UN__I,axiom, % 185.95/186.59 ! [V_B_2,T_c,V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_a] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inj__on__diff__nat,axiom, % 185.95/186.59 ! [V_k_2,V_N_2] : % 185.95/186.59 ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfP__SUP,axiom, % 185.95/186.59 ! [T_b,V_r_2,T_c] : % 185.95/186.59 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 185.95/186.59 => ( ! [B_i,B_j] : % 185.95/186.59 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 185.95/186.59 => 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)) ) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__map__freshness,axiom, % 185.95/186.59 ! [V_f_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2))) % 185.95/186.59 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.95/186.59 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_mem__splitE,axiom, % 185.95/186.59 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2))) % 185.95/186.59 => ~ ! [B_x,B_y] : % 185.95/186.59 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 185.95/186.59 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_mem__splitI2,axiom, % 185.95/186.59 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 185.95/186.59 ( ! [B_a,B_b] : % 185.95/186.59 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Eps__split,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_someI,axiom, % 185.95/186.59 ! [T_b,V_x_2,V_Pa_2] : % 185.95/186.59 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.95/186.59 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_tfl__some,axiom, % 185.95/186.59 ! [T_b,B_P] : % 185.95/186.59 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 185.95/186.59 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_someI__ex,axiom, % 185.95/186.59 ! [T_b,V_Pa_2] : % 185.95/186.59 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.95/186.59 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_some__eq__ex,axiom, % 185.95/186.59 ! [T_b,V_Pa_2] : % 185.95/186.59 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 185.95/186.59 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_some__eq__trivial,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_some__sym__eq__trivial,axiom, % 185.95/186.59 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 185.95/186.59 % 185.95/186.59 fof(fact_exE__some,axiom, % 185.95/186.59 ! [T_b,V_ca_2,V_Pa_2] : % 185.95/186.59 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.95/186.59 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 185.95/186.59 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Eps__split__eq,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_split__paired__Eps,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wfI__pf,axiom, % 185.95/186.59 ! [V_R_2,T_b] : % 185.95/186.59 ( ! [B_A] : % 185.95/186.59 ( 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))) % 185.95/186.59 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 185.95/186.59 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sigma__mono,axiom, % 185.95/186.59 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => 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))) ) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acc_OaccI,axiom, % 185.95/186.59 ! [V_r_2,V_x_2,T_b] : % 185.95/186.59 ( ! [B_y] : % 185.95/186.59 ( 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)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_not__acc__down,axiom, % 185.95/186.59 ! [V_R_2,V_x_2,T_b] : % 185.95/186.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 185.95/186.59 => ~ ! [B_z] : % 185.95/186.59 ( 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)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__image__1,axiom, % 185.95/186.59 ! [V_f_2,V_S_2,T_b,T_c] : % 185.95/186.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.95/186.59 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_card_Oneutral,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.95/186.59 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_max__ext_Osimps,axiom, % 185.95/186.59 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 185.95/186.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 185.95/186.59 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 & ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 185.95/186.59 => ? [B_xa] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 185.95/186.59 & 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)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__image__cong,axiom, % 185.95/186.59 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Groups_Oab__semigroup__mult(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 185.95/186.59 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setprod__dvd__setprod__subset2,axiom, % 185.95/186.59 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.95/186.59 ( class_Rings_Ocomm__semiring__1(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 185.95/186.59 => 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))) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Min__eqI,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_y] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Max__eqI,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_y] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__no__infinite__down__chainE,axiom, % 185.95/186.59 ! [V_f_2,V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => ~ ! [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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_setsum__reindex__cong,axiom, % 185.95/186.59 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.95/186.59 ( class_Groups_Ocomm__monoid__add(T_d) % 185.95/186.59 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.95/186.59 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.95/186.59 => ( ! [B_a] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.95/186.59 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 185.95/186.59 => 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) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_less__eq,axiom, % 185.95/186.59 ! [V_n_2,V_m_2] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__trancl,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_less__than__def,axiom, % 185.95/186.59 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acyclic__def,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.95/186.59 <=> ! [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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl_Or__into__trancl,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__subset__Field2,axiom, % 185.95/186.59 ! [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))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_r__into__trancl_H,axiom, % 185.95/186.59 ! [V_r_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__domain,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__range,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__trancl,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__trans,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__into__trancl2,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_r__r__into__trancl,axiom, % 185.95/186.59 ! [V_ca_2,V_R_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),V_R_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_R_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__mono,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => ( 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)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__unfold,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__subset__Sigma,axiom, % 185.95/186.59 ! [V_A_2,V_r_2,T_b] : % 185.95/186.59 ( 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)))) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__Int__subset,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__insert,axiom, % 185.95/186.59 ! [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)))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_reflcl__set__eq,axiom, % 185.95/186.59 ! [V_y_2,V_x_2,V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_r__into__rtrancl,axiom, % 185.95/186.59 ! [V_r_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl_Ortrancl__refl,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_IdI,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__into__rtrancl,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__unfold__right,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__unfold__left,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_reflcl__trancl,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__reflcl,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__rtrancl__absorb,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__trancl__absorb,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_refl__rtrancl,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__idemp,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__trans,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__r__diff__Id,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_in__rtrancl__UnI,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,V_x_2,T_b] : % 185.95/186.59 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.95/186.59 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__closed__trancl,axiom, % 185.95/186.59 ! [V_X_2,V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__Un__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__reflcl,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__Un__rtrancl,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__reflcl__absorb,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__subset__rtrancl,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__subset,axiom, % 185.95/186.59 ! [V_S_2,V_R_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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))) % 185.95/186.59 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__mono,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__Int__subset,axiom, % 185.95/186.59 ! [V_r_2,V_s_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_r__comp__rtrancl__eq,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__idemp__self__comp,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__unfold,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__empty,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__rtrancl,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__rtrancl,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Id__O__R,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_R__O__Id,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__Id,axiom, % 185.95/186.59 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 185.95/186.59 % 185.95/186.59 fof(fact_pair__in__Id__conv,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Relation_OId(T_b))) % 185.95/186.59 <=> V_a_2 = V_ba_2 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__trancl__trancl,axiom, % 185.95/186.59 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( 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))) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__rtrancl__trancl,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__into__trancl1,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtranclD,axiom, % 185.95/186.59 ! [V_R_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.95/186.59 => ( V_a_2 = V_ba_2 % 185.95/186.59 | ( V_a_2 != V_ba_2 % 185.95/186.59 & 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__into__trancl2,axiom, % 185.95/186.59 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__eq__or__trancl,axiom, % 185.95/186.59 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> ( V_x_2 = V_y_2 % 185.95/186.59 | ( V_x_2 != V_y_2 % 185.95/186.59 & 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))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_refl__Id,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pair__leq__def,axiom, % 185.95/186.59 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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Not__Domain__rtrancl,axiom, % 185.95/186.59 ! [V_y_2,V_R_2,V_x_2,T_b] : % 185.95/186.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 185.95/186.59 => ( 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))) % 185.95/186.59 <=> V_x_2 = V_y_2 ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acc__downwards__aux,axiom, % 185.95/186.59 ! [V_r_2,V_a_2,V_ba_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acc__downwards,axiom, % 185.95/186.59 ! [V_ba_2,V_r_2,V_a_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__insert,axiom, % 185.95/186.59 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.59 & ~ 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acyclic__insert,axiom, % 185.95/186.59 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.95/186.59 & ~ 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_refl__reflcl,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Id__def,axiom, % 185.95/186.59 ! [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))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_irrefl__diff__Id,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_pred__nat__trancl__eq__le,axiom, % 185.95/186.59 ! [V_n_2,V_m_2] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__subset__Sigma__aux,axiom, % 185.95/186.59 ! [V_A_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.95/186.59 => ( 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)))) % 185.95/186.59 => ( V_a_2 = V_ba_2 % 185.95/186.59 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_irrefl__tranclI,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ~ 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sequence__trans,axiom, % 185.95/186.59 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 185.95/186.59 ( ! [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))) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__converse,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__Id,axiom, % 185.95/186.59 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__converse,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__converse,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_equiv__comp__eq,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.59 => 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 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__UNION,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converseD,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converseI,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),V_r_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__iff,axiom, % 185.95/186.59 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.95/186.59 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_refl__on__converse,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.95/186.59 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__Int,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__converse,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_Field__converse,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__Id__on,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__inv__image,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__converse,axiom, % 185.95/186.59 ! [V_r_2,T_c,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.95/186.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__Un,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__rel__comp,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acyclic__converse,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.95/186.59 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__converse__trancl,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.95/186.59 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__converse,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__converseI,axiom, % 185.95/186.59 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__converseD,axiom, % 185.95/186.59 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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)))) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__converseI,axiom, % 185.95/186.59 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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)))) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__converseD,axiom, % 185.95/186.59 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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)))) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__subset__eq,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> 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))))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_refl__on__comp__subset,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_comp__equivI,axiom, % 185.95/186.59 ! [V_A_2,V_r_2,T_b] : % 185.95/186.59 ( 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 % 185.95/186.59 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 185.95/186.59 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__acyclic__wf__converse,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.95/186.59 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.95/186.59 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__def,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_total__on__diff__Id,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 185.95/186.59 ! [V_R_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.95/186.59 => 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)))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_relpow_Osimps_I1_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__power,axiom, % 185.95/186.59 ! [V_R_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.95/186.59 <=> ? [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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__imp__rtrancl,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_p_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__1,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__commute,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_relpow_Osimps_I2_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__add,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow__mult,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow__swap1,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_wf__exp,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_comp__funpow,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_total__on__empty,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_total__on__converse,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.95/186.59 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__0__E,axiom, % 185.95/186.59 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => V_x_2 = V_y_2 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__0__I,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__Suc__I2,axiom, % 185.95/186.59 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( 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))) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__Suc__I,axiom, % 185.95/186.59 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( 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)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow_Osimps_I2_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow__add,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow_Osimps_I1_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_trancl__power,axiom, % 185.95/186.59 ! [V_R_2,V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 185.95/186.59 <=> ? [B_n] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 185.95/186.59 & 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_total__on__def,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => ! [B_xa] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.95/186.59 => ( B_x != B_xa % 185.95/186.59 => ( 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)) % 185.95/186.59 | 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)) ) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_funpow__code__def,axiom, % 185.95/186.59 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__E2,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.59 => V_x_2 != V_z_2 ) % 185.95/186.59 => ~ ! [B_y,B_m] : % 185.95/186.59 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 185.95/186.59 => ( 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)) % 185.95/186.59 => ~ 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))) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__E,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.95/186.59 => V_x_2 != V_z_2 ) % 185.95/186.59 => ~ ! [B_y,B_m] : % 185.95/186.59 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 185.95/186.59 => ( 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))) % 185.95/186.59 => ~ 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)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_acyclicI,axiom, % 185.95/186.59 ! [V_r_2,T_b] : % 185.95/186.59 ( ! [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))) % 185.95/186.59 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__Int__eq,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__Un__separator__converseE,axiom, % 185.95/186.59 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_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_Q_2)))) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 185.95/186.59 => ! [B_y] : % 185.95/186.59 ( 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_Q_2)) % 185.95/186.59 => B_y = B_x ) ) % 185.95/186.59 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__Id__on,axiom, % 185.95/186.59 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__subset,axiom, % 185.95/186.59 ! [V_s_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 185.95/186.59 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__rel__comp,axiom, % 185.95/186.59 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.95/186.59 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__Id,axiom, % 185.95/186.59 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__rel__pow,axiom, % 185.95/186.59 ! [V_n_2,V_R_2,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valuedD,axiom, % 185.95/186.59 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => ( 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)) % 185.95/186.59 => V_y_2 = V_z_2 ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__def,axiom, % 185.95/186.59 ! [V_r_2,T_c,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.95/186.59 <=> ! [B_x,B_y] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ! [B_z] : % 185.95/186.59 ( 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)) % 185.95/186.59 => B_y = B_z ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_single__valued__confluent,axiom, % 185.95/186.59 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 185.95/186.59 => ( 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))) % 185.95/186.59 => ( 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))) % 185.95/186.59 => ( 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))) % 185.95/186.59 | 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))) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rtrancl__Un__separatorE,axiom, % 185.95/186.59 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( 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_ba_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_Q_2)))) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ! [B_y] : % 185.95/186.59 ( 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_Q_2)) % 185.95/186.59 => B_x = B_y ) ) % 185.95/186.59 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__Suc__E,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ~ ! [B_y] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ~ 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__Suc__D2,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ? [B_y] : % 185.95/186.59 ( 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)) % 185.95/186.59 & 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_rel__pow__Suc__E2,axiom, % 185.95/186.59 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ~ ! [B_y] : % 185.95/186.59 ( 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)) % 185.95/186.59 => ~ 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_tranclD2,axiom, % 185.95/186.59 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ? [B_z] : % 185.95/186.59 ( 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))) % 185.95/186.59 & 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_tranclD,axiom, % 185.95/186.59 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ? [B_z] : % 185.95/186.59 ( 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)) % 185.95/186.59 & 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_IdE,axiom, % 185.95/186.59 ! [V_p_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 185.95/186.59 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_folding_Oeq__fold,axiom, % 185.95/186.59 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__image__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__empty,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__def,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_union__fold__insert,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__sup__insert,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__inf__insert,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Ofold__inf__insert,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Ofold__sup__insert,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 185.95/186.59 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 185.95/186.59 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sup__SUPR__fold__sup,axiom, % 185.95/186.59 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sup__le__fold__sup,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => 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_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_2),V_A_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold__inf__le__inf,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_ba_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_ba_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Osup__le__fold__sup,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_2),V_A_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold1__eq__fold__idem,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Olattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Olattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Min_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Max_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_minus__fold__remove,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_folding__one_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_SUPR__fold__sup,axiom, % 185.95/186.59 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fold1__eq__fold,axiom, % 185.95/186.59 ! [V_a_2,V_A_2,T_b] : % 185.95/186.59 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Olattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Lattices_Olattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Min_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Max_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 185.95/186.59 ! [V_x_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__rec,axiom, % 185.95/186.59 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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)))))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 185.95/186.59 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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)))))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 185.95/186.59 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 185.95/186.59 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Groups_Oab__semigroup__mult(T_b) % 185.95/186.59 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 185.95/186.59 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.95/186.59 => V_y_2 = V_x_2 ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 185.95/186.59 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 185.95/186.59 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__equality,axiom, % 185.95/186.59 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.95/186.59 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 185.95/186.59 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__insert,axiom, % 185.95/186.59 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 185.95/186.59 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 185.95/186.59 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => ? [B_y_H] : % 185.95/186.59 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 185.95/186.59 & 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)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INFI__fold__inf,axiom, % 185.95/186.59 ! [V_f_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__E,axiom, % 185.95/186.59 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.95/186.59 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__D,axiom, % 185.95/186.59 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF1__E,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 185.95/186.59 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF1__D,axiom, % 185.95/186.59 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF2__D,axiom, % 185.95/186.59 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.59 ( 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_ba_2),V_ca_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF2__E,axiom, % 185.95/186.59 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.59 ( 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_ba_2),V_ca_2)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 185.95/186.59 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__INT,axiom, % 185.95/186.59 ! [V_A_2,T_c,V_I_2,T_b] : % 185.95/186.59 ( ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 185.95/186.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UN__simps_I7_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UN__extend__simps_I7_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I9_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I9_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Compl__INT,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Compl__UN,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Collect__ball__eq,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__less__iff,axiom, % 185.95/186.59 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 185.95/186.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 & class_Orderings_Olinorder(T_b) ) % 185.95/186.59 => ( 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)) % 185.95/186.59 <=> ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__Int__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.59 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b] : % 185.95/186.59 ( 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) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.59 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Pow__INT__eq,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INFI__apply,axiom, % 185.95/186.59 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__commute,axiom, % 185.95/186.59 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INFI__bool__eq,axiom, % 185.95/186.59 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__iff,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__INT__eq2,axiom, % 185.95/186.59 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__absorb,axiom, % 185.95/186.59 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__INT__eq,axiom, % 185.95/186.59 ! [V_x_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_vimage__INT,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I10_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I10_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__INT__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__lower,axiom, % 185.95/186.59 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_le__INF__iff,axiom, % 185.95/186.59 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( 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))) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I5_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I5_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__subset__iff,axiom, % 185.95/186.59 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__insert__distrib,axiom, % 185.95/186.59 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__insert,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__const,axiom, % 185.95/186.59 ! [V_M_2,T_b,V_A_2,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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 ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I2_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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 ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I1_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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 ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__constant,axiom, % 185.95/186.59 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.95/186.59 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.95/186.59 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Un__INT__distrib2,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I6_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Un__INT__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I7_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I6_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I7_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__Un,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_converse__INTER,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__subset,axiom, % 185.95/186.59 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INTER__def,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I2_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I1_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I3_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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) ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I3_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I4_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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 ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF__leI,axiom, % 185.95/186.59 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__greaterThan__UNIV,axiom, % 185.95/186.59 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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I4_J,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.95/186.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) % 185.95/186.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Image__INT__eq,axiom, % 185.95/186.59 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 185.95/186.59 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inf__INFI__fold__inf,axiom, % 185.95/186.59 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__fold__inf,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__fold__sup,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__Inter,axiom, % 185.95/186.59 ! [V_M_2,T_b] : % 185.95/186.59 ( ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 185.95/186.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UnionI,axiom, % 185.95/186.59 ! [V_A_2,V_C_2,V_X_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_InterD,axiom, % 185.95/186.59 ! [V_X_2,V_C_2,V_A_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_InterE,axiom, % 185.95/186.59 ! [V_X_2,V_C_2,V_A_2,T_b] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__simps_I8_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INT__extend__simps_I8_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF2__iff,axiom, % 185.95/186.59 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.95/186.59 ( 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_ba_2),V_ca_2)) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INF1__iff,axiom, % 185.95/186.59 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.95/186.59 ( 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_ba_2)) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__image__eq,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_INTER__eq__Inter__image,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Un__Inter,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__anti__mono,axiom, % 185.95/186.59 ! [V_A_2,V_B_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__insert,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_subset__Pow__Union,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__disjoint,axiom, % 185.95/186.59 ! [V_A_2,V_C_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__empty,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__le__iff,axiom, % 185.95/186.59 ! [V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_ba_2)) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_le__Inf__iff,axiom, % 185.95/186.59 ! [V_A_2,V_ba_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) % 185.95/186.59 <=> ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__upper,axiom, % 185.95/186.59 ! [V_A_2,V_B_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__lower,axiom, % 185.95/186.59 ! [V_A_2,V_B_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__mono,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( 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)) % 185.95/186.59 => 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))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Field__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__less__iff,axiom, % 185.95/186.59 ! [V_a_2,V_S_2,T_b] : % 185.95/186.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 & class_Orderings_Olinorder(T_b) ) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 185.95/186.59 <=> ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_less__Sup__iff,axiom, % 185.95/186.59 ! [V_S_2,V_a_2,T_b] : % 185.95/186.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 & class_Orderings_Olinorder(T_b) ) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 185.95/186.59 <=> ? [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.95/186.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__Pow__eq,axiom, % 185.95/186.59 ! [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 ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__quotient,axiom, % 185.95/186.59 ! [V_r_2,V_A_2,T_b] : % 185.95/186.59 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.95/186.59 => 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 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__Sup,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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))))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__Inf,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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)))))) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__UnionD,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_image__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sigma__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_vimage__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Int__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Int__Union2,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UN__extend__simps_I8_J,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UN__simps_I8_J,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Range__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Domain__Union,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__eq,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__insert,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__Un__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__UNIV,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_UNION__eq__Union__image,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__image__eq,axiom, % 185.95/186.59 ! [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) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__upper,axiom, % 185.95/186.59 ! [V_A_2,V_x_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__UNIV,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__lower,axiom, % 185.95/186.59 ! [V_A_2,V_x_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__Un__distrib,axiom, % 185.95/186.59 ! [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)) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__empty,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__singleton,axiom, % 185.95/186.59 ! [V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__insert,axiom, % 185.95/186.59 ! [V_A_2,V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Int__Inter__image,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__singleton,axiom, % 185.95/186.59 ! [V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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 ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__UNIV,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__empty,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__UNIV,axiom, % 185.95/186.59 ! [T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__insert,axiom, % 185.95/186.59 ! [V_A_2,V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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)) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Un__eq__Union,axiom, % 185.95/186.59 ! [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))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Un__Union__image,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__Int__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Int__eq__Inter,axiom, % 185.95/186.59 ! [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))))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__Un__subset,axiom, % 185.95/186.59 ! [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)))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__binary,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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_ba_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_ba_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__binary,axiom, % 185.95/186.59 ! [V_ba_2,V_a_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => 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_ba_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_ba_2) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_sup__Sup__fold__sup,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Sup__fin__Sup,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inf__Inf__fold__inf,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => 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) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inf__fin__Inf,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_image__INT,axiom, % 185.95/186.59 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 185.95/186.59 => 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)) ) % 185.95/186.59 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 185.95/186.59 => 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)) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_card__partition,axiom, % 185.95/186.59 ! [V_k_2,V_C_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 185.95/186.59 => ( ! [B_c] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 185.95/186.59 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 185.95/186.59 => ( ! [B_c1] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 185.95/186.59 => ! [B_c2] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 185.95/186.59 => ( B_c1 != B_c2 % 185.95/186.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 185.95/186.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__def,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Union__def,axiom, % 185.95/186.59 ! [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))) ). % 185.95/186.59 % 185.95/186.59 fof(fact_finite__Union,axiom, % 185.95/186.59 ! [V_A_2,T_b] : % 185.95/186.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 185.95/186.59 => ( ! [B_M] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 185.95/186.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_insert__partition,axiom, % 185.95/186.59 ! [V_F_2,V_x_2,T_b] : % 185.95/186.59 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ! [B_xa] : % 185.95/186.59 ( 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))) % 185.95/186.59 => ( B_x != B_xa % 185.95/186.59 => 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)) ) ) ) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inj__on__Inter,axiom, % 185.95/186.59 ! [V_f_2,T_c,T_b,V_S_2] : % 185.95/186.59 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 185.95/186.59 => ( ! [B_A] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 185.95/186.59 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_Inter__subset,axiom, % 185.95/186.59 ! [V_B_2,V_A_2,T_b] : % 185.95/186.59 ( ! [B_X] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 185.95/186.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_inj__on__INTER,axiom, % 185.95/186.59 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 185.95/186.59 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.95/186.59 => ( ! [B_i] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 185.95/186.59 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 185.95/186.59 => 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)) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 185.95/186.59 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.59 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.95/186.59 => ( 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)) % 185.95/186.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.95/186.59 => ~ ! [B_y] : % 185.95/186.59 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 185.95/186.59 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 185.95/186.59 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_ba_2),V_ca_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 185.95/186.59 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.95/186.59 ( class_Orderings_Olinorder(T_b) % 185.95/186.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.59 => ( ! [B_x] : % 185.95/186.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 185.95/186.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 185.95/186.59 % 185.95/186.59 fof(fact_InterI,axiom, % 185.95/186.59 ! [V_A_2,V_C_2,T_b] : % 185.95/186.59 ( ! [B_X] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 185.95/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 185.95/186.60 => 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))) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inf__le__fold__inf,axiom, % 185.95/186.60 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.95/186.60 ( class_Lattices_Osemilattice__inf(T_b) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.60 => ( ! [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 185.95/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_fold__sup__le__sup,axiom, % 185.95/186.60 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.95/186.60 ( class_Lattices_Osemilattice__sup(T_b) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.95/186.60 => ( ! [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 185.95/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_ba_2),V_ca_2))) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_wf__eq__minimal,axiom, % 185.95/186.60 ! [V_r_2,T_b] : % 185.95/186.60 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.95/186.60 <=> ! [B_Q] : % 185.95/186.60 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 185.95/186.60 => ? [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 185.95/186.60 & ! [B_y] : % 185.95/186.60 ( 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)) % 185.95/186.60 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 185.95/186.60 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.95/186.60 => 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)) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_transfer__nat__int__set__cong,axiom, % 185.95/186.60 ! [V_P_H_2,V_Pa_2] : % 185.95/186.60 ( ! [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.95/186.60 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.95/186.60 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 185.95/186.60 => 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)) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_folding__image__simple__idem_Oidem,axiom, % 185.95/186.60 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.60 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 185.95/186.60 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.95/186.60 => 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) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 185.95/186.60 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.60 => 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)) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 185.95/186.60 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.95/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.95/186.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.95/186.60 => 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) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_Int__Collect__mono,axiom, % 185.95/186.60 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.95/186.60 => ( ! [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.95/186.60 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.95/186.60 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 185.95/186.60 => 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_Q_2)))) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_UnionE,axiom, % 185.95/186.60 ! [V_C_2,V_A_2,T_b] : % 185.95/186.60 ( 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))) % 185.95/186.60 => ~ ! [B_X] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 185.95/186.60 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__upd__left,axiom, % 185.95/186.60 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] : % 185.95/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2))) % 185.95/186.60 => 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)) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_converseE,axiom, % 185.95/186.60 ! [V_r_2,V_yx_2,T_c,T_b] : % 185.95/186.60 ( 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))) % 185.95/186.60 => ~ ! [B_x,B_y] : % 185.95/186.60 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 185.95/186.60 => ~ 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)) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__None,axiom, % 185.95/186.60 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] : % 185.95/186.60 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__find__right,axiom, % 185.95/186.60 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] : % 185.95/186.60 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__assoc,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__empty,axiom, % 185.95/186.60 ! [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 ). % 185.95/186.60 % 185.95/186.60 fof(fact_empty__map__add,axiom, % 185.95/186.60 ! [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 ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__def,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 185.95/186.60 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 185.95/186.60 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 185.95/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 185.95/186.60 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] : % 185.95/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2))) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_dom__map__add,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__SomeD,axiom, % 185.95/186.60 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 185.95/186.60 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__Some__iff,axiom, % 185.95/186.60 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 185.95/186.60 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__upd,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inj__on__map__add__dom,axiom, % 185.95/186.60 ! [V_m_H_2,V_m_2,T_c,T_b] : % 185.95/186.60 ( 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)) % 185.95/186.60 <=> 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)) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__comm,axiom, % 185.95/186.60 ! [V_m2_2,V_m1_2,T_c,T_b] : % 185.95/186.60 ( 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)) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_finite__range__map__of__map__add,axiom, % 185.95/186.60 ! [V_l_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( 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))))) % 185.95/186.60 => 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))))) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_rel__compE,axiom, % 185.95/186.60 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 185.95/186.60 ( 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))) % 185.95/186.60 => ~ ! [B_x,B_y,B_z] : % 185.95/186.60 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 185.95/186.60 => ( 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)) % 185.95/186.60 => ~ 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)) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_finite__dom__map__of,axiom, % 185.95/186.60 ! [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)))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_finite__range__map__of,axiom, % 185.95/186.60 ! [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))))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__add__map__of__foldr,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_full__small__int__def,axiom, % 185.95/186.60 ! [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))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_small_H_Osimps,axiom, % 185.95/186.60 ! [V_f_2,V_i_2,V_d_2] : % 185.95/186.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 185.95/186.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 185.95/186.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 185.95/186.60 => 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)) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_small_H_Opsimps,axiom, % 185.95/186.60 ! [V_i_2,V_d_2,V_f_2] : % 185.95/186.60 ( 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)))) % 185.95/186.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 185.95/186.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 185.95/186.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 185.95/186.60 => 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)) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_small__int__def,axiom, % 185.95/186.60 ! [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))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_small__prod__def,axiom, % 185.95/186.60 ! [V_d_2,V_f_2,T_b,T_c] : % 185.95/186.60 ( ( class_Smallcheck_Osmall(T_c) % 185.95/186.60 & class_Smallcheck_Osmall(T_b) ) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_small_H_Opinduct,axiom, % 185.95/186.60 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] : % 185.95/186.60 ( 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)))) % 185.95/186.60 => ( ! [B_f,B_d,B_i] : % 185.95/186.60 ( 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)))) % 185.95/186.60 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 185.95/186.60 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 185.95/186.60 => 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)))) ) ) % 185.95/186.60 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) ) % 185.95/186.60 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_body__def,axiom, % 185.95/186.60 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__of__mapk__SomeI,axiom, % 185.95/186.60 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.60 => ( 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) % 185.95/186.60 => 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) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__def,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inj__mapI,axiom, % 185.95/186.60 ! [V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.60 => 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))) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__Some__iff,axiom, % 185.95/186.60 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 <=> ? [B_k_H] : % 185.95/186.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 185.95/186.60 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__simps_I2_J,axiom, % 185.95/186.60 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] : % 185.95/186.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__simps_I1_J,axiom, % 185.95/186.60 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] : % 185.95/186.60 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 => 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) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inj__map,axiom, % 185.95/186.60 ! [V_f_2,T_c,T_b] : % 185.95/186.60 ( 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))) % 185.95/186.60 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inj__map__eq__map,axiom, % 185.95/186.60 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 185.95/186.60 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.95/186.60 => ( 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) % 185.95/186.60 <=> V_xs_2 = V_ys_2 ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_inj__mapD,axiom, % 185.95/186.60 ! [V_f_2,T_c,T_b] : % 185.95/186.60 ( 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))) % 185.95/186.60 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__injective,axiom, % 185.95/186.60 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 185.95/186.60 => V_xs_2 = V_ys_2 ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__ident,axiom, % 185.95/186.60 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 185.95/186.60 % 185.95/186.60 fof(fact_List_Omap_Oidentity,axiom, % 185.95/186.60 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_List_Omap_Oid,axiom, % 185.95/186.60 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__map,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_List_Omap_Ocompositionality,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__map,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_List_Omap_Ocomp,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_foldr__map,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__empty_I1_J,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__empty_I2_J,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__comp__None__iff,axiom, % 185.95/186.60 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) % 185.95/186.60 | ? [B_k_H] : % 185.95/186.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 185.95/186.60 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__of__map,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__of__map__keys,axiom, % 185.95/186.60 ! [V_m_2,T_c,V_xs_2,T_b] : % 185.95/186.60 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2) % 185.95/186.60 => 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 ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_finite__set,axiom, % 185.95/186.60 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_set__map,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_map__eq__conv,axiom, % 185.95/186.60 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 <=> ! [B_x] : % 185.95/186.60 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 185.95/186.60 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_Option_Omap_Ocomp,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_Option_Omap_Ocompositionality,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__comp,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__o__sum__case,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_Option_Omap_Oidentity,axiom, % 185.95/186.60 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_Option_Omap_Oid,axiom, % 185.95/186.60 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_infinite__UNIV__listI,axiom, % 185.95/186.60 ! [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)))) ). % 185.95/186.60 % 185.95/186.60 fof(fact_dom__option__map,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__Some,axiom, % 185.95/186.60 ! [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)) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__eq__Some,axiom, % 185.95/186.60 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] : % 185.95/186.60 ( 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) % 185.95/186.60 <=> ? [B_z] : % 185.95/186.60 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) % 185.95/186.60 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__None,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__is__None,axiom, % 185.95/186.60 ! [V_opt_2,V_f_2,T_b,T_c] : % 185.95/186.60 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b) % 185.95/186.60 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__o__empty,axiom, % 185.95/186.60 ! [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) ). % 185.95/186.60 % 185.95/186.60 fof(fact_option__map__o__map__upd,axiom, % 185.95/186.60 ! [V_ba_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_ba_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_ba_2))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_inj__on__map__eq__map,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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) % 186.05/186.60 <=> V_xs_2 = V_ys_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__inj__on,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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))) % 186.05/186.60 => V_xs_2 = V_ys_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__fun__upd,axiom, % 186.05/186.60 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_inj__on__mapI,axiom, % 186.05/186.60 ! [V_A_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__eq__dom,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_c,T_b] : % 186.05/186.60 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__SomeD,axiom, % 186.05/186.60 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__is__SomeD,axiom, % 186.05/186.60 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_dom__map__of__conv__image__fst,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__eq__None__iff,axiom, % 186.05/186.60 ! [V_x_2,V_xys_2,T_b,T_c] : % 186.05/186.60 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b) % 186.05/186.60 <=> ~ 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Option_Omap__def,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_WT__bodies__def,axiom, % 186.05/186.60 ( c_Com_OWT__bodies % 186.05/186.60 <=> ! [B_x] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__map__restrict,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_ran__distinct,axiom, % 186.05/186.60 ! [V_al_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__map__of__compr,axiom, % 186.05/186.60 ! [V_xs_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__map,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 186.05/186.60 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 186.05/186.60 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__inject__set,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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))) % 186.05/186.60 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 186.05/186.60 <=> 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) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__is__SomeI,axiom, % 186.05/186.60 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__eq__Some__iff,axiom, % 186.05/186.60 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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) % 186.05/186.60 <=> 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Some__eq__map__of__iff,axiom, % 186.05/186.60 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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) % 186.05/186.60 <=> 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_greaterThanLessThan__upto,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_weak__map__of__SomeI,axiom, % 186.05/186.60 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ? [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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_atLeastAtMost__upto,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__upto,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__upto,axiom, % 186.05/186.60 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_atLeastLessThan__upto,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_greaterThanAtMost__upto,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nat__list__def,axiom, % 186.05/186.60 ! [V_l_2] : % 186.05/186.60 ( c_List_Onat__list(V_l_2) % 186.05/186.60 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__remove1__eq,axiom, % 186.05/186.60 ! [V_x_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1__idem,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_notin__set__remove1,axiom, % 186.05/186.60 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => ~ 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__remove1,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_ba_2,V_a_2] : % 186.05/186.60 ( V_a_2 != V_ba_2 % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_ba_2,V_xs_2)))) % 186.05/186.60 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__remove1__subset,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1__commute,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__remove1,axiom, % 186.05/186.60 ! [V_x,V_xs,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sorted__list__of__set__remove,axiom, % 186.05/186.60 ! [V_x_2,V_A_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__zip__map,axiom, % 186.05/186.60 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__zipI2,axiom, % 186.05/186.60 ! [V_xs,T_b,V_ys,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__zipI1,axiom, % 186.05/186.60 ! [V_ys,T_b,V_xs,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__same__conv__map,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__map__fst__snd,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__zip__map2,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__zip__map,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__zipE,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__zip__rightD,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__zip__leftD,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__same,axiom, % 186.05/186.60 ! [V_xs_2,V_ba_2,V_a_2,T_b] : % 186.05/186.60 ( 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_ba_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)))) % 186.05/186.60 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 & V_a_2 = V_ba_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__map2,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__map1,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__map__map,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sorted__list__of__set__insert,axiom, % 186.05/186.60 ! [V_x_2,V_A_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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)))))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__zip__upd,axiom, % 186.05/186.60 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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) % 186.05/186.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 186.05/186.60 => ( 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)) % 186.05/186.60 => 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)) ) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__zip,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__insort,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__left__comm,axiom, % 186.05/186.60 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__key__left__comm,axiom, % 186.05/186.60 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__insort,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_neq__if__length__neq,axiom, % 186.05/186.60 ! [V_ys,V_xs,T_a] : % 186.05/186.60 ( 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) % 186.05/186.60 => V_xs != V_ys ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_fun__left__comm__insort,axiom, % 186.05/186.60 ! [T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexn__length,axiom, % 186.05/186.60 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 186.05/186.60 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__map,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__eq__imp__length__eq,axiom, % 186.05/186.60 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1__insort,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_card__length,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__card,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_card__distinct,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__zip__inject,axiom, % 186.05/186.60 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 186.05/186.60 => ( 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)) % 186.05/186.60 => V_ys_2 = V_zs_2 ) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__fst__zip,axiom, % 186.05/186.60 ! [V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__snd__zip,axiom, % 186.05/186.60 ! [V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__insort,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => ( 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))) % 186.05/186.60 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__pos__if__in__set,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__eq__conv,axiom, % 186.05/186.60 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 186.05/186.60 <=> ( 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 % 186.05/186.60 & 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 ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lenlex__conv,axiom, % 186.05/186.60 ! [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)))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lenlex__def,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_finite__lists__length__eq,axiom, % 186.05/186.60 ! [V_n_2,V_A_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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))))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__eq__iff__zip__eq,axiom, % 186.05/186.60 ! [T_b,V_ys_2,V_xs_2] : % 186.05/186.60 ( V_xs_2 = V_ys_2 % 186.05/186.60 <=> ( 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) % 186.05/186.60 & ! [B_x] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__zip__is__None,axiom, % 186.05/186.60 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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) % 186.05/186.60 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__zip__is__Some,axiom, % 186.05/186.60 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 <=> ? [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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__remove1,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_dom__map__of__zip,axiom, % 186.05/186.60 ! [V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_finite__lists__length__le,axiom, % 186.05/186.60 ! [V_n_2,V_A_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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))))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nitpick_Ocard_H__def,axiom, % 186.05/186.60 ! [V_A_2,T_b] : % 186.05/186.60 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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)))) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__iff__zip,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( 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) % 186.05/186.60 & ! [B_x] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__rtrancl__refl,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__eq__len,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__rtrancl__trans,axiom, % 186.05/186.60 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => ( 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)))) % 186.05/186.60 => 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)))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__mono,axiom, % 186.05/186.60 ! [V_s_2,V_r_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrelp__listrel__eq,axiom, % 186.05/186.60 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexn_Osimps_I2_J,axiom, % 186.05/186.60 ! [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)))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_impossible__Cons,axiom, % 186.05/186.60 ! [V_x,V_ys,V_xs,T_a] : % 186.05/186.60 ( 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))) % 186.05/186.60 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__ConsD,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => ( V_y_2 = V_x_2 % 186.05/186.60 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__Cons__Cons,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_List_Oset_Osimps_I2_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__subset__Cons,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldr_Osimps_I2_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_not__Cons__self,axiom, % 186.05/186.60 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 186.05/186.60 % 186.05/186.60 fof(fact_not__Cons__self2,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Oinject,axiom, % 186.05/186.60 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ( V_a_2 = V_a_H_2 % 186.05/186.60 & V_list_2 = V_list_H_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrelp_Oequations_I2_J,axiom, % 186.05/186.60 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 186.05/186.60 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrelp_OCons,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 186.05/186.60 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map_Osimps_I2_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1_Osimps_I2_J,axiom, % 186.05/186.60 ! [V_xs,T_a,V_y,V_x] : % 186.05/186.60 ( ( V_x = V_y % 186.05/186.60 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 186.05/186.60 & ( V_x != V_y % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__key_Osimps_I2_J,axiom, % 186.05/186.60 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( ( 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))) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => 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)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct_Osimps_I2_J,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 186.05/186.60 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__Cons__code_I2_J,axiom, % 186.05/186.60 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 186.05/186.60 ( ( V_l = V_k % 186.05/186.60 => 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) ) % 186.05/186.60 & ( V_l != V_k % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osize_I4_J,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel_OCons,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ( 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))) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of_Osimps_I2_J,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__in__lex,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( ( 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)) % 186.05/186.60 & 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) ) % 186.05/186.60 | ( V_x_2 = V_y_2 % 186.05/186.60 & 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Cons,axiom, % 186.05/186.60 ! [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))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__Cons__def,axiom, % 186.05/186.60 ! [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)))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Cons1,axiom, % 186.05/186.60 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ~ ! [B_y,B_ys] : % 186.05/186.60 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 186.05/186.60 => ( 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)) % 186.05/186.60 => ~ 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Cons2,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ~ ! [B_x,B_xs] : % 186.05/186.60 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 186.05/186.60 => ( 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)) % 186.05/186.60 => ~ 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__sublist,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_pick_Osimps,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_i] : % 186.05/186.60 ( ( 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))) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__sublistI,axiom, % 186.05/186.60 ! [V_I_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__sublistD,axiom, % 186.05/186.60 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_notin__set__sublistI,axiom, % 186.05/186.60 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => ~ 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__sublist__subset,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_select__weight__cons__zero,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_pick__member,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_i_2] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__simps_I2_J,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_a) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__subtractf,axiom, % 186.05/186.60 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( class_Groups_Oab__group__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__const__mult,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] : % 186.05/186.60 ( class_Rings_Osemiring__0(T_b) % 186.05/186.60 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__mult__const,axiom, % 186.05/186.60 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( class_Rings_Osemiring__0(T_b) % 186.05/186.60 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__addf,axiom, % 186.05/186.60 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__0,axiom, % 186.05/186.60 ! [V_xs_2,T_c,T_b] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__abs,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_uminus__listsum__map,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( class_Groups_Oab__group__add(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__listsum__conv__Setsum,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_select__weight__def,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 186.05/186.60 ! [V_f_2,V_xs_2,T_b,T_c] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_c) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 186.05/186.60 ! [V_l_2,V_k_2,V_f_2,T_b] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 186.05/186.60 ! [V_j_2,V_i_2,V_f_2,T_b] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__triv,axiom, % 186.05/186.60 ! [V_xs_2,V_r_2,T_c,T_b] : % 186.05/186.60 ( class_Rings_Osemiring__1(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__map__remove1,axiom, % 186.05/186.60 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_c) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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)))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_select__weight__member,axiom, % 186.05/186.60 ! [V_s_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nitpick_Osetsum_H__def,axiom, % 186.05/186.60 ! [V_f_2,V_A_2,T_b,T_c] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_c) % 186.05/186.60 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => 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))))) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.60 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_upto_Opsimps,axiom, % 186.05/186.60 ! [V_j_2,V_i_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 186.05/186.60 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Nil2,axiom, % 186.05/186.60 ! [V_r_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Nil1,axiom, % 186.05/186.60 ! [V_r_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 186.05/186.60 ! [V_ns_2] : % 186.05/186.60 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 <=> ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 186.05/186.60 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__simps_I1_J,axiom, % 186.05/186.60 ! [T_a] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_a) % 186.05/186.60 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__is__Nil__conv,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map_Osimps_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nil__is__map__conv,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrelp_Oequations_I1_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrelp_ONil,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__not__Nil,axiom, % 186.05/186.60 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct_Osimps_I1_J,axiom, % 186.05/186.60 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1_Osimps_I1_J,axiom, % 186.05/186.60 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldr_Osimps_I1_J,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_upto__empty,axiom, % 186.05/186.60 ! [V_i,V_j] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 186.05/186.60 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__Nil,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip_Osimps_I1_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osize_I3_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__0__conv,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sorted__list__of__set__empty,axiom, % 186.05/186.60 ! [T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__empty,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__empty2,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_List_Oset_Osimps_I1_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osimps_I2_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osimps_I3_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__key_Osimps_I1_J,axiom, % 186.05/186.60 ! [V_x_2,V_f_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__empty,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__nil,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__greater__0__conv,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel_ONil,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nil__notin__lex,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nil2__notin__lex,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_upto_Osimps,axiom, % 186.05/186.60 ! [V_j,V_i] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 186.05/186.60 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__singleton,axiom, % 186.05/186.60 ! [V_x_2,T_b,V_A_2] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_upto__rec__number__of,axiom, % 186.05/186.60 ! [V_n,V_m] : % 186.05/186.60 ( ( 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))) % 186.05/186.60 => 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))) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__Nil,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__Cons__sing__Nil,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_select__weigth__select,axiom, % 186.05/186.60 ! [T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_select,axiom, % 186.05/186.60 ! [V_s_2,T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of_Osimps_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__Cons__code_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_anamorph_Osimps,axiom, % 186.05/186.60 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 186.05/186.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listset_Osimps_I1_J,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listset_Osimps_I2_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__Cons1,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__Cons,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osimps_I5_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osimps_I4_J,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_select__def,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_pick__same,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_l_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth_Osimps,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__Cons__0,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__Cons__Suc,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__map,axiom, % 186.05/186.60 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_all__set__conv__all__nth,axiom, % 186.05/186.60 ! [V_Pa_2,V_xs_2,T_b] : % 186.05/186.60 ( ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.05/186.60 <=> ! [B_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__conv__nth,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 <=> ! [B_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ! [B_j] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( B_i != B_j % 186.05/186.60 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__eq__iff__index__eq,axiom, % 186.05/186.60 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => ( 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))) % 186.05/186.60 => ( 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))) % 186.05/186.60 => ( 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) % 186.05/186.60 <=> V_i_2 = V_j_2 ) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__eq__iff__nth__eq,axiom, % 186.05/186.60 ! [T_b,V_ys_2,V_xs_2] : % 186.05/186.60 ( V_xs_2 = V_ys_2 % 186.05/186.60 <=> ( 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) % 186.05/186.60 & ! [B_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__zip,axiom, % 186.05/186.60 ! [V_ys,T_b,V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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))) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_elem__le__listsum__nat,axiom, % 186.05/186.60 ! [V_ns,V_k] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__mem,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_n_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__conv__nth,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 <=> ? [B_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__Cons_H,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_n] : % 186.05/186.60 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 186.05/186.60 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__conv__nth,axiom, % 186.05/186.60 ! [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))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__Cons__number__of,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_v] : % 186.05/186.60 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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 ) % 186.05/186.60 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__setsum__nth,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__sublist,axiom, % 186.05/186.60 ! [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))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__iff__nth,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( 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) % 186.05/186.60 & ! [B_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__zip,axiom, % 186.05/186.60 ! [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)))))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__insert__insort__key,axiom, % 186.05/186.60 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( ~ 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)))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__list__update,axiom, % 186.05/186.60 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => ( ~ 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)))))) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__list__update__neq,axiom, % 186.05/186.60 ! [V_x,V_xs,T_a,V_j,V_i] : % 186.05/186.60 ( V_i != V_j % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__id,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__code_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update_Osimps_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__nonempty,axiom, % 186.05/186.60 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__update,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_update__zip,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__list__update,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__overwrite,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__swap,axiom, % 186.05/186.60 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 186.05/186.60 ( V_i != V_i_H % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__insort__insert,axiom, % 186.05/186.60 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__beyond,axiom, % 186.05/186.60 ! [V_x,V_i,V_xs,T_a] : % 186.05/186.60 ( 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)) % 186.05/186.60 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__update,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__code_I3_J,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__code_I2_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update_Osimps_I2_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__update__subsetI,axiom, % 186.05/186.60 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__update__subset__insert,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__list__update,axiom, % 186.05/186.60 ! [V_x,V_j,V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( ( V_i = V_j % 186.05/186.60 => 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 ) % 186.05/186.60 & ( V_i != V_j % 186.05/186.60 => 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) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__same__conv,axiom, % 186.05/186.60 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 186.05/186.60 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__list__update__eq,axiom, % 186.05/186.60 ! [V_x,V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__update__memI,axiom, % 186.05/186.60 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__insert__triv,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__insort__insert,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__update__nat,axiom, % 186.05/186.60 ! [V_n,V_ns,V_k] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__insert__key__triv,axiom, % 186.05/186.60 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( 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)))) % 186.05/186.60 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_insort__insert__insort,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__Cons,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__cons__cons,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_ba_2,V_x_2,V_a_2,T_b] : % 186.05/186.60 ( 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_ba_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) % 186.05/186.60 <=> ( 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_ba_2)),V_r_2)) % 186.05/186.60 | ( V_a_2 = V_ba_2 % 186.05/186.60 & 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__append__length,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__append__length__plus,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__append,axiom, % 186.05/186.60 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__append1,axiom, % 186.05/186.60 ! [V_x,V_ys,V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__length,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1__append,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__eq__Cons__conv,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 186.05/186.60 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 186.05/186.60 | ? [B_ys_H] : % 186.05/186.60 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 186.05/186.60 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__eq__append__conv,axiom, % 186.05/186.60 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 186.05/186.60 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 186.05/186.60 | ? [B_ys_H] : % 186.05/186.60 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 186.05/186.60 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append1__eq__conv,axiom, % 186.05/186.60 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( V_xs_2 = V_ys_2 % 186.05/186.60 & V_x_2 = V_y_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__append__left__rightI,axiom, % 186.05/186.60 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_ba_2,V_a_2,T_b] : % 186.05/186.60 ( 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_ba_2)),V_r_2)) % 186.05/186.60 => 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_ba_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__Cons,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__eq__appendI,axiom, % 186.05/186.60 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 186.05/186.60 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 186.05/186.60 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 186.05/186.60 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__append,axiom, % 186.05/186.60 ! [V_ys,V_xs,T_a] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_a) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__eq__appendI,axiom, % 186.05/186.60 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 186.05/186.60 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 186.05/186.60 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 186.05/186.60 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__same__eq,axiom, % 186.05/186.60 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> V_ys_2 = V_zs_2 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_same__append__eq,axiom, % 186.05/186.60 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> V_ys_2 = V_zs_2 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__eq__append__conv2,axiom, % 186.05/186.60 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ? [B_us] : % 186.05/186.60 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 186.05/186.60 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 186.05/186.60 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 186.05/186.60 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__assoc,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__of__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldr__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__append__leftI,axiom, % 186.05/186.60 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__Nil,axiom, % 186.05/186.60 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 186.05/186.60 % 186.05/186.60 fof(fact_Nil__is__append__conv,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 186.05/186.60 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 186.05/186.60 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__Nil2,axiom, % 186.05/186.60 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 186.05/186.60 % 186.05/186.60 fof(fact_self__append__conv,axiom, % 186.05/186.60 ! [V_ys_2,T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 186.05/186.60 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_self__append__conv2,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_ys_2] : % 186.05/186.60 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__is__Nil__conv,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 186.05/186.60 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__self__conv,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 186.05/186.60 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__self__conv2,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_eq__Nil__appendI,axiom, % 186.05/186.60 ! [T_a,V_ys,V_xs] : % 186.05/186.60 ( V_xs = V_ys % 186.05/186.60 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__append,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 186.05/186.60 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 186.05/186.60 & 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__append,axiom, % 186.05/186.60 ! [V_ys,V_xs,T_a,V_n] : % 186.05/186.60 ( ( 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))) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__update__append,axiom, % 186.05/186.60 ! [V_x,V_ys,V_xs,T_a,V_n] : % 186.05/186.60 ( ( 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))) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__Nil__right,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__append,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__lex,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( 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))) % 186.05/186.60 & 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__append1,axiom, % 186.05/186.60 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__take__index__conv,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( ( 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))) % 186.05/186.60 & 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 ) % 186.05/186.60 | ? [B_i] : % 186.05/186.60 ( 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)))) % 186.05/186.60 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 186.05/186.60 & 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)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_fun__upds__append__drop,axiom, % 186.05/186.60 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_fun__upds__append2__drop,axiom, % 186.05/186.60 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__Nil2,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__Nil1,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Nil,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__eq__Nil,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__0,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sublist__upt__eq__take,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__zip,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__take,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__add__upds,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__take,axiom, % 186.05/186.60 ! [V_i,V_xs,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__take__subset,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__take__subset__set__take,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__takeD,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__apply__nontin,axiom, % 186.05/186.60 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__map,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Suc__Cons,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__1__Cons,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upd__upds__conv__if,axiom, % 186.05/186.60 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] : % 186.05/186.60 ( ( 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)))) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( ~ 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)))) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_dom__map__upds,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__all,axiom, % 186.05/186.60 ! [V_n,V_xs,T_a] : % 186.05/186.60 ( 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)) % 186.05/186.60 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__take,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__take,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n,V_i] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__Cons,axiom, % 186.05/186.60 ! [V_bs_2,V_ba_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_ba_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_ba_2)),V_as_2,V_bs_2) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Cons,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Cons_H,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_n] : % 186.05/186.60 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__list__update2__drop,axiom, % 186.05/186.60 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ( 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))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__twist,axiom, % 186.05/186.60 ! [V_bs_2,V_ba_2,V_m_2,T_c,V_as_2,V_a_2,T_b] : % 186.05/186.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2))) % 186.05/186.60 => 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_ba_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_ba_2)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Cons__number__of,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_v] : % 186.05/186.60 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_restrict__map__upds,axiom, % 186.05/186.60 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => ( 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)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Suc__conv__app__nth,axiom, % 186.05/186.60 ! [V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_snoc__listrel1__snoc__iff,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( ( 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))) % 186.05/186.60 & V_x_2 = V_y_2 ) % 186.05/186.60 | ( V_xs_2 = V_ys_2 % 186.05/186.60 & 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)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__append__leftD,axiom, % 186.05/186.60 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( ! [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)) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__acc__listrel1I,axiom, % 186.05/186.60 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 186.05/186.60 => ( 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)))) % 186.05/186.60 => 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)))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__mono,axiom, % 186.05/186.60 ! [V_s_2,V_r_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__converse,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1I2,axiom, % 186.05/186.60 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 186.05/186.60 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__eq__len,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rtrancl__listrel1__eq__len,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_not__Nil__listrel1,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_not__listrel1__Nil,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__listrel1I,axiom, % 186.05/186.60 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( ( ( 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))) % 186.05/186.60 & V_us_2 = V_vs_2 ) % 186.05/186.60 | ( V_xs_2 = V_ys_2 % 186.05/186.60 & 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))) ) ) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__listrel1__converse,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 <=> 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__reflcl__if__listrel1,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__listrel1__Cons,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( ( 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)) % 186.05/186.60 & V_xs_2 = V_ys_2 ) % 186.05/186.60 | ( V_x_2 = V_y_2 % 186.05/186.60 & 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1I1,axiom, % 186.05/186.60 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__subset__listrel,axiom, % 186.05/186.60 ! [V_r_H_2,V_r_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1I,axiom, % 186.05/186.60 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ( 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)) % 186.05/186.60 => ( 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)) % 186.05/186.60 => 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))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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)))) % 186.05/186.60 => 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)))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1__iff__update,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ? [B_y,B_n] : % 186.05/186.60 ( 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)) % 186.05/186.60 & 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))) % 186.05/186.60 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel1E,axiom, % 186.05/186.60 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ~ ! [B_x,B_y] : % 186.05/186.60 ( 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)) % 186.05/186.60 => ! [B_us,B_vs] : % 186.05/186.60 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 186.05/186.60 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate1__def,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_upd__conv__take__nth__drop,axiom, % 186.05/186.60 ! [V_a,V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__drop__subset__set__drop,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__eq__Nil,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__all,axiom, % 186.05/186.60 ! [V_n,V_xs,T_a] : % 186.05/186.60 ( 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)) % 186.05/186.60 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__via__drop,axiom, % 186.05/186.60 ! [V_ys,V_y,V_xs,V_n,T_a] : % 186.05/186.60 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 186.05/186.60 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__drop,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__rotate1,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__1__Cons,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Suc__Cons,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__map,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__dropD,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__rotate1,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__drop__subset,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct1__rotate,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 186.05/186.60 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__drop,axiom, % 186.05/186.60 ! [V_i,V_xs,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__drop,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__0,axiom, % 186.05/186.60 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__zip,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Nil,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate1__is__Nil__conv,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__drop,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__take,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__take__drop__id,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__eq__conv__conj,axiom, % 186.05/186.60 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 186.05/186.60 <=> ( 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) % 186.05/186.60 & 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Cons,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Cons_H,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_n] : % 186.05/186.60 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__drop,axiom, % 186.05/186.60 ! [V_xs,T_a,V_i,V_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__eq__append__conv__if,axiom, % 186.05/186.60 ! [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] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ( ( 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))) % 186.05/186.60 => ( 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) % 186.05/186.60 & 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) ) ) % 186.05/186.60 & ( ~ 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))) % 186.05/186.60 => ( 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 % 186.05/186.60 & 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 ) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__drop_H,axiom, % 186.05/186.60 ! [V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__simps,axiom, % 186.05/186.60 ! [V_xs,V_x,T_b,T_a] : % 186.05/186.60 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 186.05/186.60 & 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Cons__number__of,axiom, % 186.05/186.60 ! [V_xs,V_x,T_a,V_v] : % 186.05/186.60 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__add,axiom, % 186.05/186.60 ! [V_xs,T_a,V_j,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate1__length01,axiom, % 186.05/186.60 ! [V_xs,T_a] : % 186.05/186.60 ( 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))) % 186.05/186.60 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__append1,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_zip__append2,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_id__take__nth__drop,axiom, % 186.05/186.60 ! [V_xs,T_a,V_i] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__hd__drop,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__drop__conv__nth,axiom, % 186.05/186.60 ! [V_n,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => ( 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))) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__map,axiom, % 186.05/186.60 ! [V_f_2,T_c,T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd_Osimps,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__append2,axiom, % 186.05/186.60 ! [V_ys,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__append,axiom, % 186.05/186.60 ! [V_ys,T_a,V_xs] : % 186.05/186.60 ( ( V_xs = c_List_Olist_ONil(T_a) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__in__set,axiom, % 186.05/186.60 ! [T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__conv__nth,axiom, % 186.05/186.60 ! [T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate1__hd__tl,axiom, % 186.05/186.60 ! [T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_hd__rotate__conv__nth,axiom, % 186.05/186.60 ! [V_n,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__Suc,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__tl,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl__drop,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl__append2,axiom, % 186.05/186.60 ! [V_ys,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__rotate,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__conv__mod,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl_Osimps_I2_J,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__map,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__tl,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__rotate,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__rotate,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 186.05/186.60 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__tl,axiom, % 186.05/186.60 ! [V_xs,T_a] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__rotate,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl_Osimps_I1_J,axiom, % 186.05/186.60 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__is__Nil__conv,axiom, % 186.05/186.60 ! [V_xs_2,V_n_2,T_b] : % 186.05/186.60 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.60 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__tl,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__def,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__Suc,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate1__rotate__swap,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl__append,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate0,axiom, % 186.05/186.60 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__add,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__id,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n] : % 186.05/186.60 ( 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) % 186.05/186.60 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__length01,axiom, % 186.05/186.60 ! [V_n,V_xs,T_a] : % 186.05/186.60 ( 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))) % 186.05/186.60 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__tl,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_tl__take,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__Suc,axiom, % 186.05/186.60 ! [V_n,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_rotate__drop__take,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_fold1__set,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 186.05/186.60 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osize_I2_J,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__Nil,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldr__conv__foldl,axiom, % 186.05/186.60 ! [V_a_2,V_xs_2,T_b] : % 186.05/186.60 ( class_Groups_Oab__semigroup__add(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__absorb0,axiom, % 186.05/186.60 ! [V_zs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__assoc,axiom, % 186.05/186.60 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 186.05/186.60 ( class_Groups_Osemigroup__add(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_start__le__sum,axiom, % 186.05/186.60 ! [V_ns_2,V_n_2,V_m_2] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__map,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__size__map,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__Cons,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__append,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__foldl,axiom, % 186.05/186.60 ! [T_b] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__foldr1,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_foldl__foldr1__lemma,axiom, % 186.05/186.60 ! [V_xs_2,V_a_2,T_b] : % 186.05/186.60 ( class_Groups_Omonoid__add(T_b) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sum__eq__0__conv,axiom, % 186.05/186.60 ! [V_ns_2,V_m_2] : % 186.05/186.60 ( 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) % 186.05/186.60 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.60 & ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 186.05/186.60 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list_Osize_I1_J,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 186.05/186.60 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 186.05/186.60 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Sup__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Inf__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,T_b] : % 186.05/186.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Sup__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Lattices_Olattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Inf__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Lattices_Olattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Min__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Max__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_min__max_OInf__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_min__max_OSup__fin__set__fold,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( class_Orderings_Olinorder(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_SUPR__set__fold,axiom, % 186.05/186.60 ! [V_f_2,V_xs_2,T_c,T_b] : % 186.05/186.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_INFI__set__fold,axiom, % 186.05/186.60 ! [V_f_2,V_xs_2,T_c,T_b] : % 186.05/186.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__size__estimation,axiom, % 186.05/186.60 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__size__estimation_H,axiom, % 186.05/186.60 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 186.05/186.60 => 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__upds__fold__map__upd,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_elem__le__sum,axiom, % 186.05/186.60 ! [V_ns_2,V_n_2] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__size__conv__listsum,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__subset,axiom, % 186.05/186.60 ! [V_A_2,V_r_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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))))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__accI,axiom, % 186.05/186.60 ! [V_r_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists_ONil,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_equiv__listrel,axiom, % 186.05/186.60 ! [V_r_2,V_A_2,T_b] : % 186.05/186.60 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listrel__refl__on,axiom, % 186.05/186.60 ! [V_r_2,V_A_2,T_b] : % 186.05/186.60 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__UNIV,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__in__lists__conv,axiom, % 186.05/186.60 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 186.05/186.60 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__mono,axiom, % 186.05/186.60 ! [V_B_2,V_A_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_Cons__in__lists__iff,axiom, % 186.05/186.60 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 186.05/186.60 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__lists__conv__set,axiom, % 186.05/186.60 ! [V_A_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 186.05/186.60 <=> ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__eq__set,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__empty,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists__accD,axiom, % 186.05/186.60 ! [V_r_2,V_xs_2,T_b] : % 186.05/186.60 ( 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)))) % 186.05/186.60 => 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)))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__append__rightI,axiom, % 186.05/186.60 ! [V_r_2,V_x_2,T_b,V_y_2] : % 186.05/186.60 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__Nil__left,axiom, % 186.05/186.60 ! [V_r_2,V_y_2,T_b] : % 186.05/186.60 ( 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))) % 186.05/186.60 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__list__update,axiom, % 186.05/186.60 ! [V_x,V_k,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => ( ( 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)) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 186.05/186.60 & ( 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)) % 186.05/186.60 => 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) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_listsum__mono,axiom, % 186.05/186.60 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 186.05/186.60 ( ( class_Groups_Omonoid__add(T_c) % 186.05/186.60 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 186.05/186.60 => ( ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 186.05/186.60 => 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)))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__append,axiom, % 186.05/186.60 ! [V_xs,T_a,V_ys] : % 186.05/186.60 ( ( V_ys = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 186.05/186.60 & ( V_ys != c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__appendR,axiom, % 186.05/186.60 ! [V_xs,T_a,V_ys] : % 186.05/186.60 ( V_ys != c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__appendL,axiom, % 186.05/186.60 ! [V_xs,T_a,V_ys] : % 186.05/186.60 ( V_ys = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last_Osimps,axiom, % 186.05/186.60 ! [V_x,T_a,V_xs] : % 186.05/186.60 ( ( V_xs = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 186.05/186.60 & ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__ConsR,axiom, % 186.05/186.60 ! [V_x,T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__ConsL,axiom, % 186.05/186.60 ! [V_x,T_a,V_xs] : % 186.05/186.60 ( V_xs = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__map,axiom, % 186.05/186.60 ! [V_f_2,T_c,T_b,V_xs_2] : % 186.05/186.60 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => 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)) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__in__set,axiom, % 186.05/186.60 ! [T_b,V_as_2] : % 186.05/186.60 ( V_as_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__snoc,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__drop,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_last__conv__nth,axiom, % 186.05/186.60 ! [T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__linear,axiom, % 186.05/186.60 ! [V_y_2,V_x_2,V_r_2,T_b] : % 186.05/186.60 ( ! [B_a,B_b] : % 186.05/186.60 ( 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)) % 186.05/186.60 | B_a = B_b % 186.05/186.60 | 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)) ) % 186.05/186.60 => ( 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))) % 186.05/186.60 | V_x_2 = V_y_2 % 186.05/186.60 | 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))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lexord__irreflexive,axiom, % 186.05/186.60 ! [V_y_2,V_r_2,T_b] : % 186.05/186.60 ( ! [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)) % 186.05/186.60 => ~ 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_lists_Osimps,axiom, % 186.05/186.60 ! [V_A_2,V_a_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 186.05/186.60 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 186.05/186.60 | ? [B_a,B_l] : % 186.05/186.60 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 186.05/186.60 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 186.05/186.60 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_list__size__pointwise,axiom, % 186.05/186.60 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 186.05/186.60 ( ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 186.05/186.60 => 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))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__take,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_nth__take__lemma,axiom, % 186.05/186.60 ! [V_ys,V_xs,T_a,V_k] : % 186.05/186.60 ( 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))) % 186.05/186.60 => ( 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))) % 186.05/186.60 => ( ! [B_i] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 186.05/186.60 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 186.05/186.60 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_map__butlast,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__butlast,axiom, % 186.05/186.60 ! [T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast_Osimps_I1_J,axiom, % 186.05/186.60 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__butlastD,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 186.05/186.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast_Osimps_I2_J,axiom, % 186.05/186.60 ! [V_x,T_a,V_xs] : % 186.05/186.60 ( ( V_xs = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 186.05/186.60 & ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__append,axiom, % 186.05/186.60 ! [V_xs,T_a,V_ys] : % 186.05/186.60 ( ( V_ys = c_List_Olist_ONil(T_a) % 186.05/186.60 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 186.05/186.60 & ( V_ys != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__drop,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_drop__butlast,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_in__set__butlast__appendI,axiom, % 186.05/186.60 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 186.05/186.60 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 186.05/186.60 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 186.05/186.60 => 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))))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__snoc,axiom, % 186.05/186.60 ! [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 ). % 186.05/186.60 % 186.05/186.60 fof(fact_take__butlast,axiom, % 186.05/186.60 ! [V_xs,T_a,V_n] : % 186.05/186.60 ( 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))) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__butlast,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__conv__take,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_butlast__list__update,axiom, % 186.05/186.60 ! [V_x,V_xs,T_a,V_k] : % 186.05/186.60 ( ( 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)) % 186.05/186.60 => 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) ) % 186.05/186.60 & ( 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)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_append__butlast__last__id,axiom, % 186.05/186.60 ! [T_a,V_xs] : % 186.05/186.60 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.60 => 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 ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_snoc__eq__iff__butlast,axiom, % 186.05/186.60 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 186.05/186.60 ( 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 % 186.05/186.60 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 186.05/186.60 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 186.05/186.60 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_transpose__aux__max,axiom, % 186.05/186.60 ! [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)))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_partition__set,axiom, % 186.05/186.60 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 186.05/186.60 ( 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) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__is__subset,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_length__filter__le,axiom, % 186.05/186.60 ! [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))) ). % 186.05/186.60 % 186.05/186.60 fof(fact_set__filter,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__append,axiom, % 186.05/186.60 ! [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)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_sum__length__filter__compl,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter_Osimps_I2_J,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.05/186.60 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.60 => 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)) ) % 186.05/186.60 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__id__conv,axiom, % 186.05/186.60 ! [V_xs_2,V_Pa_2,T_b] : % 186.05/186.60 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 186.05/186.60 <=> ! [B_x] : % 186.05/186.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.60 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__insort__triv,axiom, % 186.05/186.60 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 186.05/186.60 ( class_Orderings_Olinorder(T_c) % 186.05/186.60 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.60 => 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) ) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_distinct__filter,axiom, % 186.05/186.60 ! [V_Pa_2,V_xs_2,T_b] : % 186.05/186.60 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.60 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__remove1,axiom, % 186.05/186.60 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_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_Q_2),V_xs_2)) ). % 186.05/186.60 % 186.05/186.60 fof(fact_remove1__filter__not,axiom, % 186.05/186.60 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.05/186.60 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.60 => 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) ) ). % 186.05/186.60 % 186.05/186.60 fof(fact_filter__filter,axiom, % 186.05/186.60 ! [V_xs_2,V_Q_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Q_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_Q_2)),V_Pa_2)),V_xs_2) ). % 186.05/186.60 % 186.05/186.60 fof(fact_partition__filter1,axiom, % 186.05/186.60 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__empty__conv,axiom, % 186.05/186.61 ! [V_xs_2,V_Pa_2,T_b] : % 186.05/186.61 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.61 <=> ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter_Osimps_I1_J,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_partition__filter__conv,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_partition__filter2,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__map,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__filter__map,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__filter__less,axiom, % 186.05/186.61 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => 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))) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_set__minus__filter__out,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_partition__P,axiom, % 186.05/186.61 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 186.05/186.61 ( 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) % 186.05/186.61 => ( ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 186.05/186.61 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.05/186.61 & ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 186.05/186.61 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_partition_Osimps_I1_J,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__in__sublist,axiom, % 186.05/186.61 ! [V_s_2,V_xs_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_partition_Osimps_I2_J,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__filter__conv__card,axiom, % 186.05/186.61 ! [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))))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__filter__def,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__max__length,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__of__filter__in,axiom, % 186.05/186.61 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] : % 186.05/186.61 ( 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) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2)) % 186.05/186.61 => 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) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__map__map,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__filter__simps_I1_J,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__filter__simps_I2_J,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Osimps_I1_J,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__empty,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.05/186.61 <=> ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 186.05/186.61 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Osimps_I2_J,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sublist__shift__lemma__Suc,axiom, % 186.05/186.61 ! [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)))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_select__weigth__drop__zero,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_pick__drop__zero,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_nth__transpose,axiom, % 186.05/186.61 ! [V_xs_2,T_b,V_i_2] : % 186.05/186.61 ( 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)))) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__transpose,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__filter__map__filter,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_insort__key__remove1,axiom, % 186.05/186.61 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 186.05/186.61 ( class_Orderings_Olinorder(T_c) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 186.05/186.61 => ( 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 % 186.05/186.61 => 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 ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sublist__def,axiom, % 186.05/186.61 ! [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))))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted_ONil,axiom, % 186.05/186.61 ! [T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__single,axiom, % 186.05/186.61 ! [V_x,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__same,axiom, % 186.05/186.61 ! [V_xs_2,V_g_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__map__same,axiom, % 186.05/186.61 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__filter,axiom, % 186.05/186.61 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.05/186.61 => 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))) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__upt,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_last__upt,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__butlast,axiom, % 186.05/186.61 ! [V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_take__upt,axiom, % 186.05/186.61 ! [V_n,V_m,V_i] : % 186.05/186.61 ( 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)) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__conv__Nil,axiom, % 186.05/186.61 ! [V_i,V_j] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 186.05/186.61 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__eq__Nil__conv,axiom, % 186.05/186.61 ! [V_j_2,V_i_2] : % 186.05/186.61 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 186.05/186.61 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__many__eq,axiom, % 186.05/186.61 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( 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))) % 186.05/186.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 186.05/186.61 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__many,axiom, % 186.05/186.61 ! [V_zs,V_y,V_x,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 186.05/186.61 => 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))) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__add__eq__append,axiom, % 186.05/186.61 ! [V_k,V_j,V_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__Suc__append,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__Suc,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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))) ) % 186.05/186.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__Cons,axiom, % 186.05/186.61 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 186.05/186.61 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 & ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__append,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 186.05/186.61 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 186.05/186.61 & ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ! [B_xa] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 186.05/186.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_drop__upt,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__drop,axiom, % 186.05/186.61 ! [V_n,V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_hd__upt,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__insort__insert,axiom, % 186.05/186.61 ! [V_x_2,V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 => 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)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__rec,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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)) ) % 186.05/186.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__conv__Cons,axiom, % 186.05/186.61 ! [V_j,V_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_atLeastLessThan__upt,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_set__upt,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__distinct__set__unique,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 186.05/186.61 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 186.05/186.61 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 186.05/186.61 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__insort,axiom, % 186.05/186.61 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( 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)) % 186.05/186.61 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_distinct__upt,axiom, % 186.05/186.61 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__remove1,axiom, % 186.05/186.61 ! [V_a,V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__upt,axiom, % 186.05/186.61 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__upto,axiom, % 186.05/186.61 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__list__of__set__range,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__0,axiom, % 186.05/186.61 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted_Oequations_I1_J,axiom, % 186.05/186.61 ! [T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__take,axiom, % 186.05/186.61 ! [V_n,V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__tl,axiom, % 186.05/186.61 ! [V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__rec__number__of,axiom, % 186.05/186.61 ! [V_n,V_m] : % 186.05/186.61 ( ( 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))) % 186.05/186.61 => 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))) ) % 186.05/186.61 & ( ~ 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))) % 186.05/186.61 => 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) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__insort__key,axiom, % 186.05/186.61 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( 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))) % 186.05/186.61 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__map__remove1,axiom, % 186.05/186.61 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.05/186.61 => 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))) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__Suc__upt,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__insort__insert__key,axiom, % 186.05/186.61 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.05/186.61 => 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))) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_upt__eq__Cons__conv,axiom, % 186.05/186.61 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 186.05/186.61 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 186.05/186.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 186.05/186.61 & V_i_2 = V_x_2 % 186.05/186.61 & 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 ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__insort,axiom, % 186.05/186.61 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.05/186.61 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => 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)) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__nth,axiom, % 186.05/186.61 ! [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 ). % 186.05/186.61 % 186.05/186.61 fof(fact_atLeastAtMost__upt,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_atLeast__upt,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 186.05/186.61 ! [V_n_2,V_m_2,V_f_2,T_b] : % 186.05/186.61 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 186.05/186.61 ! [V_n_2,V_m_2,V_f_2,T_b] : % 186.05/186.61 ( class_Groups_Ocomm__monoid__add(T_b) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_nth__upt,axiom, % 186.05/186.61 ! [V_j,V_k,V_i] : % 186.05/186.61 ( 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)) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_greaterThanAtMost__upt,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted_Oequations_I2_J,axiom, % 186.05/186.61 ! [V_a1_2,V_a2_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 186.05/186.61 <=> ( ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 186.05/186.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 186.05/186.61 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_greaterThanLessThan__upt,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_nth__map__upt,axiom, % 186.05/186.61 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__list__of__set,axiom, % 186.05/186.61 ! [V_A_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.05/186.61 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 186.05/186.61 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 186.05/186.61 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_atMost__upto,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_insort__remove1,axiom, % 186.05/186.61 ! [V_xs_2,V_a_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 => 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 ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__nth__mono,axiom, % 186.05/186.61 ! [V_j,V_i,V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => ( 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))) % 186.05/186.61 => 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))) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__equals__nth__mono,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 <=> ! [B_j] : % 186.05/186.61 ( 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))) % 186.05/186.61 => ! [B_i] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 186.05/186.61 => 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))) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__sorted__distinct__set__unique,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 186.05/186.61 ( class_Orderings_Olinorder(T_c) % 186.05/186.61 => ( 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))) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 186.05/186.61 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 186.05/186.61 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 186.05/186.61 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 186.05/186.61 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sublist__shift__lemma,axiom, % 186.05/186.61 ! [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))))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__rectangle,axiom, % 186.05/186.61 ! [V_n_2,T_b,V_xs_2] : % 186.05/186.61 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.05/186.61 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 186.05/186.61 => ( ! [B_i] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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 ) % 186.05/186.61 => 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)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Opsimps_I2_J,axiom, % 186.05/186.61 ! [V_xss_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Opsimps_I1_J,axiom, % 186.05/186.61 ! [T_b] : % 186.05/186.61 ( 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)))) % 186.05/186.61 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__column,axiom, % 186.05/186.61 ! [V_i_2,V_xs_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => ( 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))) % 186.05/186.61 => 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) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__aux__filter__head,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_inj__on__rev,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__concat,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__concat,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__eq__Cons__iff,axiom, % 186.05/186.61 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 186.05/186.61 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 186.05/186.61 <=> 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev_Osimps_I2_J,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat_Osimps_I2_J,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__singleton__conv,axiom, % 186.05/186.61 ! [V_x_2,V_xs_2,T_b] : % 186.05/186.61 ( 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)) % 186.05/186.61 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_singleton__rev__conv,axiom, % 186.05/186.61 ! [V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( 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) % 186.05/186.61 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__eq__Nil__conv,axiom, % 186.05/186.61 ! [V_xss_2,T_b] : % 186.05/186.61 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 186.05/186.61 <=> ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 186.05/186.61 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_Nil__eq__concat__conv,axiom, % 186.05/186.61 ! [V_xss_2,T_b] : % 186.05/186.61 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 186.05/186.61 <=> ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 186.05/186.61 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev_Osimps_I1_J,axiom, % 186.05/186.61 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat_Osimps_I1_J,axiom, % 186.05/186.61 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 186.05/186.61 % 186.05/186.61 fof(fact_Nil__is__rev__conv,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 186.05/186.61 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__is__Nil__conv,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 186.05/186.61 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__concat,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__map,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__concat,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__conv__foldl,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__foldl__cons,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_foldl__conv__concat,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_distinct__rev,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 186.05/186.61 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__append,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__append,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_set__concat,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__rev,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_listsum__rev,axiom, % 186.05/186.61 ! [V_xs,T_a] : % 186.05/186.61 ( class_Groups_Ocomm__monoid__add(T_a) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__is__rev__conv,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 186.05/186.61 <=> V_xs_2 = V_ys_2 ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__swap,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 186.05/186.61 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__rev__ident,axiom, % 186.05/186.61 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 186.05/186.61 % 186.05/186.61 fof(fact_foldr__foldl,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_foldl__foldr,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_set__rev,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_zip__rev,axiom, % 186.05/186.61 ! [V_ys,T_b,V_xs,T_a] : % 186.05/186.61 ( 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) % 186.05/186.61 => 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)) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__filter,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_last__rev,axiom, % 186.05/186.61 ! [T_a,V_xs] : % 186.05/186.61 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.61 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_hd__rev,axiom, % 186.05/186.61 ! [T_a,V_xs] : % 186.05/186.61 ( V_xs != c_List_Olist_ONil(T_a) % 186.05/186.61 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__transpose,axiom, % 186.05/186.61 ! [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)))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__take,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__drop,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rotate__rev,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Osimps_I3_J,axiom, % 186.05/186.61 ! [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))))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__nth,axiom, % 186.05/186.61 ! [V_xs,T_a,V_n] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__injective,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 186.05/186.61 => ( 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) % 186.05/186.61 => ( ! [B_x] : % 186.05/186.61 ( 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)))) % 186.05/186.61 => 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)) ) % 186.05/186.61 => V_xs_2 = V_ys_2 ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__eq__concat__iff,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,T_b] : % 186.05/186.61 ( ! [B_x] : % 186.05/186.61 ( 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)))) % 186.05/186.61 => 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)) ) % 186.05/186.61 => ( 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) % 186.05/186.61 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 186.05/186.61 <=> V_xs_2 = V_ys_2 ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_rev__update,axiom, % 186.05/186.61 ! [V_y,V_xs,T_a,V_k] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_concat__map__singleton,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__rev__nth__mono,axiom, % 186.05/186.61 ! [V_j,V_i,V_xs,T_a] : % 186.05/186.61 ( class_Orderings_Olinorder(T_a) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.05/186.61 => ( 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))) % 186.05/186.61 => 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))) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_foldr__max__sorted,axiom, % 186.05/186.61 ! [V_y_2,V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 186.05/186.61 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 186.05/186.61 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 186.05/186.61 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.61 => 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) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose_Opsimps_I3_J,axiom, % 186.05/186.61 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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))))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__transpose__sorted,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.05/186.61 => 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) ) % 186.05/186.61 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.05/186.61 => 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))) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__column__length,axiom, % 186.05/186.61 ! [V_i_2,V_xs_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => ( 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))) % 186.05/186.61 => 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)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__aux__filter__tail,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_nth__nth__transpose__sorted,axiom, % 186.05/186.61 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => ( 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)))) % 186.05/186.61 => ( 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)))) % 186.05/186.61 => 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) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transpose__transpose,axiom, % 186.05/186.61 ! [V_xs_2,T_b] : % 186.05/186.61 ( 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))) % 186.05/186.61 => 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) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 186.05/186.61 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__map,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_return__list__def,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_zip__takeWhile__snd,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_zip__takeWhile__fst,axiom, % 186.05/186.61 ! [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)) ). % 186.05/186.61 % 186.05/186.61 fof(fact_set__takeWhileD,axiom, % 186.05/186.61 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 186.05/186.61 ( 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)))) % 186.05/186.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__eq__all__conv,axiom, % 186.05/186.61 ! [V_xs_2,V_Pa_2,T_b] : % 186.05/186.61 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 186.05/186.61 <=> ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__takeWhile__le,axiom, % 186.05/186.61 ! [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))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__eq__take,axiom, % 186.05/186.61 ! [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) ). % 186.05/186.61 % 186.05/186.61 fof(fact_distinct__takeWhile,axiom, % 186.05/186.61 ! [V_Pa_2,V_xs_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.61 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile_Osimps_I1_J,axiom, % 186.05/186.61 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 186.05/186.61 % 186.05/186.61 fof(fact_sorted__takeWhile,axiom, % 186.05/186.61 ! [V_Pa_2,V_xs_2,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.05/186.61 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile_Osimps_I2_J,axiom, % 186.05/186.61 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.05/186.61 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) % 186.05/186.61 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__tail,axiom, % 186.05/186.61 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__append1,axiom, % 186.05/186.61 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.05/186.61 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.05/186.61 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_nth__length__takeWhile,axiom, % 186.05/186.61 ! [V_xs_2,V_Pa_2,T_b] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.05/186.61 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__nth,axiom, % 186.05/186.61 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 186.05/186.61 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_map__upds__def,axiom, % 186.05/186.61 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_takeWhile__not__last,axiom, % 186.05/186.61 ! [T_b,V_xs_2] : % 186.05/186.61 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.05/186.61 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.05/186.61 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 186.05/186.61 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 186.05/186.61 ( class_Orderings_Olinorder(T_b) % 186.05/186.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 186.05/186.61 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_transfer__nat__int__list__return__embed,axiom, % 186.05/186.61 ! [V_l] : % 186.05/186.61 ( c_List_Onat__list(V_l) % 186.05/186.61 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__remdups__concat,axiom, % 186.05/186.61 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_distinct__remdups,axiom, % 186.05/186.61 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 186.05/186.61 % 186.05/186.61 fof(fact_length__remdups__leq,axiom, % 186.05/186.61 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ). % 186.05/186.61 % 186.05/186.61 %----Arity declarations (201) % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 186.05/186.61 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Obounded__lattice(T_1) % 186.05/186.61 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 186.05/186.61 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Obounded__lattice(T_1) % 186.05/186.61 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Obounded__lattice(T_1) % 186.05/186.61 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Olattice(T_1) % 186.05/186.61 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Olattice(T_1) % 186.05/186.61 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Odistrib__lattice(T_1) % 186.05/186.61 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Oboolean__algebra(T_1) % 186.05/186.61 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Orderings_Opreorder,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Orderings_Opreorder(T_1) % 186.05/186.61 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Finite__Set_Ofinite,axiom, % 186.05/186.61 ! [T_1,T_2] : % 186.05/186.61 ( ( class_Finite__Set_Ofinite(T_2) % 186.05/186.61 & class_Finite__Set_Ofinite(T_1) ) % 186.05/186.61 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Lattices_Olattice,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Lattices_Olattice(T_1) % 186.05/186.61 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Orderings_Oorder,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Orderings_Oorder(T_1) % 186.05/186.61 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Orderings_Otop,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Orderings_Otop(T_1) % 186.05/186.61 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Orderings_Oord,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Orderings_Oord(T_1) % 186.05/186.61 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Orderings_Obot,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Orderings_Obot(T_1) % 186.05/186.61 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Groups_Ouminus,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Groups_Ouminus(T_1) % 186.05/186.61 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_fun__Groups_Ominus,axiom, % 186.05/186.61 ! [T_2,T_1] : % 186.05/186.61 ( class_Groups_Ominus(T_1) % 186.05/186.61 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 186.05/186.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 186.05/186.61 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 186.05/186.61 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 186.05/186.61 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 186.05/186.61 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 186.05/186.61 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 186.05/186.61 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 186.05/186.61 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 186.05/186.61 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 186.05/186.61 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 186.05/186.61 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 186.05/186.61 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 186.05/186.61 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 186.05/186.61 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 186.05/186.61 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 186.05/186.61 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 186.05/186.61 class_Divides_Osemiring__div(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 186.05/186.61 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 186.05/186.61 class_Groups_Oab__group__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 186.05/186.61 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 186.05/186.61 class_Rings_Oordered__ring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 186.05/186.61 class_Orderings_Opreorder(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 186.05/186.61 class_Orderings_Olinorder(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 186.05/186.61 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 186.05/186.61 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 186.05/186.61 class_Groups_Omonoid__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 186.05/186.61 class_Smallcheck_Osmall(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 186.05/186.61 class_Rings_Osemiring__1(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 186.05/186.61 class_Rings_Osemiring__0(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 186.05/186.61 class_Lattices_Olattice(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 186.05/186.61 class_Groups_Ogroup__add(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 186.05/186.61 class_Divides_Oring__div(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 186.05/186.61 class_Rings_Omult__zero(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 186.05/186.61 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 186.05/186.61 class_Orderings_Oorder(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 186.05/186.61 class_Int_Oring__char__0(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 186.05/186.61 class_Int_Onumber__ring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 186.05/186.61 class_Rings_Osemiring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Orderings_Oord,axiom, % 186.05/186.61 class_Orderings_Oord(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 186.05/186.61 class_Groups_Ouminus(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 186.05/186.61 class_Groups_Osgn__if(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 186.05/186.61 class_Groups_Oabs__if(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 186.05/186.61 class_Rings_Oring__1(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ominus,axiom, % 186.05/186.61 class_Groups_Ominus(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Power_Opower,axiom, % 186.05/186.61 class_Power_Opower(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Ozero,axiom, % 186.05/186.61 class_Groups_Ozero(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oring,axiom, % 186.05/186.61 class_Rings_Oring(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Oidom,axiom, % 186.05/186.61 class_Rings_Oidom(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Int_Onumber,axiom, % 186.05/186.61 class_Int_Onumber(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Groups_Oone,axiom, % 186.05/186.61 class_Groups_Oone(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Int__Oint__Rings_Odvd,axiom, % 186.05/186.61 class_Rings_Odvd(tc_Int_Oint) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 186.05/186.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 186.05/186.61 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 186.05/186.61 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 186.05/186.61 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 186.05/186.61 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 186.05/186.61 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 186.05/186.61 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 186.05/186.61 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 186.05/186.61 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 186.05/186.61 class_Orderings_Owellorder(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 186.05/186.61 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 186.05/186.61 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 186.05/186.61 class_Orderings_Opreorder(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 186.05/186.61 class_Orderings_Olinorder(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 186.05/186.61 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 186.05/186.61 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 186.05/186.61 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 186.05/186.61 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 186.05/186.61 class_Lattices_Olattice(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 186.05/186.61 class_Rings_Omult__zero(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 186.05/186.61 class_Orderings_Oorder(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 186.05/186.61 class_Rings_Osemiring(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 186.05/186.61 class_Orderings_Oord(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 186.05/186.61 class_Orderings_Obot(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 186.05/186.61 class_Groups_Ominus(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Power_Opower,axiom, % 186.05/186.61 class_Power_Opower(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 186.05/186.61 class_Groups_Ozero(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Int_Onumber,axiom, % 186.05/186.61 class_Int_Onumber(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Groups_Oone,axiom, % 186.05/186.61 class_Groups_Oone(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 186.05/186.61 class_Rings_Odvd(tc_Nat_Onat) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 186.05/186.61 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 186.05/186.61 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 186.05/186.61 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 186.05/186.61 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 186.05/186.61 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 186.05/186.61 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 186.05/186.61 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 186.05/186.61 class_Orderings_Opreorder(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 186.05/186.61 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 186.05/186.61 class_Lattices_Olattice(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 186.05/186.61 class_Orderings_Oorder(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 186.05/186.61 class_Orderings_Otop(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 186.05/186.61 class_Orderings_Oord(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 186.05/186.61 class_Orderings_Obot(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 186.05/186.61 class_Groups_Ouminus(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 186.05/186.61 class_Groups_Ominus(tc_HOL_Obool) ). % 186.05/186.61 % 186.05/186.61 fof(arity_sum__Finite__Set_Ofinite,axiom, % 186.05/186.61 ! [T_1,T_2] : % 186.05/186.61 ( ( class_Finite__Set_Ofinite(T_2) % 186.05/186.61 & class_Finite__Set_Ofinite(T_1) ) % 186.05/186.61 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 186.05/186.61 ! [T_1] : % 186.05/186.61 ( class_Finite__Set_Ofinite(T_1) % 186.05/186.61 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_prod__Finite__Set_Ofinite,axiom, % 186.05/186.61 ! [T_1,T_2] : % 186.05/186.61 ( ( class_Finite__Set_Ofinite(T_2) % 186.05/186.61 & class_Finite__Set_Ofinite(T_1) ) % 186.05/186.61 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_prod__Smallcheck_Osmall,axiom, % 186.05/186.61 ! [T_1,T_2] : % 186.05/186.61 ( ( class_Smallcheck_Osmall(T_2) % 186.05/186.61 & class_Smallcheck_Osmall(T_1) ) % 186.05/186.61 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 186.05/186.61 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 186.05/186.61 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 186.05/186.61 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 186.05/186.61 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 186.05/186.61 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 186.05/186.61 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 186.05/186.61 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 186.05/186.61 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 186.05/186.61 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 186.05/186.61 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 186.05/186.61 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 186.05/186.61 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 186.05/186.61 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 186.05/186.61 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 186.05/186.61 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 186.05/186.61 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 186.05/186.61 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 186.05/186.61 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 186.05/186.61 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 186.05/186.61 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 186.05/186.61 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 186.05/186.61 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 186.05/186.61 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 186.05/186.61 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 186.05/186.61 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 186.05/186.61 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 186.05/186.61 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 186.05/186.61 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 186.05/186.61 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 186.05/186.61 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 186.05/186.61 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 186.05/186.61 % 186.05/186.61 %----Helper facts (20) % 186.05/186.61 fof(help_c__COMBI__1,axiom, % 186.05/186.61 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 186.05/186.61 % 186.05/186.61 fof(help_c__COMBK__1,axiom, % 186.05/186.61 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 186.05/186.61 % 186.05/186.61 fof(help_c__COMBB__1,axiom, % 186.05/186.61 ! [V_R_2,V_Q_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_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__COMBC__1,axiom, % 186.05/186.61 ! [V_R_2,V_Q_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_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__COMBS__1,axiom, % 186.05/186.61 ! [V_R_2,V_Q_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_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fequal__1,axiom, % 186.05/186.61 ! [V_y_2,V_x_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 186.05/186.61 | V_x_2 = V_y_2 ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fequal__2,axiom, % 186.05/186.61 ! [V_y_2,V_x_2] : % 186.05/186.61 ( V_x_2 != V_y_2 % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fFalse__1,axiom, % 186.05/186.61 ~ hBOOL(c_fFalse) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fTrue__1,axiom, % 186.05/186.61 hBOOL(c_fTrue) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fNot__1,axiom, % 186.05/186.61 ! [V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 186.05/186.61 | ~ hBOOL(V_Pa_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fNot__2,axiom, % 186.05/186.61 ! [V_Pa_2] : % 186.05/186.61 ( ~ ~ hBOOL(V_Pa_2) % 186.05/186.61 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fconj__1,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(V_Pa_2) % 186.05/186.61 | ~ hBOOL(V_Q_2) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fconj__2,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 186.05/186.61 | hBOOL(V_Pa_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fconj__3,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 186.05/186.61 | hBOOL(V_Q_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fdisj__1,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(V_Pa_2) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fdisj__2,axiom, % 186.05/186.61 ! [V_Pa_2,V_Q_2] : % 186.05/186.61 ( ~ hBOOL(V_Q_2) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fdisj__3,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) % 186.05/186.61 | hBOOL(V_Pa_2) % 186.05/186.61 | hBOOL(V_Q_2) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fimplies__1,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( hBOOL(V_Pa_2) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fimplies__2,axiom, % 186.05/186.61 ! [V_Pa_2,V_Q_2] : % 186.05/186.61 ( ~ hBOOL(V_Q_2) % 186.05/186.61 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 186.05/186.61 % 186.05/186.61 fof(help_c__fimplies__3,axiom, % 186.05/186.61 ! [V_Q_2,V_Pa_2] : % 186.05/186.61 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) % 186.05/186.61 | ~ hBOOL(V_Pa_2) % 186.05/186.61 | hBOOL(V_Q_2) ) ). % 186.05/186.61 % 186.05/186.61 %----Conjectures (2) % 186.05/186.61 fof(conj_0,hypothesis, % 186.05/186.61 ! [B_n] : % 186.05/186.61 ( ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 186.05/186.61 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) % 186.05/186.61 => ! [B_Z,B_s] : % 186.05/186.61 ( ( v_P(B_Z,B_s) % 186.05/186.61 & hBOOL(hAPP(v_b,B_s)) ) % 186.05/186.61 => ! [B_s_H] : % 186.05/186.61 ( c_Natural_Oevaln(v_c,B_s,B_n,B_s_H) % 186.05/186.61 => v_P(B_Z,B_s_H) ) ) ) ). % 186.05/186.61 % 186.05/186.61 fof(conj_1,conjecture, % 186.05/186.61 ! [B_n] : % 186.05/186.61 ( ! [B_x] : % 186.05/186.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 186.05/186.61 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) % 186.05/186.61 => ! [B_Z,B_s] : % 186.05/186.61 ( v_P(B_Z,B_s) % 186.05/186.61 => ! [B_s_H] : % 186.05/186.61 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),B_s,B_n,B_s_H) % 186.05/186.61 => ( v_P(B_Z,B_s_H) % 186.05/186.61 & ~ hBOOL(hAPP(v_b,B_s_H)) ) ) ) ) ). % 186.05/186.61 % 186.05/186.61 %------------------------------------------------------------------------------ % 186.05/186.61 %------------------------------------------- % 186.05/186.61 % Proof found % 186.05/186.61 % SZS status Theorem for theBenchmark % 186.05/186.61 % SZS output start Proof % 186.05/186.61 %ClaNum:10035(EqnAxiom:2803) % 186.05/186.61 %VarNum:68131(SingletonVarNum:20215) % 186.05/186.61 %MaxLitNum:8 % 186.05/186.61 %MaxfuncDepth:13 % 186.05/186.61 %SharedTerms:1059 % 186.05/186.61 %goalClause: 3001 3438 4563 5462 % 186.05/186.61 %singleGoalClaCount:2 % 186.05/186.61 [2807]P1(a177) % 186.05/186.61 [2808]P2(a850) % 186.05/186.61 [2809]P2(a1) % 186.05/186.61 [2810]P2(a101) % 186.05/186.61 [2811]P3(a850) % 186.05/186.61 [2812]P3(a1) % 186.05/186.61 [2813]P3(a101) % 186.05/186.61 [2814]P4(a850) % 186.05/186.61 [2815]P4(a1) % 186.05/186.61 [2816]P4(a101) % 186.05/186.61 [2817]P5(a850) % 186.05/186.61 [2818]P5(a1) % 186.05/186.61 [2819]P5(a101) % 186.05/186.61 [2820]P66(a850) % 186.05/186.61 [2821]P66(a1) % 186.05/186.61 [2822]P66(a101) % 186.05/186.61 [2823]P67(a850) % 186.05/186.61 [2824]P67(a1) % 186.05/186.61 [2825]P67(a101) % 186.05/186.61 [2826]P68(a1) % 186.05/186.61 [2827]P73(a850) % 186.05/186.61 [2828]P73(a1) % 186.05/186.61 [2829]P73(a101) % 186.05/186.61 [2830]P137(a850) % 186.05/186.61 [2831]P137(a1) % 186.05/186.61 [2832]P85(a850) % 186.05/186.61 [2833]P85(a1) % 186.05/186.61 [2834]P85(a101) % 186.05/186.61 [2835]P74(a850) % 186.05/186.61 [2836]P74(a1) % 186.05/186.61 [2837]P74(a101) % 186.05/186.61 [2838]P80(a850) % 186.05/186.61 [2839]P80(a1) % 186.05/186.61 [2840]P80(a101) % 186.05/186.61 [2841]P110(a1) % 186.05/186.61 [2842]P81(a850) % 186.05/186.61 [2843]P81(a1) % 186.05/186.61 [2844]P81(a101) % 186.05/186.61 [2845]P117(a850) % 186.05/186.61 [2846]P117(a1) % 186.05/186.61 [2847]P117(a101) % 186.05/186.61 [2848]P86(a850) % 186.05/186.61 [2849]P86(a1) % 186.05/186.61 [2850]P86(a101) % 186.05/186.61 [2851]P99(a850) % 186.05/186.61 [2852]P99(a844) % 186.05/186.61 [2853]P99(a1) % 186.05/186.61 [2854]P99(a101) % 186.05/186.61 [2855]P103(a850) % 186.05/186.61 [2856]P103(a844) % 186.05/186.61 [2857]P103(a1) % 186.05/186.61 [2858]P103(a101) % 186.05/186.61 [2859]P100(a850) % 186.05/186.61 [2860]P100(a1) % 186.05/186.61 [2861]P100(a101) % 186.05/186.61 [2862]P102(a850) % 186.05/186.61 [2863]P102(a844) % 186.05/186.61 [2864]P102(a1) % 186.05/186.61 [2865]P102(a101) % 186.05/186.61 [2866]P111(a1) % 186.05/186.61 [2867]P120(a1) % 186.05/186.61 [2868]P121(a1) % 186.05/186.61 [2869]P64(a850) % 186.05/186.61 [2870]P64(a1) % 186.05/186.61 [2871]P64(a101) % 186.05/186.61 [2872]P69(a1) % 186.05/186.61 [2873]P70(a850) % 186.05/186.61 [2874]P70(a1) % 186.05/186.61 [2875]P70(a101) % 186.05/186.61 [2876]P75(a850) % 186.05/186.61 [2877]P75(a1) % 186.05/186.61 [2878]P75(a101) % 186.05/186.61 [2879]P76(a850) % 186.05/186.61 [2880]P76(a1) % 186.05/186.61 [2881]P76(a101) % 186.05/186.61 [2882]P87(a1) % 186.05/186.61 [2883]P133(a1) % 186.05/186.61 [2884]P104(a1) % 186.05/186.61 [2885]P77(a1) % 186.05/186.61 [2886]P6(a1) % 186.05/186.61 [2887]P122(a850) % 186.05/186.61 [2888]P122(a1) % 186.05/186.61 [2889]P122(a101) % 186.05/186.61 [2890]P134(a1) % 186.05/186.61 [2891]P127(a850) % 186.05/186.61 [2892]P127(a1) % 186.05/186.61 [2893]P127(a101) % 186.05/186.61 [2894]P138(a850) % 186.05/186.61 [2895]P138(a1) % 186.05/186.61 [2896]P138(a101) % 186.05/186.61 [2897]P109(a850) % 186.05/186.61 [2898]P109(a1) % 186.05/186.61 [2899]P109(a101) % 186.05/186.61 [2900]P135(a850) % 186.05/186.61 [2901]P135(a1) % 186.05/186.61 [2902]P135(a101) % 186.05/186.61 [2903]P118(a1) % 186.05/186.61 [2904]P119(a1) % 186.05/186.61 [2905]P123(a850) % 186.05/186.61 [2906]P123(a1) % 186.05/186.61 [2907]P123(a101) % 186.05/186.61 [2908]P115(a850) % 186.05/186.61 [2909]P115(a1) % 186.05/186.61 [2910]P115(a101) % 186.05/186.61 [2911]P82(a1) % 186.05/186.61 [2912]P124(a1) % 186.05/186.61 [2913]P78(a850) % 186.05/186.61 [2914]P78(a1) % 186.05/186.61 [2915]P78(a101) % 186.05/186.61 [2916]P128(a850) % 186.05/186.61 [2917]P128(a1) % 186.05/186.61 [2918]P128(a101) % 186.05/186.61 [2919]P129(a1) % 186.05/186.61 [2920]P131(a850) % 186.05/186.61 [2921]P131(a1) % 186.05/186.61 [2922]P131(a101) % 186.05/186.61 [2923]P130(a850) % 186.05/186.61 [2924]P130(a1) % 186.05/186.61 [2925]P130(a101) % 186.05/186.61 [2926]P125(a850) % 186.05/186.61 [2927]P125(a1) % 186.05/186.61 [2928]P125(a101) % 186.05/186.61 [2929]P126(a1) % 186.05/186.61 [2930]P90(a844) % 186.05/186.61 [2931]P7(a850) % 186.05/186.61 [2932]P7(a1) % 186.05/186.61 [2933]P7(a101) % 186.05/186.61 [2934]P8(a1) % 186.05/186.61 [2935]P84(a844) % 186.05/186.61 [2936]P84(a1) % 186.05/186.61 [2937]P71(a850) % 186.05/186.61 [2938]P71(a844) % 186.05/186.61 [2939]P71(a1) % 186.05/186.61 [2940]P71(a101) % 186.05/186.61 [2941]P88(a1) % 186.05/186.61 [2942]P79(a1) % 186.05/186.61 [2943]P89(a850) % 186.05/186.61 [2944]P89(a1) % 186.05/186.61 [2945]P89(a101) % 186.05/186.61 [2946]P132(a1) % 186.05/186.61 [2947]P65(a1) % 186.05/186.61 [2948]P105(a850) % 186.05/186.61 [2949]P105(a1) % 186.05/186.61 [2950]P105(a101) % 186.05/186.61 [2951]P136(a850) % 186.05/186.61 [2952]P136(a1) % 186.05/186.61 [2953]P136(a101) % 186.05/186.61 [2954]P112(a850) % 186.05/186.61 [2955]P112(a1) % 186.05/186.61 [2956]P112(a101) % 186.05/186.61 [2957]P108(a1) % 186.05/186.61 [2958]P92(a850) % 186.05/186.61 [2959]P92(a844) % 186.05/186.61 [2960]P92(a1) % 186.05/186.61 [2961]P93(a850) % 186.05/186.61 [2962]P93(a844) % 186.05/186.61 [2963]P93(a1) % 186.05/186.61 [2964]P9(a844) % 186.05/186.61 [2965]P106(a844) % 186.05/186.61 [2966]P94(a844) % 186.05/186.61 [2967]P59(a844) % 186.05/186.61 [2968]P59(a853) % 186.05/186.61 [2969]P101(a850) % 186.05/186.61 [2970]P101(a844) % 186.05/186.61 [2971]P95(a844) % 186.05/186.61 [2972]P97(a850) % 186.05/186.61 [2973]P97(a844) % 186.05/186.61 [2974]P97(a1) % 186.05/186.61 [2975]P98(a850) % 186.05/186.61 [2976]P98(a844) % 186.05/186.61 [2977]P98(a1) % 186.05/186.61 [2978]P72(a850) % 186.05/186.61 [2979]P72(a1) % 186.05/186.61 [2980]P72(a101) % 186.05/186.61 [2981]P107(a850) % 186.05/186.61 [2982]P139(a1) % 186.05/186.61 [2983]P139(a853) % 186.05/186.61 [2984]P83(a850) % 186.05/186.61 [2985]P83(a1) % 186.05/186.61 [2986]P83(a101) % 186.05/186.61 [2987]P96(a844) % 186.05/186.61 [2999]P36(a850,a237) % 186.05/186.61 [3000]P36(a850,a323) % 186.05/186.61 [3001]P142(a329,a774) % 186.05/186.61 [4357]~E(a99,a85) % 186.05/186.61 [4358]~P1(a178) % 186.05/186.61 [2804]E(f2(a1),a85) % 186.05/186.61 [2805]E(f3(a101),a4) % 186.05/186.61 [2806]E(f102(a101),a5) % 186.05/186.61 [2988]E(f34(a25),f2(a850)) % 186.05/186.61 [2989]E(f86(a177),f2(a850)) % 186.05/186.61 [2990]E(f86(a178),f2(a850)) % 186.05/186.61 [2991]E(f179(a850),f103(a850)) % 186.05/186.61 [2992]E(f180(a850),f2(a850)) % 186.05/186.61 [2993]E(f236(a850),f104(a850)) % 186.05/186.61 [2994]E(f105(a1),f39(a1)) % 186.05/186.61 [2995]P10(f2(a1)) % 186.05/186.61 [2996]P10(f80(a1)) % 186.05/186.61 [3039]P1(f775(a26,a25)) % 186.05/186.61 [3048]P36(f856(a850,a850),a40) % 186.05/186.61 [3077]E(f166(a846,a845,a29),a30) % 186.05/186.61 [3389]E(f325(a850,a850,a237,a237),a40) % 186.05/186.61 [3438]P39(f35(a859,a861),a774,a600,a776) % 186.05/186.61 [4359]~E(f80(a1),f2(a1)) % 186.05/186.61 [2997]E(f113(f2(a850)),f2(a850)) % 186.05/186.61 [2998]E(f6(f2(a101)),f2(a850)) % 186.05/186.61 [3003]E(f775(f81(a1),a85),a85) % 186.05/186.61 [3007]E(f775(a5,f2(a850)),f2(a101)) % 186.05/186.61 [3008]E(f775(a114,f2(a850)),f80(a850)) % 186.05/186.61 [3009]E(f775(a107,f80(a1)),f80(a850)) % 186.05/186.61 [3010]E(f775(a5,f80(a850)),f80(a101)) % 186.05/186.61 [3012]E(f775(f106(a1),a85),f2(a1)) % 186.05/186.61 [3013]E(f775(f106(a101),a85),f2(a101)) % 186.05/186.61 [3014]E(f775(a107,f2(a1)),f2(a850)) % 186.05/186.61 [3015]E(f775(f181(a845),a25),f2(a850)) % 186.05/186.61 [3016]E(f775(f181(a844),a177),f2(a850)) % 186.05/186.61 [3017]E(f775(f181(a844),a178),f2(a850)) % 186.05/186.61 [3018]E(f775(f106(a850),a85),f2(a850)) % 186.05/186.61 [3024]E(f775(f81(a1),f80(a1)),a99) % 186.05/186.61 [3032]E(f775(f181(a101),f2(a101)),f2(a850)) % 186.05/186.61 [3033]E(f775(f102(a1),f2(a850)),f2(a1)) % 186.05/186.61 [3034]E(f775(f102(a1),f80(a850)),f80(a1)) % 186.05/186.61 [3035]E(f775(f81(a1),f2(a1)),f2(a1)) % 186.05/186.61 [3044]E(f775(a107,f80(a1)),f775(a114,f2(a850))) % 186.05/186.61 [3046]E(f324(f856(a850,a850),a40),a41) % 186.05/186.61 [3047]E(f326(f856(a850,a850),a40),a70) % 186.05/186.61 [3068]E(f775(f257(a850),f2(a850)),f180(f857(a850,a844))) % 186.05/186.61 [3069]E(f775(f258(a850),f2(a850)),f239(f857(a850,a844))) % 186.05/186.61 [3079]P38(f180(f857(a1,a844))) % 186.05/186.61 [3114]E(f775(f775(f3(a101),f2(a101)),f80(a101)),f2(a101)) % 186.05/186.61 [3186]P1(f775(f775(f233(a1),a99),f2(a1))) % 186.05/186.61 [3211]P1(f775(f775(f233(a1),f2(a1)),f80(a1))) % 186.05/186.61 [3213]P1(f775(f775(f232(a1),f2(a1)),f80(a1))) % 186.05/186.61 [3380]P1(f775(f63(a846),f169(a846,a845,a30))) % 186.05/186.61 [3422]E(f775(f775(f281(a850,a850,a850),a323),f300(a850,a323)),a237) % 186.05/186.61 [3460]P40(a1,a850,a107,f775(f232(a1),f2(a1))) % 186.05/186.61 [3463]E(f775(f775(f46(a850,f857(a850,a844)),f239(f857(a850,a844))),f257(a850)),f239(f857(a850,a844))) % 186.05/186.61 [3464]E(f775(f775(f46(a850,f857(a850,a844)),f239(f857(a850,a844))),f293(a850)),f239(f857(a850,a844))) % 186.05/186.61 [3465]E(f775(f775(f46(a850,f857(a850,a844)),f239(f857(a850,a844))),f258(a850)),f239(f857(a850,a844))) % 186.05/186.61 [3466]E(f775(f775(f47(a850,f857(a850,a844)),f239(f857(a850,a844))),f296(a850)),f180(f857(a850,a844))) % 186.05/186.61 [3482]P29(a850,a1,f102(a1),f239(f857(a850,a844))) % 186.05/186.61 [3495]P40(a850,a1,f102(a1),f775(f18(a844,a850),a177)) % 186.05/186.61 [3626]E(f775(f75(a850,a101,a1,a5),a107),f106(a101)) % 186.05/186.61 [3844]P55(a101,a850,a22,a5,f239(f857(a850,a844))) % 186.05/186.61 [3852]P55(a1,f857(f856(a850,a850),a844),a109,a91,a100) % 186.05/186.61 [4121]E(f252(a1,a1,a1,a1,f39(a1),f81(a1)),a58) % 186.05/186.61 [4390]~E(f775(f106(a1),a99),f775(f106(a1),a85)) % 186.05/186.61 [4391]~P1(f775(a186,f2(a1))) % 186.05/186.61 [4392]~P1(f775(a186,f80(a1))) % 186.05/186.61 [4448]~P1(f775(f775(f233(a1),a85),f2(a1))) % 186.05/186.61 [3062]E(f775(f775(f3(a1),a99),a99),a85) % 186.05/186.61 [3076]E(f775(f102(a1),f775(a114,f2(a850))),f80(a1)) % 186.05/186.61 [3138]E(f775(f42(a853),f239(f857(a853,a844))),f80(a850)) % 186.05/186.61 [3160]P1(f775(a186,f775(f106(a1),a99))) % 186.05/186.61 [3161]P1(f775(f775(f233(a1),a99),a85)) % 186.05/186.61 [3163]P1(f775(f775(f232(a1),a99),a85)) % 186.05/186.61 [3222]E(f775(f775(f302(a850),f2(a850)),f180(f857(a850,a844))),f775(f293(a850),f2(a850))) % 186.05/186.61 [3278]P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),a85))) % 186.05/186.61 [3289]E(f775(f303(a850,a850,a114),f239(f857(a850,a844))),f775(f296(a850),f2(a850))) % 186.05/186.61 [3327]P12(f856(a850,a850),f239(f857(f856(a850,a850),a844)),a111) % 186.05/186.61 [3633]E(f775(f75(a850,a1,a101,f102(a1)),a22),a23) % 186.05/186.61 [3693]P36(a850,f775(f256(f856(a850,a850)),f775(f251(a850,a850,a844),f233(a850)))) % 186.05/186.61 [4439]~P1(f775(a186,f775(f106(a1),a85))) % 186.05/186.61 [4440]~P1(f775(f775(f233(a1),a99),a99)) % 186.05/186.61 [4441]~P1(f775(f775(f233(a1),a85),a99)) % 186.05/186.61 [4442]~P1(f775(f775(f233(a1),a85),a85)) % 186.05/186.61 [4443]~P1(f775(f775(f232(a1),a85),a99)) % 186.05/186.61 [4458]~P1(f775(f63(a850),f239(f857(a850,a844)))) % 186.05/186.61 [4459]~P1(f775(f63(a1),f239(f857(a1,a844)))) % 186.05/186.61 [4286]E(f775(f251(a1,a1,a844),f775(f775(f10(f857(a1,a844),f857(a1,a844),a1),f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f233(a1),f2(a1))))),f775(f775(f9(a1,a1,f857(a1,a844)),f775(f775(f10(f857(a1,f857(a1,a844)),f857(a1,f857(a1,a844)),a1),f9(a1,a1,a844)),f775(f775(f10(f857(a1,a1),f857(a1,f857(a1,a844)),a1),f775(f10(a1,f857(a1,a844),a1),a330)),a212))),f80(a1)))),a208) % 186.05/186.61 [3362]E(f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99),f775(f81(a1),a99)) % 186.05/186.61 [3404]E(f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99),f775(f775(f3(a1),a85),a99)) % 186.05/186.61 [3558]E(f775(f775(f61(f856(a850,a850)),f239(f857(f856(a850,a850),a844))),a111),a100) % 186.05/186.61 [3588]E(f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f80(a1)) % 186.05/186.61 [3589]E(f775(f106(a101),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f80(a101)) % 186.05/186.61 [3590]E(f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f80(a850)) % 186.05/186.61 [3593]E(f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(a114,f2(a850))) % 186.05/186.61 [3982]E(f775(f775(f103(f857(f856(f856(a850,a850),f856(a850,a850)),a844)),a40),f300(f856(a850,a850),f180(f857(f856(f856(a850,a850),f856(a850,a850)),a844)))),a72) % 186.05/186.61 [4053]E(f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),f2(a850)),f2(a850))),f180(f857(f856(a850,a850),a844))))),f2(a1)) % 186.05/186.61 [4054]E(f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),f80(a850)),f2(a850))),f180(f857(f856(a850,a850),a844))))),f80(a1)) % 186.05/186.61 [4068]E(f775(f256(f856(a850,a850)),f775(f251(a850,a850,a844),f775(f775(f10(a850,f857(a850,a844),a850),f775(f9(a850,a850,a844),a330)),a114))),a323) % 186.05/186.61 [4037]E(f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),f775(a114,f775(a114,f2(a850)))) % 186.05/186.61 [4040]E(f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),f775(f775(f82(a850),f80(a850)),f80(a850))) % 186.05/186.61 [4041]E(f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),f775(f42(a844),f239(f857(a844,a844)))) % 186.05/186.61 [4106]P10(f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))) % 186.05/186.61 [4180]P30(f857(f856(a850,a850),a844),f775(f775(f241(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844),f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)),a41),a71)) % 186.05/186.61 [4181]P30(f857(f856(a850,a850),a844),f775(f775(f241(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844),f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)),a70),a73)) % 186.05/186.61 [4218]E(f775(f775(f103(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)),f326(f856(a850,a850),a72)),f775(f775(f302(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f180(f857(f856(a850,a850),a844))),f180(f857(f856(a850,a850),a844)))),f180(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)))),a73) % 186.05/186.61 [4219]E(f775(f775(f103(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)),f324(f856(a850,a850),a72)),f775(f775(f302(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f180(f857(f856(a850,a850),a844))),f180(f857(f856(a850,a850),a844)))),f180(f857(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a844)))),a71) % 186.05/186.61 [4108]E(f775(a107,f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(a114,f775(a114,f2(a850)))) % 186.05/186.61 [4157]E(f775(f102(a1),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))) % 186.05/186.61 [4190]P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.61 [4191]E(f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99)),f775(a114,f775(a114,f775(a114,f2(a850))))) % 186.05/186.61 [4231]P10(f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))) % 186.05/186.61 [4258]E(f775(f102(a1),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))) % 186.05/186.61 [4272]P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99)))) % 186.05/186.61 [3002]P11(x30021,a330) % 186.05/186.61 [3390]P29(a850,a850,a114,x33901) % 186.05/186.61 [3019]P36(a1,f108(x30191)) % 186.05/186.61 [3020]P36(a1,f110(x30201)) % 186.05/186.61 [3023]P37(x30231,f183(x30231)) % 186.05/186.61 [3065]P36(f857(x30651,a844),f299(x30651)) % 186.05/186.61 [3105]E(f52(a1,x31051,x31051),f2(a1)) % 186.05/186.61 [3157]P19(x31571,f857(x31571,a844),f302(x31571)) % 186.05/186.61 [4361]~E(f775(a27,x43611),a25) % 186.05/186.61 [4363]~E(f775(a114,x43631),x43631) % 186.05/186.61 [4375]~E(f775(a114,x43751),f2(a850)) % 186.05/186.61 [3004]E(f775(f181(a850),x30041),x30041) % 186.05/186.61 [3005]E(f775(f106(a1),x30051),x30051) % 186.05/186.61 [3021]E(f775(a91,f333(x30211)),x30211) % 186.05/186.61 [3022]E(f238(x30221,f2(a101)),f2(a101)) % 186.05/186.61 [3036]E(f116(x30361,f115(x30361)),f115(x30361)) % 186.05/186.61 [3040]E(f34(f775(a27,x30401)),f2(a850)) % 186.05/186.61 [3041]E(f775(f141(x30411),f115(x30411)),f115(x30411)) % 186.05/186.61 [3042]E(f775(f157(x30421),f115(x30421)),f115(x30421)) % 186.05/186.61 [3043]E(f775(f142(x30431),f115(x30431)),f115(x30431)) % 186.05/186.61 [3049]E(f775(f106(a1),x30491),f775(f105(a1),x30491)) % 186.05/186.61 [3051]E(f775(a5,f775(a22,x30511)),x30511) % 186.05/186.61 [3052]E(f775(a22,f775(a5,x30521)),x30521) % 186.05/186.61 [3053]E(f775(a91,f775(a109,x30531)),x30531) % 186.05/186.61 [3054]P10(f775(f102(a1),x30541)) % 186.05/186.61 [3058]E(f775(f181(f854(x30581)),f183(x30581)),f2(a850)) % 186.05/186.61 [3059]E(f775(f181(f851(x30591)),f115(x30591)),f2(a850)) % 186.05/186.61 [3064]E(f775(f181(a845),f775(a27,x30641)),f2(a850)) % 186.05/186.61 [3074]E(f226(x30741,f183(x30741)),f180(f857(x30741,a844))) % 186.05/186.61 [3082]E(f775(f775(f82(a850),x30821),f2(a850)),x30821) % 186.05/186.61 [3083]E(f775(f775(f82(a1),x30831),f2(a1)),x30831) % 186.05/186.61 [3084]E(f775(f775(f83(a850),x30841),f80(a850)),x30841) % 186.05/186.61 [3085]E(f775(f775(f83(a1),x30851),f80(a1)),x30851) % 186.05/186.61 [3086]E(f775(f775(f3(a850),x30861),f2(a850)),x30861) % 186.05/186.61 [3087]E(f775(f775(f179(a850),x30871),f2(a850)),x30871) % 186.05/186.61 [3088]E(f775(f775(f83(a850),x30881),f2(a850)),f2(a850)) % 186.05/186.61 [3089]E(f775(f775(f43(a1),x30891),f2(a1)),f2(a1)) % 186.05/186.61 [3090]E(f775(f775(f236(a850),x30901),f2(a850)),f2(a850)) % 186.05/186.61 [3096]E(f775(f158(x30961),f115(x30961)),f180(f857(x30961,a844))) % 186.05/186.61 [3100]P1(f775(f127(x31001),f115(x31001))) % 186.05/186.61 [3106]E(f775(f143(x31061,x31061),f7(x31061)),f39(f851(x31061))) % 186.05/186.61 [3107]E(f775(f143(x31071,x31071),f39(x31071)),f39(f851(x31071))) % 186.05/186.61 [3108]E(f775(f196(x31081,x31081),f7(x31081)),f39(f854(x31081))) % 186.05/186.61 [3109]E(f775(f196(x31091,x31091),f39(x31091)),f39(f854(x31091))) % 186.05/186.61 [3110]E(f52(a1,x31101,f2(a1)),x31101) % 186.05/186.61 [3111]E(f775(f232(a850),f775(a114,x31111)),f775(f233(a850),x31111)) % 186.05/186.61 [3112]E(f775(f257(a850),f775(a114,x31121)),f775(f293(a850),x31121)) % 186.05/186.61 [3113]E(f775(f258(a850),f775(a114,x31131)),f775(f296(a850),x31131)) % 186.05/186.61 [3115]E(f52(a1,f2(a1),x31151),f2(a1)) % 186.05/186.61 [3122]E(f775(f775(f82(a850),x31221),f80(a850)),f775(a114,x31221)) % 186.05/186.61 [3132]E(f775(f294(a850,x31321),f2(a850)),f180(f857(a850,a844))) % 186.05/186.61 [3143]E(f295(a850,f2(a850),x31431),f775(f293(a850),x31431)) % 186.05/186.61 [3189]E(f775(f775(f3(a850),f775(a114,x31891)),f80(a850)),x31891) % 186.05/186.61 [3202]E(f54(f2(a1),x32021),f775(f775(f241(a1,a1),f2(a1)),f2(a1))) % 186.05/186.61 [3252]P1(f775(f775(f233(a850),x32521),f775(a114,x32521))) % 186.05/186.61 [3266]P1(f775(f775(f233(a850),f2(a850)),f775(a114,x32661))) % 186.05/186.61 [3545]E(f775(f775(f3(a101),f775(a5,f775(a114,f775(a22,x35451)))),f80(a101)),x35451) % 186.05/186.61 [3615]P1(f775(f775(f232(a1),f775(f81(a1),f775(f102(a1),x36151))),f2(a1))) % 186.05/186.61 [3768]P1(f775(f775(f233(a1),f775(f81(a1),f775(f102(a1),f775(a114,x37681)))),f2(a1))) % 186.05/186.61 [4398]~E(f239(f857(x43981,a844)),f180(f857(x43981,a844))) % 186.05/186.61 [4451]~P1(f775(f775(f233(a850),x44511),f2(a850))) % 186.05/186.61 [4467]~P1(f775(f775(f233(a1),f775(f102(a1),x44671)),f2(a1))) % 186.05/186.61 [3063]E(f164(x30631,f115(f851(x30631))),f115(f851(x30631))) % 186.05/186.61 [3066]E(f775(f775(f83(a1),a85),x30661),a85) % 186.05/186.61 [3067]E(f775(f775(f82(a1),a85),x30671),x30671) % 186.05/186.61 [3070]E(f775(a107,f775(f102(a1),x30701)),x30701) % 186.05/186.61 [3071]E(f775(f775(f82(a1),x30711),a85),x30711) % 186.05/186.61 [3072]E(f775(f775(f3(a1),x30721),a85),x30721) % 186.05/186.61 [3075]E(f775(f775(f3(a850),x30751),x30751),f2(a850)) % 186.05/186.61 [3080]E(f775(f81(a1),f775(f81(a1),x30801)),x30801) % 186.05/186.61 [3081]E(f775(f42(a850),f775(f257(a850),x30811)),x30811) % 186.05/186.61 [3091]E(f775(f775(f82(a850),f2(a850)),x30911),x30911) % 186.05/186.61 [3092]E(f775(f775(f82(a1),f2(a1)),x30921),x30921) % 186.05/186.61 [3093]E(f775(f775(f83(a850),f80(a850)),x30931),x30931) % 186.05/186.61 [3094]E(f775(f775(f83(a1),f80(a1)),x30941),x30941) % 186.05/186.61 [3095]E(f775(f775(f179(a850),f2(a850)),x30951),x30951) % 186.05/186.61 [3101]E(f775(f775(f83(a850),f2(a850)),x31011),f2(a850)) % 186.05/186.61 [3102]E(f775(f775(f43(a1),f2(a1)),x31021),f2(a1)) % 186.05/186.61 [3103]E(f775(f775(f3(a850),f2(a850)),x31031),f2(a850)) % 186.05/186.61 [3104]E(f775(f775(f236(a850),f2(a850)),x31041),f2(a850)) % 186.05/186.61 [3120]E(f775(f294(a850,f2(a850)),x31201),f775(f257(a850),x31201)) % 186.05/186.61 [3121]E(f775(f775(f83(a1),a99),x31211),f775(f81(a1),x31211)) % 186.05/186.61 [3124]E(f775(a107,f775(f106(a1),x31241)),f775(f106(a850),x31241)) % 186.05/186.61 [3125]E(f775(a22,f775(f106(a101),x31251)),f775(f106(a850),x31251)) % 186.05/186.61 [3126]E(f775(f42(a850),f775(f293(a850),x31261)),f775(a114,x31261)) % 186.05/186.61 [3136]E(f775(f775(f82(a850),f80(a850)),x31361),f775(a114,x31361)) % 186.05/186.61 [3139]E(f775(f105(a1),f775(f102(a1),x31391)),f775(f102(a1),x31391)) % 186.05/186.61 [3140]E(f775(f77(a1),f775(f102(a1),x31401)),f775(f102(a1),x31401)) % 186.05/186.61 [3145]E(f775(f42(x31451),f180(f857(x31451,a844))),f2(a850)) % 186.05/186.61 [3147]E(f775(f775(f43(a850),x31471),f775(a114,f2(a850))),x31471) % 186.05/186.61 [3158]E(f52(a850,x31581,f775(a114,f2(a850))),f2(a850)) % 186.05/186.61 [3159]E(f52(a1,x31591,f775(f106(a1),a99)),f2(a1)) % 186.05/186.61 [3173]E(f775(f775(f43(a1),x31731),f775(f106(a1),a99)),f775(f81(a1),x31731)) % 186.05/186.61 [3177]E(f130(a850,f775(f294(a850,x31771),f2(a850))),f115(a850)) % 186.05/186.61 [3178]E(f775(f775(f3(a1),x31781),f80(a1)),f775(f775(f82(a1),x31781),a99)) % 186.05/186.61 [3179]E(f775(f775(f82(a1),x31791),f80(a1)),f775(f775(f3(a1),x31791),a99)) % 186.05/186.61 [3182]P1(f775(f775(f187(a25),x31821),x31821)) % 186.05/186.61 [3183]P1(f775(f775(f232(a850),x31831),x31831)) % 186.05/186.61 [3184]P1(f775(f775(f232(a1),x31841),x31841)) % 186.05/186.61 [3185]P1(f775(f775(f279(a850),x31851),x31851)) % 186.05/186.61 [3190]E(f775(f81(a1),f775(f106(a1),x31901)),f775(f106(a1),f775(f81(a1),x31901))) % 186.05/186.61 [3191]P1(f775(f63(a850),f775(f257(a850),x31911))) % 186.05/186.61 [3192]P1(f775(f63(a850),f775(f293(a850),x31921))) % 186.05/186.61 [3200]E(f149(x32001,f239(f857(x32001,a844))),f239(f857(f851(x32001),a844))) % 186.05/186.61 [3205]P1(f775(f775(f232(a850),f2(a850)),x32051)) % 186.05/186.61 [3216]E(f775(f775(f82(a850),f113(x32161)),f775(a114,f2(a850))),f113(f775(a114,x32161))) % 186.05/186.61 [3217]E(f775(f256(x32171),f775(f18(a844,x32171),a177)),f239(f857(x32171,a844))) % 186.05/186.61 [3218]E(f775(f256(x32181),f775(f18(a844,x32181),a178)),f180(f857(x32181,a844))) % 186.05/186.61 [3221]E(f775(f775(f302(a850),x32211),f775(f257(a850),x32211)),f775(f257(a850),f775(a114,x32211))) % 186.05/186.61 [3232]E(f775(f775(f82(a1),f80(a1)),f775(f102(a1),x32321)),f775(f102(a1),f775(a114,x32321))) % 186.05/186.61 [3255]E(f180(f857(f856(x32551,x32551),a844)),f260(x32551,f180(f857(x32551,a844)))) % 186.05/186.61 [3256]E(f775(f301(x32561),f239(f857(x32561,a844))),f239(f857(f857(x32561,a844),a844))) % 186.05/186.61 [3257]E(f775(f81(f857(x32571,a844)),f239(f857(x32571,a844))),f180(f857(x32571,a844))) % 186.05/186.61 [3258]E(f775(f81(f857(x32581,a844)),f180(f857(x32581,a844))),f239(f857(x32581,a844))) % 186.05/186.61 [3260]P1(f775(f63(x32601),f180(f857(x32601,a844)))) % 186.05/186.61 [3262]E(f775(f294(a850,x32621),f775(a114,x32621)),f775(f775(f302(a850),x32621),f180(f857(a850,a844)))) % 186.05/186.61 [3263]E(f87(f856(a850,a850),f55(x32631,f2(a850))),f775(f775(f241(a850,a850),f2(a850)),x32631)) % 186.05/186.61 [3277]E(f775(f775(f302(a850),f775(a114,x32771)),f775(f293(a850),x32771)),f775(f293(a850),f775(a114,x32771))) % 186.05/186.61 [3280]P36(x32801,f180(f857(f856(x32801,x32801),a844))) % 186.05/186.61 [3283]P1(f775(f775(f232(a1),f2(a1)),f775(f102(a1),x32831))) % 186.05/186.61 [3291]E(f775(f775(f82(a850),f775(f181(a850),x32911)),f775(a114,f2(a850))),f775(f181(a850),f775(a114,x32911))) % 186.05/186.61 [3397]P38(f775(f303(a850,a1,f102(a1)),x33971)) % 186.05/186.61 [3437]P47(x34371,f180(f857(x34371,a844)),f180(f857(f856(x34371,x34371),a844))) % 186.05/186.61 [3457]E(f775(f775(f241(a1,a1),f775(f106(a1),a99)),f775(f775(f3(a1),x34571),f80(a1))),f57(f775(f106(a1),a99),x34571)) % 186.05/186.61 [3507]P58(x35071,f775(f18(f857(x35071,a844),x35071),f775(f18(a844,x35071),a178))) % 186.05/186.61 [3516]E(f282(a850,f279(a850),x35161,x35161),f775(f775(f302(a850),x35161),f180(f857(a850,a844)))) % 186.05/186.61 [3707]P1(f775(f775(f334(f857(f856(a850,a850),a844)),f333(x37071)),a100)) % 186.05/186.61 [3732]P1(f775(f775(f334(f857(f856(a850,a850),a844)),f775(a109,x37321)),a100)) % 186.05/186.61 [3862]P29(x38621,f857(x38621,a844),f775(f775(f9(x38621,f857(x38621,a844),f857(x38621,a844)),f302(x38621)),f180(f857(x38621,a844))),f239(f857(x38621,a844))) % 186.05/186.61 [4394]~E(f775(f775(f82(a1),x43941),x43941),a99) % 186.05/186.61 [4438]~E(f775(a5,f775(a114,f775(a22,x44381))),f2(a101)) % 186.05/186.61 [4444]~P1(f775(a186,f775(f102(a1),x44441))) % 186.05/186.61 [4447]~P1(f775(f775(f233(a850),x44471),x44471)) % 186.05/186.61 [4460]~P1(f775(f775(f232(a850),f775(a114,x44601)),x44601)) % 186.05/186.61 [3207]E(f775(a107,f775(f81(a1),f775(f102(a1),x32071))),f2(a850)) % 186.05/186.61 [3210]E(f775(f775(f82(a1),f775(f81(a1),x32101)),x32101),f2(a1)) % 186.05/186.61 [3215]E(f775(f42(a1),f775(f294(a1,f2(a1)),x32151)),f775(a107,x32151)) % 186.05/186.61 [3225]E(f775(f775(f242(a850),f775(a114,f2(a850))),x32251),f775(a114,f2(a850))) % 186.05/186.61 [3324]E(f775(f276(x33241),f180(f857(f856(x33241,x33241),a844))),f180(f857(x33241,a844))) % 186.05/186.61 [3332]E(f45(f857(x33321,a844),f239(f857(f857(x33321,a844),a844))),f180(f857(x33321,a844))) % 186.05/186.61 [3333]E(f45(f857(x33331,a844),f180(f857(f857(x33331,a844),a844))),f239(f857(x33331,a844))) % 186.05/186.61 [3334]E(f44(f857(x33341,a844),f239(f857(f857(x33341,a844),a844))),f239(f857(x33341,a844))) % 186.05/186.61 [3335]E(f44(f857(x33351,a844),f180(f857(f857(x33351,a844),a844))),f180(f857(x33351,a844))) % 186.05/186.61 [3340]P1(f775(f775(f279(a850),f775(a114,f2(a850))),x33401)) % 186.05/186.61 [3378]E(f775(f775(f302(f851(x33781)),f115(x33781)),f180(f857(f851(x33781),a844))),f150(x33781,f115(f857(x33781,a844)))) % 186.05/186.61 [3379]E(f775(f775(f302(f851(x33791)),f115(x33791)),f180(f857(f851(x33791),a844))),f149(x33791,f180(f857(x33791,a844)))) % 186.05/186.61 [3421]E(f775(f775(f82(a850),f6(x34211)),f775(a114,f2(a850))),f6(f775(a5,f775(a114,f775(a22,x34211))))) % 186.05/186.61 [3449]E(f775(f42(a1),f775(f303(a850,a1,f102(a1)),x34491)),f775(f42(a850),x34491)) % 186.05/186.61 [3452]P1(f775(f775(f232(a850),x34521),f775(f775(f83(a850),x34521),x34521))) % 186.05/186.61 [3488]E(f775(f303(a1,a850,a107),f295(a1,f2(a1),f775(f102(a1),x34881))),f775(f293(a850),x34881)) % 186.05/186.61 [3502]E(f775(f775(f43(a850),f775(a114,f2(a850))),f775(f106(a850),x35021)),f775(a107,f775(f775(f43(a1),f80(a1)),f775(f106(a1),x35021)))) % 186.05/186.61 [3504]E(f775(f158(a850),f130(a850,f775(f294(a850,f2(a850)),f775(a114,x35041)))),f775(f293(a850),x35041)) % 186.05/186.61 [3505]E(f775(f775(f82(a850),f775(f181(a101),x35051)),f775(a114,f2(a850))),f775(f181(a101),f775(a5,f775(a114,f775(a22,x35051))))) % 186.05/186.61 [3521]E(f775(f303(a1,a850,a107),f775(f303(a850,a1,f102(a1)),x35211)),x35211) % 186.05/186.61 [3550]E(f775(f775(f302(a850),f2(a850)),f775(f303(a850,a850,a114),f775(f257(a850),x35501))),f775(f257(a850),f775(a114,x35501))) % 186.05/186.61 [3557]P53(x35571,x35571,f300(x35571,f180(f857(f856(x35571,x35571),a844)))) % 186.05/186.61 [3563]P1(f775(a186,f775(f81(a1),f775(f102(a1),f775(a114,x35631))))) % 186.05/186.61 [3574]E(f775(f775(f3(f857(a850,a844)),f775(f258(a850),x35741)),f775(f775(f302(a850),x35741),f180(f857(a850,a844)))),f775(f258(a850),f775(a114,x35741))) % 186.05/186.61 [3591]E(f775(f775(f82(a1),f775(f775(f3(a1),a85),x35911)),f775(f775(f3(a1),a85),x35911)),f775(f775(f3(a1),a85),f775(f775(f82(a1),x35911),x35911))) % 186.05/186.61 [3605]E(f775(f775(f302(f857(x36051,a844)),f180(f857(x36051,a844))),f180(f857(f857(x36051,a844),a844))),f775(f301(x36051),f180(f857(x36051,a844)))) % 186.05/186.61 [3634]E(f775(f775(f3(f857(a850,a844)),f775(f296(a850),x36341)),f775(f775(f302(a850),f775(a114,x36341)),f180(f857(a850,a844)))),f775(f296(a850),f775(a114,x36341))) % 186.05/186.61 [3643]E(f775(f775(f302(f854(x36431)),f183(x36431)),f775(f303(x36431,f854(x36431),f227(x36431)),f239(f857(x36431,a844)))),f239(f857(f854(x36431),a844))) % 186.05/186.61 [3744]E(f775(f106(a850),f775(f775(f82(a1),x37441),x37441)),f775(f775(f88(a850,a850),f775(f106(a850),x37441)),f775(f775(f20(a850,a850,a850),f82(a850)),f7(a850)))) % 186.05/186.61 [4132]P19(x41321,f857(x41321,a844),f775(f775(f10(f857(x41321,a844),f857(f857(x41321,a844),f857(x41321,a844)),x41321),f775(f9(f857(x41321,a844),f857(x41321,a844),f857(x41321,a844)),f3(f857(x41321,a844)))),f775(f775(f9(x41321,f857(x41321,a844),f857(x41321,a844)),f302(x41321)),f180(f857(x41321,a844))))) % 186.05/186.61 [4217]E(f775(f256(f856(a1,a1)),f775(f251(a1,a1,a844),f775(f775(f10(f857(a1,a844),f857(a1,a844),a1),f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),x42171)))),f233(a1)))),f110(x42171)) % 186.05/186.61 [4249]E(f775(f256(f856(a1,a1)),f775(f251(a1,a1,a844),f775(f775(f20(a1,f857(a1,a844),f857(a1,a844)),f775(f775(f10(f857(a844,a844),f857(f857(a1,a844),f857(a1,a844)),a1),f10(a844,a844,a1)),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),x42491)))),f233(a1)))),f108(x42491)) % 186.05/186.61 [4301]E(f775(f256(f856(f857(x43011,a844),f857(x43011,a844))),f775(f251(f857(x43011,a844),f857(x43011,a844),a844),f775(f775(f9(f857(x43011,a844),f857(f857(x43011,a844),a844),f857(f857(x43011,a844),a844)),f775(f775(f10(f857(f857(x43011,a844),f857(a844,a844)),f857(f857(f857(x43011,a844),a844),f857(f857(x43011,a844),a844)),f857(x43011,a844)),f20(f857(x43011,a844),a844,a844)),f775(f775(f10(f857(f857(x43011,a844),a844),f857(f857(x43011,a844),f857(a844,a844)),f857(x43011,a844)),f775(f10(a844,f857(a844,a844),f857(x43011,a844)),a331)),f233(f857(x43011,a844))))),f63(x43011)))),f299(x43011)) % 186.05/186.61 [4464]~P1(f775(f63(f851(x44641)),f239(f857(f851(x44641),a844)))) % 186.05/186.61 [4477]~P1(f775(f775(f232(a1),f2(a1)),f775(f81(a1),f775(f102(a1),f775(a114,x44771))))) % 186.05/186.61 [3356]E(f775(f775(f3(a1),f775(f775(f82(a1),x33561),a99)),a99),x33561) % 186.05/186.61 [3372]E(f775(f158(a850),f130(a850,f775(f294(a850,f2(a850)),x33721))),f775(f257(a850),x33721)) % 186.05/186.61 [3611]E(f775(f775(f82(a1),f775(f775(f82(a1),f80(a1)),x36111)),x36111),f775(f775(f3(a1),f775(f775(f82(a1),x36111),x36111)),a99)) % 186.05/186.61 [3661]E(f775(f278(x36611,x36611),f300(x36611,f180(f857(f856(x36611,x36611),a844)))),f300(x36611,f180(f857(f856(x36611,x36611),a844)))) % 186.05/186.61 [3710]P1(f775(f775(f232(a850),x37101),f775(f775(f83(a850),x37101),f775(f775(f83(a850),x37101),x37101)))) % 186.05/186.61 [3986]P1(f775(f63(a850),f775(f256(a850),f775(f775(f9(a850,a850,a844),f233(a850)),x39861)))) % 186.05/186.61 [3987]P1(f775(f63(a850),f775(f256(a850),f775(f775(f9(a850,a850,a844),f232(a850)),x39871)))) % 186.05/186.61 [4268]E(f775(f256(f856(x42681,x42681)),f775(f775(f10(f857(x42681,a844),a844,f856(x42681,x42681)),f89(x42681)),f775(f775(f9(f856(x42681,x42681),f857(x42681,f856(x42681,x42681)),f857(x42681,a844)),f775(f775(f10(f857(f856(x42681,x42681),a844),f857(f857(x42681,f856(x42681,x42681)),f857(x42681,a844)),f856(x42681,x42681)),f10(f856(x42681,x42681),a844,x42681)),a330)),f775(f775(f20(x42681,x42681,f856(x42681,x42681)),f241(x42681,x42681)),f7(x42681))))),f300(x42681,f180(f857(f856(x42681,x42681),a844)))) % 186.05/186.61 [4466]~E(f775(f775(f3(a1),f775(f775(f82(a1),x44661),x44661)),a99),a85) % 186.05/186.61 [4468]~E(f775(f775(f82(a1),f775(f775(f82(a1),f80(a1)),x44681)),x44681),f2(a1)) % 186.05/186.61 [3756]E(f775(f775(f82(a1),f775(f775(f3(a1),a99),x37561)),f775(f775(f3(a1),a99),x37561)),f775(f775(f3(a1),a99),f775(f775(f3(a1),f775(f775(f82(a1),x37561),x37561)),a99))) % 186.05/186.61 [3870]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),a99),x38701)),f775(f775(f3(a1),a99),x38701))),a99),f775(f775(f3(a1),a99),f775(f775(f82(a1),x38701),x38701))) % 186.05/186.61 [3906]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f82(a1),x39061),a99)),f775(f775(f82(a1),x39061),a99))),a99),f775(f775(f82(a1),f775(f775(f82(a1),x39061),x39061)),a99)) % 186.05/186.61 [3945]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),a99),x39451)),f775(f775(f3(a1),a99),x39451))),a99),f775(f775(f3(a1),a85),f775(f775(f3(a1),f775(f775(f82(a1),x39451),x39451)),a99))) % 186.05/186.61 [4049]E(f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x40491),f2(a850))),f180(f857(f856(a850,a850),a844))))),f775(f102(a1),x40491)) % 186.05/186.61 [4059]E(f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),f337(x40591)),f490(x40591))),f180(f857(f856(a850,a850),a844))))),x40591) % 186.05/186.61 [4089]E(f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x40891)),f775(f303(a850,a1,f102(a1)),f775(f256(a850),f775(f775(f10(a1,a844,a850),x40891),f102(a1))))) % 186.05/186.61 [4140]P38(f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x41401))) % 186.05/186.61 [4160]P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x41601),f180(f857(f856(a850,a850),a844)))),a73)) % 186.05/186.61 [4166]E(f775(f303(a1,a850,a107),f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),f775(f775(f10(a850,a844,a1),x41661),a107)))),f775(f256(a850),x41661)) % 186.05/186.61 [4315]E(f306(a850,f775(f775(f46(f856(a850,a850),f857(a850,a844)),f775(a109,x43151)),f775(f251(a850,a850,f857(a850,a844)),f775(f775(f9(a850,f857(a850,a844),f857(a850,f857(a850,a844))),f775(f775(f10(f857(a850,f857(f857(a850,a844),f857(a850,a844))),f857(f857(a850,a844),f857(a850,f857(a850,a844))),a850),f9(a850,f857(a850,a844),f857(a850,a844))),f775(f775(f10(f857(a850,a850),f857(a850,f857(f857(a850,a844),f857(a850,a844))),a850),f775(f10(a850,f857(f857(a850,a844),f857(a850,a844)),a850),f302(a850))),f3(a850)))),f180(f857(a850,a844)))))),f775(a107,x43151)) % 186.05/186.61 [3799]E(f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),x37991),x37991)),a99)),a99),f775(f775(f82(a1),x37991),x37991)) % 186.05/186.61 [3845]E(f775(f775(f3(a1),f775(f775(f3(a1),f775(f775(f82(a1),x38451),x38451)),a99)),a99),f775(f775(f82(a1),f775(f775(f3(a1),x38451),a99)),f775(f775(f3(a1),x38451),a99))) % 186.05/186.61 [4066]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f82(a1),f775(f81(a1),x40661)),a99)),f775(f775(f82(a1),f775(f81(a1),x40661)),a99))),a99),f775(f81(a1),f775(f775(f3(a1),f775(f775(f82(a1),x40661),x40661)),a99))) % 186.05/186.61 [4109]E(f775(f775(f82(a850),x41091),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(a114,f775(a114,x41091))) % 186.05/186.61 [4110]E(f775(f775(f83(a850),x41101),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f82(a850),x41101),x41101)) % 186.05/186.61 [4111]E(f775(f775(f43(a850),f775(f775(f82(a850),x41111),x41111)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x41111) % 186.05/186.61 [4193]E(f52(a850,f775(a114,f775(a114,x41931)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a850,x41931,f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.61 [4332]E(f775(a91,f775(f775(f46(f856(a850,a850),f857(f856(a850,a850),a844)),f775(a109,x43321)),f775(f251(a850,a850,f857(f856(a850,a850),a844)),f775(f775(f10(f857(a850,f857(f856(a850,a850),a844)),f857(a850,f857(f856(a850,a850),a844)),a850),f775(f10(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844),a850),f277(f856(a850,a850),f856(a850,a850),a111))),f775(f775(f9(a850,f857(f856(a850,a850),a844),f857(a850,f857(f856(a850,a850),a844))),f775(f775(f10(f857(a850,f857(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f857(f857(f856(a850,a850),a844),f857(a850,f857(f856(a850,a850),a844))),a850),f9(a850,f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f10(f857(a850,f856(a850,a850)),f857(a850,f857(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),a850),f775(f10(f856(a850,a850),f857(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),a850),f302(f856(a850,a850)))),f775(f9(a850,a850,f856(a850,a850)),f241(a850,a850))))),f180(f857(f856(a850,a850),a844))))))),f775(f81(a1),x43321)) % 186.05/186.61 [4188]E(f775(f775(f82(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x41881),f775(a114,f775(a114,x41881))) % 186.05/186.61 [4189]E(f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x41891),f775(f775(f82(a850),x41891),x41891)) % 186.05/186.61 [4222]E(f775(f775(f43(a850),f775(a114,f775(a114,x42221))),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(a114,f775(f775(f43(a850),x42221),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.61 [4273]E(f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x42731),f775(a114,f775(a114,f775(a114,x42731)))) % 186.05/186.61 [4353]E(f775(f251(a1,a1,f856(a1,a1)),f775(f775(f20(a1,f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f857(f856(a1,a1),f856(a1,a1))),f857(f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),a1),f20(a1,f856(a1,a1),f856(a1,a1))),f775(f775(f10(f857(a1,f856(a1,a1)),f857(a1,f857(f856(a1,a1),f856(a1,a1))),a1),f775(f20(a1,f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),f775(f775(f10(a844,f857(f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),a1),f98(f856(a1,a1))),f775(f775(f10(a1,a844,a1),f775(f232(a1),f2(a1))),f775(f775(f9(a1,a1,a1),f3(a1)),x43531))))),f775(f775(f9(a1,f857(a1,a1),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f856(a1,a1)),f857(f857(a1,a1),f857(a1,f856(a1,a1))),a1),f10(a1,f856(a1,a1),a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f775(f775(f9(a1,a1,a1),f775(f775(f10(a1,f857(a1,a1),a1),f82(a1)),f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f80(a1))))),f775(f775(f9(a1,a1,a1),f3(a1)),x43531))))),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))),f50(x43531)) % 186.05/186.61 [3400]P39(a25,x34001,x34002,x34001) % 186.05/186.61 [3057]P18(a1,f163(x30571,x30572)) % 186.05/186.61 [3153]P47(x31531,x31532,f260(x31531,x31532)) % 186.05/186.61 [3154]P53(x31541,x31541,f260(x31541,x31542)) % 186.05/186.61 [3424]P29(x34241,x34241,f7(x34241),x34242) % 186.05/186.61 [3425]P29(x34251,x34251,f39(x34251),x34252) % 186.05/186.61 [3432]P34(x34321,x34322,f115(x34321),f115(x34321)) % 186.05/186.61 [3433]P29(x34331,f854(x34331),f227(x34331),x34332) % 186.05/186.61 [3443]P29(f851(x34431),f851(x34431),f142(x34431),x34432) % 186.05/186.61 [4367]~E(f35(x43671,x43672),a25) % 186.05/186.61 [4368]~E(f36(x43681,x43682),a25) % 186.05/186.61 [4369]~E(f28(x43691,x43692),a25) % 186.05/186.61 [3025]E(f775(f7(x30251),x30252),x30252) % 186.05/186.61 [3026]E(f775(f256(x30261),x30262),x30262) % 186.05/186.61 [3028]E(f775(f39(x30281),x30282),x30282) % 186.05/186.61 [3037]E(f775(f184(x30371),x30372),f117(x30371)) % 186.05/186.61 [3045]E(f34(f28(x30451,x30452)),f2(a850)) % 186.05/186.61 [3055]E(f87(x30551,f775(a330,x30552)),x30552) % 186.05/186.61 [3056]E(f92(x30561,f775(a330,x30562)),x30562) % 186.05/186.61 [3073]E(f775(f181(a845),f28(x30731,x30732)),f2(a850)) % 186.05/186.61 [3078]E(f775(f126(x30781,x30782),f115(x30781)),f115(x30781)) % 186.05/186.61 [3097]E(f300(x30971,f300(x30971,x30972)),f300(x30971,x30972)) % 186.05/186.61 [3118]E(f775(f775(f125(x31181),x31182),f115(x31181)),x31182) % 186.05/186.61 [3127]E(f775(f775(f159(x31271),x31272),f115(x31271)),f115(x31271)) % 186.05/186.61 [3128]E(f775(f775(f128(x31281),x31282),f115(x31281)),f115(x31281)) % 186.05/186.61 [3130]E(f228(x31301,x31302,f183(x31301)),f2(a850)) % 186.05/186.61 [3131]E(f144(x31311,x31312,f115(x31311)),f2(a850)) % 186.05/186.61 [3133]E(f151(x31331,x31332,f115(x31331)),f115(x31331)) % 186.05/186.61 [3134]E(f162(x31341,x31342,f115(x31341)),f115(x31341)) % 186.05/186.61 [3135]E(f160(x31351,f115(x31351),x31352),f115(x31351)) % 186.05/186.61 [3141]E(f775(f259(x31411,x31411),f260(x31411,x31412)),x31412) % 186.05/186.61 [3142]E(f775(f261(x31421,x31421),f260(x31421,x31422)),x31422) % 186.05/186.61 [3151]P1(f775(a26,f28(x31511,x31512))) % 186.05/186.61 [3152]E(f775(f278(x31521,x31521),f260(x31521,x31522)),f260(x31521,x31522)) % 186.05/186.61 [3165]E(f300(f851(x31651),f146(x31651,x31652)),f147(x31651,f300(x31651,x31652))) % 186.05/186.61 [3167]P1(f775(f127(a1),f163(x31671,x31672))) % 186.05/186.61 [3175]E(f775(f259(x31751,x31751),f300(x31751,x31752)),f239(f857(x31751,a844))) % 186.05/186.61 [3176]E(f775(f261(x31761,x31761),f300(x31761,x31762)),f239(f857(x31761,a844))) % 186.05/186.61 [3180]P1(f775(f127(x31801),f152(x31801,x31802))) % 186.05/186.61 [3188]E(f775(f158(a1),f163(x31881,x31882)),f295(a1,x31881,x31882)) % 186.05/186.61 [3203]P54(x32031,f180(f857(x32031,a844)),x32032) % 186.05/186.61 [3208]E(f775(f250(a1,a1),f53(x32081,x32082)),f52(a1,x32081,x32082)) % 186.05/186.61 [3209]E(f775(f294(a850,x32091),f775(a114,x32092)),f295(a850,x32091,x32092)) % 186.05/186.61 [3236]E(f295(a850,f775(a114,x32361),x32362),f297(a850,x32361,x32362)) % 186.05/186.61 [3239]P47(x32391,f239(f857(x32391,a844)),f300(x32391,x32392)) % 186.05/186.61 [3302]E(f775(f775(f3(a850),x33021),f775(a114,x33022)),f775(f42(a850),f298(a850,x33022,x33021))) % 186.05/186.61 [3357]E(f156(x33571,x33572,f115(x33571)),f775(f775(f241(f851(x33571),f851(x33571)),f115(x33571)),f115(x33571))) % 186.05/186.61 [3376]E(f775(f251(x33761,x33762,f856(x33761,x33762)),f241(x33761,x33762)),f39(f856(x33761,x33762))) % 186.05/186.61 [3381]P1(f775(f775(f334(f851(x33811)),f115(x33811)),f149(x33811,x33812))) % 186.05/186.61 [3382]E(f775(f181(f851(x33821)),f116(x33821,x33822)),f775(f775(f3(a850),f775(f181(f851(x33821)),x33822)),f80(a850))) % 186.05/186.61 [3391]P1(f775(f63(a850),f295(a850,x33911,x33912))) % 186.05/186.61 [3392]P1(f775(f63(a850),f297(a850,x33921,x33922))) % 186.05/186.61 [3393]P1(f775(f63(a850),f298(a850,x33931,x33932))) % 186.05/186.61 [3394]P1(f775(f63(a1),f295(a1,x33941,x33942))) % 186.05/186.61 [3395]P1(f775(f63(a1),f297(a1,x33951,x33952))) % 186.05/186.61 [3396]P1(f775(f63(a1),f298(a1,x33961,x33962))) % 186.05/186.61 [3501]E(f775(f303(a850,a850,a114),f295(a850,x35011,x35012)),f295(a850,f775(a114,x35011),f775(a114,x35012))) % 186.05/186.61 [3518]E(f775(f775(f281(x35181,x35181,x35181),f300(x35181,x35182)),f300(x35181,x35182)),f300(x35181,x35182)) % 186.05/186.61 [3548]E(f775(f775(f241(a1,a1),f775(f775(f43(a1),x35481),x35482)),f52(a1,x35481,x35482)),f53(x35481,x35482)) % 186.05/186.61 [3549]E(f775(f775(f241(a101,a101),f775(f775(f43(a101),x35491),x35492)),f52(a101,x35491,x35492)),f24(x35491,x35492)) % 186.05/186.61 [3578]E(f775(f775(f241(a850,a850),f775(f775(f43(a850),x35781),x35782)),f52(a850,x35781,x35782)),f87(f856(a850,a850),f55(x35781,x35782))) % 186.05/186.61 [3630]P1(f775(f775(f233(a850),f775(f775(f3(a850),x36301),x36302)),f775(a114,x36301))) % 186.05/186.61 [3731]E(f775(f775(f82(a1),f775(f775(f83(a1),x37311),f775(f775(f43(a1),x37312),x37311))),f52(a1,x37312,x37311)),x37312) % 186.05/186.61 [3735]E(f775(f775(f46(a850,f857(f856(f851(x37351),f851(x37351)),a844)),f239(f857(a850,a844))),f133(x37351,x37352)),f135(x37351,x37352)) % 186.05/186.61 [3960]P1(f775(f775(f334(f856(f851(x39601),f851(x39601))),f775(f775(f241(f851(x39601),f851(x39601)),f115(x39601)),f115(x39601))),f147(x39601,x39602))) % 186.05/186.61 [4123]E(f252(x41231,x41231,x41232,x41232,f7(x41231),f7(x41232)),f39(f856(x41231,x41232))) % 186.05/186.61 [4125]E(f252(x41251,x41251,x41252,x41252,f39(x41251),f39(x41252)),f39(f856(x41251,x41252))) % 186.05/186.61 [4377]~E(f775(f227(x43771),x43772),f183(x43771)) % 186.05/186.61 [4395]~P37(x43951,f775(f227(x43951),x43952)) % 186.05/186.61 [3116]E(f775(f231(x31161),f775(f227(x31161),x31162)),x31162) % 186.05/186.61 [3117]E(f775(f142(x31171),f775(f142(x31171),x31172)),x31172) % 186.05/186.61 [3119]E(f775(f775(f128(x31191),f2(a850)),x31192),x31192) % 186.05/186.61 [3129]E(f775(f775(f159(x31291),f2(a850)),x31292),f115(x31291)) % 186.05/186.61 [3137]E(f775(f775(f125(x31371),f115(x31371)),x31372),x31372) % 186.05/186.61 [3144]E(f775(f181(f854(x31441)),f775(f227(x31441),x31442)),f2(a850)) % 186.05/186.61 [3146]E(f44(f857(x31461,a844),f775(f301(x31461),x31462)),x31462) % 186.05/186.61 [3148]E(f775(f158(x31481),f775(f141(x31481),x31482)),f775(f158(x31481),x31482)) % 186.05/186.61 [3149]E(f775(f158(x31491),f775(f142(x31491),x31492)),f775(f158(x31491),x31492)) % 186.05/186.61 [3156]E(f775(f775(f3(a101),x31561),x31562),f775(f775(a4,x31561),x31562)) % 186.05/186.61 [3169]E(f775(f775(f82(a850),x31691),x31692),f775(f775(f82(a850),x31692),x31691)) % 186.05/186.61 [3170]E(f775(f775(f82(a1),x31701),x31702),f775(f775(f82(a1),x31702),x31701)) % 186.05/186.61 [3171]E(f775(f775(f83(a850),x31711),x31712),f775(f775(f83(a850),x31712),x31711)) % 186.05/186.61 [3172]E(f775(f775(f83(a1),x31721),x31722),f775(f775(f83(a1),x31722),x31721)) % 186.05/186.61 [3195]E(f775(f775(f173(x31951,x31951),f2(a850)),x31952),f39(x31951)) % 186.05/186.61 [3196]E(f775(f181(f851(x31961)),f775(f141(x31961),x31962)),f775(f181(f851(x31961)),x31962)) % 186.05/186.61 [3197]E(f775(f181(f851(x31971)),f775(f142(x31971),x31972)),f775(f181(f851(x31971)),x31972)) % 186.05/186.61 [3198]E(f160(x31981,x31982,f180(f857(a850,a844))),f115(x31981)) % 186.05/186.61 [3199]E(f775(f775(f143(x31991,x31991),f7(x31991)),x31992),x31992) % 186.05/186.61 [3201]E(f775(f240(a1,a1),f53(x32011,x32012)),f775(f775(f43(a1),x32011),x32012)) % 186.05/186.61 [3219]E(f34(f35(x32191,x32192)),f775(f775(f82(a850),f34(x32192)),f775(a114,f2(a850)))) % 186.05/186.61 [3220]E(f775(f276(x32201),f775(f278(x32201,x32201),x32202)),f775(f276(x32201),x32202)) % 186.05/186.61 [3224]P1(f775(f63(x32241),f775(f158(x32241),x32242))) % 186.05/186.61 [3231]E(f775(f775(f82(a1),x32311),f775(f81(a1),x32312)),f775(f775(f3(a1),x32311),x32312)) % 186.05/186.61 [3238]P28(x32381,x32382,f180(f857(f849(x32381),a844))) % 186.05/186.61 [3242]E(f775(f303(x32421,x32421,f7(x32421)),x32422),x32422) % 186.05/186.61 [3243]E(f775(f303(x32431,x32431,f39(x32431)),x32432),x32432) % 186.05/186.61 [3244]E(f775(f305(x32441,x32441,f7(x32441)),x32442),x32442) % 186.05/186.61 [3245]E(f775(f305(x32451,x32451,f39(x32451)),x32452),x32452) % 186.05/186.61 [3246]P1(f775(f239(f857(x32461,a844)),x32462)) % 186.05/186.61 [3248]E(f775(f42(a850),f775(f294(a850,x32481),x32482)),f775(f775(f3(a850),x32482),x32481)) % 186.05/186.61 [3249]E(f775(f294(a850,f775(a114,x32491)),x32492),f298(a850,x32491,x32492)) % 186.05/186.61 [3261]E(f775(f775(f302(x32611),x32612),f180(f857(x32611,a844))),f775(f256(x32611),f775(a330,x32612))) % 186.05/186.61 [3267]E(f775(f775(f302(x32671),x32672),f180(f857(x32671,a844))),f226(x32671,f775(f227(x32671),x32672))) % 186.05/186.61 [3269]E(f300(x32691,f775(f278(x32691,x32691),x32692)),f775(f278(x32691,x32691),f300(x32691,x32692))) % 186.05/186.61 [3273]E(f775(f775(f82(a850),f775(a114,x32731)),x32732),f775(f775(f82(a850),x32731),f775(a114,x32732))) % 186.05/186.61 [3274]E(f775(f775(f3(a850),f775(a114,x32741)),f775(a114,x32742)),f775(f775(f3(a850),x32741),x32742)) % 186.05/186.61 [3279]E(f775(f42(a850),f297(a850,x32791,x32792)),f775(f775(f3(a850),x32792),x32791)) % 186.05/186.61 [3288]P36(x32881,f775(f775(f280(a850,x32881),a237),x32882)) % 186.05/186.61 [3290]P18(a850,f130(a850,f775(f294(a850,x32901),x32902))) % 186.05/186.61 [3292]P1(f775(f63(a850),f775(f294(a850,x32921),x32922))) % 186.05/186.61 [3293]P1(f775(f63(a1),f775(f294(a1,x32931),x32932))) % 186.05/186.61 [3295]E(f775(f278(f851(x32951),f851(x32951)),f146(x32951,x32952)),f146(x32951,f775(f278(x32951,x32951),x32952))) % 186.05/186.61 [3296]E(f775(f181(a845),f35(x32961,x32962)),f775(f775(f82(a850),f775(f181(a845),x32962)),f775(a114,f2(a850)))) % 186.05/186.61 [3298]E(f775(f294(a1,x32981),f775(f775(f82(a1),x32982),f80(a1))),f295(a1,x32981,x32982)) % 186.05/186.61 [3301]E(f775(f775(f43(a1),f775(f81(a1),x33011)),f775(f81(a1),x33012)),f775(f775(f43(a1),x33011),x33012)) % 186.05/186.61 [3309]E(f171(x33091,x33092,f775(f18(f854(x33092),x33091),f183(x33092))),f180(f857(x33092,a844))) % 186.05/186.61 [3310]E(f169(x33101,x33102,f775(f18(f854(x33102),x33101),f183(x33102))),f180(f857(x33101,a844))) % 186.05/186.61 [3311]E(f775(f775(f173(f856(x33111,x33111),a844),f80(a850)),x33112),x33112) % 186.05/186.61 [3313]E(f775(f775(f3(f857(x33131,a844)),x33132),f180(f857(x33131,a844))),x33132) % 186.05/186.61 [3314]E(f775(f775(f103(f857(x33141,a844)),x33142),f180(f857(x33141,a844))),x33142) % 186.05/186.61 [3315]E(f775(f775(f104(f857(x33151,a844)),x33152),f239(f857(x33151,a844))),x33152) % 186.05/186.61 [3316]E(f775(f240(a850,a850),f87(f856(a850,a850),f55(x33161,x33162))),f775(f775(f43(a850),x33161),x33162)) % 186.05/186.61 [3322]E(f307(x33221,f775(a23,x33222),f775(f81(a1),f775(a23,x33222))),f775(f775(f310(a1),x33221),x33222)) % 186.05/186.61 [3323]E(f295(a1,f775(f775(f82(a1),x33231),f80(a1)),x33232),f297(a1,x33231,x33232)) % 186.05/186.61 [3328]E(f775(f250(a850,a850),f87(f856(a850,a850),f55(x33281,x33282))),f52(a850,x33281,x33282)) % 186.05/186.61 [3336]E(f308(x33361,f775(a23,x33362),f775(f81(a1),f775(a23,x33362))),f309(a1,x33361,x33362)) % 186.05/186.61 [3339]P1(f775(f775(f334(x33391),x33392),f239(f857(x33391,a844)))) % 186.05/186.61 [3343]E(f775(f775(f3(a850),f775(a114,x33431)),x33432),f775(f42(a850),f295(a850,x33432,x33431))) % 186.05/186.61 [3368]E(f775(f775(f3(f857(x33681,a844)),x33682),f239(f857(x33681,a844))),f180(f857(x33681,a844))) % 186.05/186.61 [3369]E(f775(f775(f103(f857(x33691,a844)),x33692),f239(f857(x33691,a844))),f239(f857(x33691,a844))) % 186.05/186.61 [3370]E(f775(f775(f104(f857(x33701,a844)),x33702),f180(f857(x33701,a844))),f180(f857(x33701,a844))) % 186.05/186.61 [3384]E(f52(a1,f775(f102(a1),x33841),f775(f102(a1),x33842)),f775(f102(a1),f52(a850,x33841,x33842))) % 186.05/186.61 [3385]E(f52(a1,f775(f81(a1),x33851),f775(f81(a1),x33852)),f775(f81(a1),f52(a1,x33851,x33852))) % 186.05/186.61 [3398]E(f775(f181(f851(x33981)),f775(f157(x33981),x33982)),f775(f775(f3(a850),f775(f181(f851(x33981)),x33982)),f80(a850))) % 186.05/186.61 [3426]E(f775(f775(f43(a1),f52(a1,x34261,x34262)),x34262),f2(a1)) % 186.05/186.61 [3435]E(f775(a5,f52(a850,f775(a22,x34351),f775(a22,x34352))),f52(a101,x34351,x34352)) % 186.05/186.61 [3468]E(f775(a5,f775(f775(f82(a850),f775(a22,x34681)),f775(a22,x34682))),f775(f775(f82(a101),x34681),x34682)) % 186.05/186.61 [3469]E(f775(a5,f775(f775(f83(a850),f775(a22,x34691)),f775(a22,x34692))),f775(f775(f83(a101),x34691),x34692)) % 186.05/186.61 [3470]E(f775(a5,f775(f775(f43(a850),f775(a22,x34701)),f775(a22,x34702))),f775(f775(f43(a101),x34701),x34702)) % 186.05/186.61 [3471]E(f775(a5,f775(f775(f3(a850),f775(a22,x34711)),f775(a22,x34712))),f775(f775(f3(a101),x34711),x34712)) % 186.05/186.61 [3480]E(f775(f303(a850,a850,a114),f775(f294(a850,x34801),x34802)),f775(f294(a850,f775(a114,x34801)),f775(a114,x34802))) % 186.05/186.61 [3506]P1(f775(f55(x35061,x35062),f87(f856(a850,a850),f55(x35061,x35062)))) % 186.05/186.61 [3523]E(f775(f775(f82(a850),f775(f775(f82(a850),f34(x35231)),f34(x35232))),f775(a114,f2(a850))),f34(f36(x35231,x35232))) % 186.05/186.61 [3524]E(f52(a850,f775(a114,f52(a850,x35241,x35242)),x35242),f52(a850,f775(a114,x35241),x35242)) % 186.05/186.61 [3538]E(f775(f775(f47(f857(x35381,a844),f857(x35381,a844)),x35382),f7(f857(x35381,a844))),f45(f857(x35381,a844),x35382)) % 186.05/186.61 [3539]E(f775(f775(f46(f857(x35391,a844),f857(x35391,a844)),x35392),f7(f857(x35391,a844))),f44(f857(x35391,a844),x35392)) % 186.05/186.61 [3542]P1(f775(f775(f334(f857(x35421,a844)),x35422),f775(f301(x35421),x35422))) % 186.05/186.61 [3547]E(f52(a1,f775(f81(a1),f52(a1,x35471,x35472)),x35472),f52(a1,f775(f81(a1),x35471),x35472)) % 186.05/186.61 [3559]P1(f775(f775(f232(f857(x35591,a844)),x35592),f239(f857(x35591,a844)))) % 186.05/186.61 [3561]E(f775(f775(f281(x35611,x35611,x35611),f300(x35611,x35612)),f300(x35611,f300(x35611,x35612))),f300(x35611,x35612)) % 186.05/186.61 [3562]E(f775(f775(f103(f857(x35621,a844)),f775(f261(x35621,x35621),x35622)),f775(f259(x35621,x35621),x35622)),f775(f276(x35621),x35622)) % 186.05/186.61 [3584]E(f314(x35841,x35842,f239(f857(x35841,a844)),f239(f857(x35842,a844))),f239(f857(f858(x35841,x35842),a844))) % 186.05/186.61 [3635]P1(f775(f775(f232(a850),f52(a850,x36351,x36352)),x36351)) % 186.05/186.61 [3659]P1(f775(f775(f232(a1),f775(f81(a1),f775(f102(a1),x36591))),f775(f102(a1),x36592))) % 186.05/186.61 [3684]P1(f775(f775(f334(f857(x36841,a844)),f180(f857(x36841,a844))),f775(f301(x36841),x36842))) % 186.05/186.61 [3689]E(f300(x36891,f775(f775(f281(x36891,x36891,x36891),x36892),f300(x36891,x36892))),f300(x36891,x36892)) % 186.05/186.61 [3692]E(f775(f775(f281(x36921,x36921,x36921),f300(x36921,x36922)),x36922),f775(f775(f281(x36921,x36921,x36921),x36922),f300(x36921,x36922))) % 186.05/186.61 [3694]E(f775(a107,f775(f775(f82(a1),f775(f775(f3(a1),x36941),x36942)),f80(a1))),f775(f42(a1),f295(a1,x36942,x36941))) % 186.05/186.61 [3711]E(f775(f259(x37111,x37111),f775(f775(f281(x37111,x37111,x37111),x37112),f300(x37111,x37112))),f775(f259(x37111,x37111),x37112)) % 186.05/186.61 [3712]E(f775(f261(x37121,x37121),f775(f775(f281(x37121,x37121,x37121),x37122),f300(x37121,x37122))),f775(f261(x37121,x37121),x37122)) % 186.05/186.61 [3727]E(f775(f775(f82(a850),f775(f775(f82(a850),f775(f181(a845),x37271)),f775(f181(a845),x37272))),f775(a114,f2(a850))),f775(f181(a845),f36(x37271,x37272))) % 186.05/186.61 [3739]P29(a850,a850,f775(f775(f9(a850,a850,a850),f82(a850)),x37391),x37392) % 186.05/186.61 [3741]P18(a850,f775(f142(a850),f775(f775(f143(f851(x37411),a850),f181(f851(x37411))),f164(x37411,x37412)))) % 186.05/186.61 [3788]P1(f775(f775(f233(a1),f775(f81(a1),f775(f102(a1),f775(a114,x37881)))),f775(f102(a1),x37882))) % 186.05/186.61 [3828]E(f775(f132(f851(x38281),x38281,f775(f9(x38281,f851(x38281),f851(x38281)),f140(x38281)),f115(x38281)),x38282),f775(f142(x38281),x38282)) % 186.05/186.61 [3877]P1(f775(f775(f232(f857(f856(f851(x38771),f851(x38771)),a844)),f147(x38771,x38772)),f300(f851(x38771),f146(x38771,x38772)))) % 186.05/186.61 [3910]P1(f775(f55(x39101,x39102),f775(f775(f241(a850,a850),f775(f775(f43(a850),x39101),x39102)),f52(a850,x39101,x39102)))) % 186.05/186.61 [3921]P1(f775(f775(f232(f857(f856(f851(x39211),f851(x39211)),a844)),f146(x39211,f300(x39211,x39212))),f300(f851(x39211),f146(x39211,x39212)))) % 186.05/186.61 [4152]E(f775(f775(f253(f856(a101,a101),a101,f856(a101,a101),f856(x41521,f856(a101,a101))),f264(f775(f155(a101),f775(f775(f143(f856(a101,x41521),a101),f240(a101,x41521)),x41522)))),f775(f775(f10(x41521,f857(f856(a101,a101),f856(x41521,f856(a101,a101))),a101),f241(x41521,f856(a101,a101))),f265(x41521,x41522))),f263(x41521,x41522)) % 186.05/186.61 [4331]E(f775(f251(f857(f856(x43311,x43311),a844),f857(f856(x43311,x43311),a844),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f775(f775(f9(f857(f856(x43311,x43311),a844),f857(f857(f856(x43311,x43311),a844),f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844))),f857(f857(f856(x43311,x43311),a844),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844))))),f775(f775(f10(f857(f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844)),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f857(f857(f857(f856(x43311,x43311),a844),f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844))),f857(f857(f856(x43311,x43311),a844),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844))))),f857(f856(x43311,x43311),a844)),f10(f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844)),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844))),f857(f856(x43311,x43311),a844))),f775(f775(f10(f857(f857(x43312,x43311),f857(f857(f856(x43312,x43312),a844),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f857(f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844)),f857(f857(x43312,x43311),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f857(f856(x43311,x43311),a844)),f20(f857(x43312,x43311),f857(f856(x43312,x43312),a844),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f775(f775(f10(f857(f857(x43312,x43311),f857(f856(x43312,x43312),a844)),f857(f857(x43312,x43311),f857(f857(f856(x43312,x43312),a844),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f857(f856(x43311,x43311),a844)),f775(f10(f857(f856(x43312,x43312),a844),f857(f857(f856(x43312,x43312),a844),f856(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844))),f857(x43312,x43311)),f241(f857(f856(x43312,x43312),a844),f857(f856(x43312,x43312),a844)))),f280(x43311,x43312))))),f280(x43311,x43312))),f76(x43311,x43312)) % 186.05/186.61 [4445]~E(f775(f301(x44451),x44452),f180(f857(f857(x44451,a844),a844))) % 186.05/186.61 [4463]~P1(f775(f775(f334(x44631),x44632),f180(f857(x44631,a844)))) % 186.05/186.61 [4472]~P1(f775(f775(f233(f857(x44721,a844)),x44722),f180(f857(x44721,a844)))) % 186.05/186.61 [3251]E(f775(f775(f3(a850),x32511),f775(f775(f82(a850),x32511),x32512)),f2(a850)) % 186.05/186.61 [3253]E(f775(f775(f103(f857(x32531,a844)),x32532),x32532),x32532) % 186.05/186.61 [3254]E(f775(f775(f104(f857(x32541,a844)),x32542),x32542),x32542) % 186.05/186.61 [3281]E(f775(f775(f3(f857(x32811,a844)),x32812),x32812),f180(f857(x32811,a844))) % 186.05/186.61 [3284]E(f775(f133(x32841,x32842),f2(a850)),f180(f857(f856(f851(x32841),f851(x32841)),a844))) % 186.05/186.61 [3285]E(f775(f775(f82(a850),x32851),f775(a114,x32852)),f775(a114,f775(f775(f82(a850),x32851),x32852))) % 186.05/186.61 [3297]E(f188(f775(f102(a1),x32971),f775(f102(a1),x32972)),f775(f102(a1),f775(f775(f3(a850),x32971),x32972))) % 186.05/186.61 [3300]E(f775(f775(f43(a1),f775(f81(a1),x33001)),x33002),f775(f775(f43(a1),x33001),f775(f81(a1),x33002))) % 186.05/186.61 [3304]E(f775(f42(a1),f775(f294(a1,x33041),x33042)),f775(a107,f775(f775(f3(a1),x33042),x33041))) % 186.05/186.61 [3307]E(f775(f775(f82(a850),f775(a114,x33071)),x33072),f775(a114,f775(f775(f82(a850),x33071),x33072))) % 186.05/186.61 [3312]E(f775(f81(f857(x33121,a844)),f775(f81(f857(x33121,a844)),x33122)),x33122) % 186.05/186.61 [3325]E(f164(x33251,f775(f775(f140(f851(x33251)),f115(x33251)),x33252)),f164(x33251,x33252)) % 186.05/186.61 [3329]E(f775(f775(f82(a850),x33291),f775(f775(f83(a850),x33291),x33292)),f775(f775(f83(a850),x33291),f775(a114,x33292))) % 186.05/186.61 [3337]E(f775(f775(a4,f775(a5,x33371)),f775(a5,x33372)),f775(a5,f775(f775(f3(a850),x33371),x33372))) % 186.05/186.61 [3348]E(f775(f775(f83(a1),f775(f81(a1),x33481)),x33482),f775(f81(a1),f775(f775(f83(a1),x33481),x33482))) % 186.05/186.61 [3350]E(f775(f775(f242(a1),f775(f102(a1),x33501)),x33502),f775(f102(a1),f775(f775(f242(a850),x33501),x33502))) % 186.05/186.61 [3351]E(f775(f775(f82(a101),f775(a5,x33511)),f775(a5,x33512)),f775(a5,f775(f775(f82(a850),x33511),x33512))) % 186.05/186.61 [3352]E(f775(f775(f83(a101),f775(a5,x33521)),f775(a5,x33522)),f775(a5,f775(f775(f83(a850),x33521),x33522))) % 186.05/186.61 [3353]E(f775(f775(f236(a850),f775(a114,x33531)),f775(a114,x33532)),f775(a114,f775(f775(f236(a850),x33531),x33532))) % 186.05/186.61 [3354]E(f775(f775(f179(a850),f775(a114,x33541)),f775(a114,x33542)),f775(a114,f775(f775(f179(a850),x33541),x33542))) % 186.05/186.61 [3360]E(f775(f158(a850),f130(a850,f775(f294(a850,x33601),x33602))),f775(f294(a850,x33601),x33602)) % 186.05/186.61 [3361]E(f306(x33611,f775(f775(f302(x33611),x33612),f180(f857(x33611,a844)))),x33612) % 186.05/186.61 [3366]E(f775(f259(x33661,x33662),f180(f857(f856(x33661,x33662),a844))),f180(f857(x33662,a844))) % 186.05/186.61 [3367]E(f775(f261(x33671,x33672),f180(f857(f856(x33671,x33672),a844))),f180(f857(x33671,a844))) % 186.05/186.61 [3371]E(f775(a107,f775(f775(f3(a1),x33711),x33712)),f775(f42(a1),f297(a1,x33712,x33711))) % 186.05/186.61 [3375]E(f775(f775(f82(a850),x33751),f775(f775(f83(a850),x33752),x33751)),f775(f775(f83(a850),f775(a114,x33752)),x33751)) % 186.05/186.61 [3377]E(f775(f775(f61(x33771),f180(f857(x33771,a844))),x33772),f180(f857(f857(x33771,a844),a844))) % 186.05/186.61 [3386]E(f775(f181(f851(a850)),f130(a850,f775(f294(a850,x33861),x33862))),f775(f775(f3(a850),x33862),x33861)) % 186.05/186.61 [3405]E(f775(f775(f103(f857(x34051,a844)),f180(f857(x34051,a844))),x34052),x34052) % 186.05/186.61 [3406]E(f775(f775(f104(f857(x34061,a844)),f239(f857(x34061,a844))),x34062),x34062) % 186.05/186.61 [3409]E(f775(f775(f82(a1),f775(f81(a1),x34091)),f775(f81(a1),x34092)),f775(f81(a1),f775(f775(f82(a1),x34091),x34092))) % 186.05/186.61 [3412]E(f775(f775(f82(a1),f775(f102(a1),x34121)),f775(f102(a1),x34122)),f775(f102(a1),f775(f775(f82(a850),x34121),x34122))) % 186.05/186.61 [3413]E(f775(f775(f82(a1),f775(f106(a1),x34131)),f775(f106(a1),x34132)),f775(f106(a1),f775(f775(f82(a1),x34131),x34132))) % 186.05/186.61 [3415]E(f775(f775(f83(a1),f775(f102(a1),x34151)),f775(f102(a1),x34152)),f775(f102(a1),f775(f775(f83(a850),x34151),x34152))) % 186.05/186.61 [3416]E(f775(f775(f83(a1),f775(f106(a1),x34161)),f775(f106(a1),x34162)),f775(f106(a1),f775(f775(f83(a1),x34161),x34162))) % 186.05/186.61 [3417]E(f775(f775(f43(a1),f775(f102(a1),x34171)),f775(f102(a1),x34172)),f775(f102(a1),f775(f775(f43(a850),x34171),x34172))) % 186.05/186.61 [3436]E(f775(f775(f8(x34361,a850),f775(f18(a850,x34361),f80(a850))),x34362),f775(f42(x34361),x34362)) % 186.05/186.61 [3444]E(f775(f81(a1),f52(a1,f775(f81(a1),x34441),x34442)),f52(a1,x34441,f775(f81(a1),x34442))) % 186.05/186.61 [3446]E(f775(f158(a1),f163(x34461,f775(f775(f3(a1),x34462),f80(a1)))),f775(f294(a1,x34461),x34462)) % 186.05/186.61 [3450]P1(f775(f775(f232(a850),x34501),f775(f775(f82(a850),x34502),x34501))) % 186.05/186.61 [3451]P1(f775(f775(f232(a850),x34511),f775(f775(f82(a850),x34511),x34512))) % 186.05/186.61 [3454]E(f775(f775(f3(f857(x34541,a844)),f180(f857(x34541,a844))),x34542),f180(f857(x34541,a844))) % 186.05/186.61 [3455]E(f775(f775(f103(f857(x34551,a844)),f239(f857(x34551,a844))),x34552),f239(f857(x34551,a844))) % 186.05/186.61 [3456]E(f775(f775(f104(f857(x34561,a844)),f180(f857(x34561,a844))),x34562),f180(f857(x34561,a844))) % 186.05/186.61 [3461]E(f775(f775(f241(a1,a1),x34611),f775(f81(a1),x34612)),f775(a58,f775(f775(f241(a1,a1),x34611),x34612))) % 186.05/186.61 [3462]E(f775(f294(a1,f775(f775(f82(a1),x34621),f80(a1))),x34622),f298(a1,x34621,x34622)) % 186.05/186.61 [3472]E(f775(f775(f83(a850),x34721),f775(f775(f43(a850),x34722),x34721)),f775(f775(f3(a850),x34722),f52(a850,x34722,x34721))) % 186.05/186.61 [3473]E(f775(f775(f83(a1),x34731),f775(f775(f43(a1),x34732),x34731)),f775(f775(f3(a1),x34732),f52(a1,x34732,x34731))) % 186.05/186.61 [3477]E(f775(f158(a1),f163(f775(f775(f82(a1),x34771),f80(a1)),x34772)),f297(a1,x34771,x34772)) % 186.05/186.61 [3481]P1(f775(f775(f232(f857(x34811,a844)),x34812),x34812)) % 186.05/186.61 [3486]E(f775(f775(f103(f857(x34861,a844)),x34862),f775(f81(f857(x34861,a844)),x34862)),f239(f857(x34861,a844))) % 186.05/186.61 [3487]E(f775(f775(f104(f857(x34871,a844)),x34872),f775(f81(f857(x34871,a844)),x34872)),f180(f857(x34871,a844))) % 186.05/186.61 [3493]E(f775(f775(f3(a850),f775(f775(f3(a850),x34931),f80(a850))),x34932),f775(f775(f3(a850),x34931),f775(a114,x34932))) % 186.05/186.61 [3498]E(f775(f775(f3(f857(x34981,a844)),f239(f857(x34981,a844))),x34982),f775(f81(f857(x34981,a844)),x34982)) % 186.05/186.61 [3499]E(f775(f775(f3(a1),f775(f106(a1),x34991)),f775(f106(a1),x34992)),f775(f106(a1),f775(f775(f82(a1),x34991),f775(f81(a1),x34992)))) % 186.05/186.61 [3511]E(f775(f158(a850),f130(a850,f775(f294(a850,x35111),f775(a114,x35112)))),f295(a850,x35111,x35112)) % 186.05/186.61 [3540]E(f775(f775(f173(f856(x35401,x35401),a844),f2(a850)),x35402),f300(x35401,f180(f857(f856(x35401,x35401),a844)))) % 186.05/186.61 [3544]P1(f775(f127(a850),f130(a850,f775(f294(a850,x35441),x35442)))) % 186.05/186.61 [3560]E(f775(f303(a1,a850,a107),f295(a1,f775(f102(a1),x35601),f775(f102(a1),x35602))),f295(a850,x35601,x35602)) % 186.05/186.61 [3570]E(f175(a850,f2(a850),f7(a850),f775(f775(f3(a850),x35701),x35702)),f775(f775(f3(a850),x35701),f775(a114,x35702))) % 186.05/186.61 [3571]E(f775(a107,f775(f775(f3(a1),x35711),f775(f775(f82(a1),x35712),f80(a1)))),f775(f42(a1),f298(a1,x35712,x35711))) % 186.05/186.61 [3606]E(f775(f775(f143(a850,a850),a114),f130(a850,f775(f294(a850,x36061),x36062))),f130(a850,f775(f294(a850,f775(a114,x36061)),f775(a114,x36062)))) % 186.05/186.61 [3613]E(f775(f158(a1),f163(f775(f775(f82(a1),x36131),f80(a1)),f775(f775(f3(a1),x36132),f80(a1)))),f298(a1,x36131,x36132)) % 186.05/186.61 [3627]P1(f775(f775(f232(f857(x36271,a844)),f180(f857(x36271,a844))),x36272)) % 186.05/186.61 [3631]E(f87(x36311,f775(f775(f9(x36311,x36311,a844),a330),x36312)),x36312) % 186.05/186.61 [3632]E(f92(x36321,f775(f775(f9(x36321,x36321,a844),a330),x36322)),x36322) % 186.05/186.61 [3636]E(f775(f158(a850),f130(a850,f775(f294(a850,f775(a114,x36361)),f775(a114,x36362)))),f297(a850,x36361,x36362)) % 186.05/186.61 [3662]E(f775(f775(f248(x36621,x36622),f239(f857(x36621,a844))),f775(f18(f857(x36622,a844),x36621),f239(f857(x36622,a844)))),f239(f857(f856(x36621,x36622),a844))) % 186.05/186.61 [3698]E(f775(f256(x36981),f775(f775(f10(a844,a844,x36981),a328),x36982)),f775(f81(f857(x36981,a844)),f775(f256(x36981),x36982))) % 186.05/186.61 [3701]E(f775(f256(x37011),f775(f775(f9(x37011,x37011,a844),a330),x37012)),f775(f775(f302(x37011),x37012),f180(f857(x37011,a844)))) % 186.05/186.61 [3708]E(f775(f775(f82(a1),f775(f775(f82(a1),x37081),x37081)),f775(f775(f82(a1),x37082),x37082)),f775(f775(f82(a1),f775(f775(f82(a1),x37081),x37082)),f775(f775(f82(a1),x37081),x37082))) % 186.05/186.61 [3709]E(f775(f775(f3(a1),f775(f775(f82(a1),x37091),x37091)),f775(f775(f82(a1),x37092),x37092)),f775(f775(f82(a1),f775(f775(f3(a1),x37091),x37092)),f775(f775(f3(a1),x37091),x37092))) % 186.05/186.61 [3724]P1(f775(f775(f232(a850),f775(f42(x37241),f775(f158(x37241),x37242))),f775(f181(f851(x37241)),x37242))) % 186.05/186.61 [3725]P1(f775(f775(f232(a850),f775(f181(f851(x37251)),f152(x37251,x37252))),f775(f181(f851(x37251)),x37252))) % 186.05/186.61 [3736]E(f775(f256(x37361),f775(f775(f9(x37361,f857(x37361,a844),a844),f334(x37361)),x37362)),x37362) % 186.05/186.61 [3752]E(f775(f775(f159(x37521),f775(f775(f3(a850),f775(f181(f851(x37521)),x37522)),f80(a850))),x37522),f116(x37521,x37522)) % 186.05/186.61 [3775]E(f175(a850,f2(a850),f775(f775(f10(a850,a850,a850),a114),f775(f236(a850),x37751)),x37752),f775(f775(f236(a850),f775(a114,x37751)),x37752)) % 186.05/186.61 [3779]E(f44(f857(x37791,a844),f775(f303(f857(f856(x37791,x37791),a844),f857(x37791,a844),f276(x37791)),x37792)),f775(f276(x37791),f44(f857(f856(x37791,x37791),a844),x37792))) % 186.05/186.61 [3780]E(f175(a850,f775(a114,x37801),f775(f775(f10(a850,a850,a850),a114),f775(f179(a850),x37801)),x37802),f775(f775(f179(a850),f775(a114,x37801)),x37802)) % 186.05/186.61 [3782]E(f775(f775(f241(a1,a1),f775(f775(f43(a1),f775(f77(a1),x37821)),f775(f77(a1),x37822))),f52(a1,f775(f77(a1),x37821),f775(f77(a1),x37822))),f60(x37821,x37822)) % 186.05/186.61 [3802]P1(f775(f775(f232(f857(f857(x38021,a844),a844)),x38022),f775(f301(x38021),f44(f857(x38021,a844),x38022)))) % 186.05/186.61 [3833]E(f775(f775(f46(x38331,f857(x38331,a844)),x38332),f775(f775(f9(x38331,f857(x38331,a844),f857(x38331,a844)),f302(x38331)),f180(f857(x38331,a844)))),x38332) % 186.05/186.61 [3834]E(f775(f775(f281(x38341,x38341,x38341),f775(f278(x38341,x38341),x38342)),f300(x38341,f775(f278(x38341,x38341),x38342))),f775(f278(x38341,x38341),f775(f775(f281(x38341,x38341,x38341),x38342),f300(x38341,x38342)))) % 186.05/186.61 [3902]E(f775(f158(x39021),f775(f132(f851(x39021),f851(x39021),f125(x39021),f115(x39021)),x39022)),f775(f775(f46(f851(x39021),f857(x39021,a844)),f775(f158(f851(x39021)),x39022)),f158(x39021))) % 186.05/186.61 [3933]E(f775(f775(f103(f857(f856(x39331,x39331),a844)),f300(x39331,f180(f857(f856(x39331,x39331),a844)))),f775(f775(f281(x39331,x39331,x39331),f300(x39331,x39332)),x39332)),f300(x39331,x39332)) % 186.05/186.61 [3971]E(f775(f775(f167(x39711,x39711),x39712),x39712),f775(f775(f143(x39711,f856(x39711,x39711)),f775(f775(f20(x39711,x39711,f856(x39711,x39711)),f241(x39711,x39711)),f7(x39711))),x39712)) % 186.05/186.61 [4085]E(f775(f132(a850,f851(x40851),f775(f9(f851(x40851),a850,a850),f775(f775(f10(a850,f857(a850,a850),f851(x40851)),f179(a850)),f181(f851(x40851)))),f2(a850)),f775(f142(f851(x40851)),x40852)),f775(f181(f851(f851(x40851))),f164(x40851,x40852))) % 186.05/186.61 [4165]E(f775(f775(f280(f856(a850,f851(x41651)),f851(x41651)),f325(a850,f851(x41651),a237,f135(x41651,x41652))),f775(f775(f20(f851(x41651),f851(x41651),f856(a850,f851(x41651))),f775(f775(f10(a850,f857(f851(x41651),f856(a850,f851(x41651))),f851(x41651)),f241(a850,f851(x41651))),f181(f851(x41651)))),f7(f851(x41651)))),f136(x41651,x41652)) % 186.05/186.61 [4288]E(f775(f256(x42881),f775(f775(f10(f857(f857(x42881,a844),a844),a844,x42881),f90(f857(x42881,a844))),f775(f775(f10(f857(f857(x42881,a844),a844),f857(f857(x42881,a844),a844),x42881),f775(f20(f857(x42881,a844),a844,a844),f775(f775(f10(a844,f857(a844,a844),f857(x42881,a844)),a335),f775(f775(f9(f857(x42881,a844),f857(f857(x42881,a844),a844),a844),f334(f857(x42881,a844))),x42882)))),f334(x42881)))),f45(f857(x42881,a844),x42882)) % 186.05/186.61 [4473]~P1(f775(f775(f233(a1),f775(f102(a1),x44731)),f775(f81(a1),f775(f102(a1),x44732)))) % 186.05/186.61 [3373]E(f775(f775(f3(a850),f775(f775(f82(a850),x33731),x33732)),x33732),x33731) % 186.05/186.61 [3374]E(f775(f775(f3(a850),f775(f775(f82(a850),x33741),x33742)),x33741),x33742) % 186.05/186.61 [3445]E(f775(f775(f82(a850),f775(f775(f3(a850),x34451),x34452)),x34452),f775(f775(f179(a850),x34451),x34452)) % 186.05/186.61 [3546]E(f775(f775(f83(a850),f775(f775(f43(a850),x35461),x35462)),x35462),f775(f775(f3(a850),x35461),f52(a850,x35461,x35462))) % 186.05/186.61 [3575]E(f775(f158(a850),f130(a850,f775(f294(a850,f775(a114,x35751)),x35752))),f298(a850,x35751,x35752)) % 186.05/186.61 [3583]E(f775(f102(a1),f211(f775(a107,f775(f77(a1),x35831)),f775(a107,f775(f77(a1),x35832)))),f775(f775(a212,x35831),x35832)) % 186.05/186.61 [3585]E(f775(f775(f103(f857(x35851,a844)),f775(f81(f857(x35851,a844)),x35852)),x35852),f239(f857(x35851,a844))) % 186.05/186.61 [3586]E(f775(f775(f104(f857(x35861,a844)),f775(f81(f857(x35861,a844)),x35862)),x35862),f180(f857(x35861,a844))) % 186.05/186.61 [3602]P1(f775(f775(f232(a850),f775(f775(f43(a850),x36021),x36022)),x36021)) % 186.05/186.61 [3603]P1(f775(f775(f232(a850),f775(f775(f3(a850),x36031),x36032)),x36031)) % 186.05/186.61 [3628]P1(f775(f775(f233(a850),x36281),f775(a114,f775(f775(f82(a850),x36282),x36281)))) % 186.05/186.61 [3629]P1(f775(f775(f233(a850),x36291),f775(a114,f775(f775(f82(a850),x36291),x36292)))) % 186.05/186.61 [3648]E(f775(f775(f83(a850),f775(a107,f775(f77(a1),x36481))),f775(a107,f775(f77(a1),x36482))),f775(a107,f775(f77(a1),f775(f775(f83(a1),x36481),x36482)))) % 186.05/186.61 [3658]P1(f775(f775(f232(a1),f2(a1)),f775(f775(f242(a1),f775(f77(a1),x36581)),x36582))) % 186.05/186.61 [3730]E(f775(f277(f851(x37301),f851(x37301),f147(x37301,x37302)),f775(f775(f302(f851(x37301)),f115(x37301)),f180(f857(f851(x37301),a844)))),f775(f775(f302(f851(x37301)),f115(x37301)),f180(f857(f851(x37301),a844)))) % 186.05/186.61 [3748]E(f775(f775(f103(f857(f856(x37481,x37481),a844)),f300(x37481,x37482)),f300(x37481,f180(f857(f856(x37481,x37481),a844)))),f300(x37481,x37482)) % 186.05/186.61 [3764]E(f775(f775(f43(a1),f775(f106(a1),f775(f775(f82(a1),x37641),x37641))),f775(f106(a1),f775(f775(f82(a1),x37642),x37642))),f775(f775(f43(a1),f775(f106(a1),x37641)),f775(f106(a1),x37642))) % 186.05/186.61 [3823]E(f775(f775(f242(a1),x38231),f775(f106(a850),f775(f775(f82(a1),x38232),x38232))),f775(f775(f88(a1,a1),f775(f775(f242(a1),x38231),f775(f106(a850),x38232))),f775(f775(f20(a1,a1,a1),f83(a1)),f7(a1)))) % 186.05/186.61 [3829]E(f775(f256(f857(x38291,a844)),f775(f775(f9(f857(x38291,a844),f857(x38291,a844),a844),f232(f857(x38291,a844))),x38292)),f775(f301(x38291),x38292)) % 186.05/186.61 [3876]E(f775(f303(a1,a1,f775(f775(f9(a1,a1,a1),f82(a1)),x38761)),f775(f294(a1,f2(a1)),f775(f775(f3(a1),x38762),x38761))),f775(f294(a1,x38761),x38762)) % 186.05/186.61 [3879]P48(x38791,f775(f775(f3(f857(f856(x38791,x38791),a844)),x38792),f300(x38791,f180(f857(f856(x38791,x38791),a844))))) % 186.05/186.61 [3899]E(f775(f181(f851(x38991)),f775(f132(f851(x38991),f851(x38991),f125(x38991),f115(x38991)),x38992)),f775(f155(a850),f775(f775(f143(f851(x38991),a850),f181(f851(x38991))),x38992))) % 186.05/186.61 [3904]P47(x39041,f239(f857(x39041,a844)),f775(f775(f103(f857(f856(x39041,x39041),a844)),x39042),f300(x39041,f180(f857(f856(x39041,x39041),a844))))) % 186.05/186.61 [3950]E(f175(a850,f2(a850),f775(f775(f10(a850,a850,a850),a114),f775(f775(f9(a850,a850,a850),f236(a850)),x39501)),x39502),f775(f775(f236(a850),x39502),f775(a114,x39501))) % 186.05/186.61 [3953]E(f175(a850,f775(a114,x39531),f775(f775(f10(a850,a850,a850),a114),f775(f775(f9(a850,a850,a850),f179(a850)),x39531)),x39532),f775(f775(f179(a850),x39532),f775(a114,x39531))) % 186.05/186.61 [3956]E(f775(f303(x39561,f851(x39561),f775(f775(f9(x39561,f851(x39561),f851(x39561)),f140(x39561)),f115(x39561))),x39562),f161(x39561,x39562,f775(f775(f302(f851(x39561)),f115(x39561)),f180(f857(f851(x39561),a844))))) % 186.05/186.61 [3957]E(f775(f775(f103(f857(f856(x39571,x39571),a844)),f775(f775(f281(x39571,x39571,x39571),x39572),f300(x39571,x39572))),f300(x39571,f180(f857(f856(x39571,x39571),a844)))),f300(x39571,x39572)) % 186.05/186.61 [3965]P1(f775(f775(f232(f857(f856(x39651,x39651),a844)),f260(x39651,x39652)),f775(f775(f248(x39651,x39651),x39652),f775(f18(f857(x39651,a844),x39651),x39652)))) % 186.05/186.61 [3969]E(f775(f303(a1,a850,a107),f775(f775(f103(f857(a1,a844)),f775(f303(a850,a1,f102(a1)),x39691)),f775(f303(a850,a1,f102(a1)),x39692))),f775(f775(f103(f857(a850,a844)),x39691),x39692)) % 186.05/186.61 [3970]E(f775(f303(a1,a850,a107),f775(f775(f104(f857(a1,a844)),f775(f303(a850,a1,f102(a1)),x39701)),f775(f303(a850,a1,f102(a1)),x39702))),f775(f775(f104(f857(a850,a844)),x39701),x39702)) % 186.05/186.61 [3974]E(f775(f256(x39741),f775(f775(f10(a844,a844,x39741),a328),f775(f775(f9(x39741,f857(x39741,a844),a844),f334(x39741)),x39742))),f775(f81(f857(x39741,a844)),x39742)) % 186.05/186.61 [4001]E(f775(f132(f851(x40011),f851(x40011),f125(x40011),f115(x40011)),f775(f775(f143(f851(x40011),f851(x40011)),f142(x40011)),f775(f142(f851(x40011)),x40012))),f775(f142(x40011),f775(f132(f851(x40011),f851(x40011),f125(x40011),f115(x40011)),x40012))) % 186.05/186.61 [4028]E(f775(f775(f46(a850,f857(f856(x40281,x40281),a844)),f239(f857(a850,a844))),f775(f775(f9(a850,f857(f856(x40281,x40281),a844),f857(f856(x40281,x40281),a844)),f173(f856(x40281,x40281),a844)),x40282)),f300(x40281,x40282)) % 186.05/186.61 [4050]E(f87(x40501,f775(f775(f10(f857(x40501,a844),a844,x40501),f775(a330,x40502)),f775(f775(f9(x40501,f857(x40501,a844),f857(x40501,a844)),f302(x40501)),f180(f857(x40501,a844))))),f306(x40501,x40502)) % 186.05/186.61 [4058]E(f775(f181(f851(x40581)),f152(x40581,f775(f132(f851(x40581),f851(x40581),f125(x40581),f115(x40581)),x40582))),f775(f42(x40581),f775(f775(f46(f851(x40581),f857(x40581,a844)),f775(f158(f851(x40581)),x40582)),f158(x40581)))) % 186.05/186.61 [4073]E(f775(f775(f103(f857(f856(x40731,x40731),a844)),x40732),f775(f775(f281(x40731,x40731,x40731),f775(f775(f281(x40731,x40731,x40731),x40732),f300(x40731,x40732))),x40732)),f775(f775(f281(x40731,x40731,x40731),x40732),f300(x40731,x40732))) % 186.05/186.61 [4094]P1(f775(f775(f232(f857(f856(x40941,x40941),a844)),f775(f775(f281(x40941,x40941,x40941),x40942),f300(x40941,x40942))),f775(f775(f248(x40941,x40941),f775(f276(x40941),x40942)),f775(f18(f857(x40941,a844),x40941),f775(f276(x40941),x40942))))) % 186.05/186.61 [4141]E(f775(f256(f851(x41411)),f775(f775(f9(f851(x41411),f857(x41411,a844),a844),f775(f775(f10(f857(x41411,a844),f857(f857(x41411,a844),a844),f851(x41411)),f232(f857(x41411,a844))),f158(x41411))),x41412)),f149(x41411,x41412)) % 186.05/186.61 [4153]E(f775(f145(f851(x41531),x41531,f115(x41531),f775(f775(f10(f851(x41531),f857(f851(x41531),f851(x41531)),x41531),f775(f9(f851(x41531),f851(x41531),f851(x41531)),f125(x41531))),f775(f775(f9(x41531,f851(x41531),f851(x41531)),f140(x41531)),f115(x41531)))),x41532),f775(f141(x41531),x41532)) % 186.05/186.61 [4192]P29(f857(x41921,x41922),f857(f856(x41921,x41922),a844),f775(f775(f10(f857(f856(x41921,x41922),a844),f857(f856(x41921,x41922),a844),f857(x41921,x41922)),f256(f856(x41921,x41922))),f775(f775(f10(f857(x41921,f857(x41922,a844)),f857(f856(x41921,x41922),a844),f857(x41921,x41922)),f251(x41921,x41922,a844)),f775(f10(x41922,f857(x41922,a844),x41921),f775(f9(x41922,x41922,a844),a330)))),f239(f857(f857(x41921,x41922),a844))) % 186.05/186.61 [4197]E(f52(a1,f775(f106(a1),f775(f775(f82(a1),x41971),x41971)),f775(f106(a1),f775(f775(f82(a1),x41972),x41972))),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a1,f775(f106(a1),x41971),f775(f106(a1),x41972)))) % 186.05/186.61 [4238]E(f775(f775(f46(x42381,f857(f856(x42381,x42381),a844)),x42382),f775(f775(f9(x42381,f857(f856(x42381,x42381),a844),f857(f856(x42381,x42381),a844)),f775(f775(f10(f856(x42381,x42381),f857(f857(f856(x42381,x42381),a844),f857(f856(x42381,x42381),a844)),x42381),f302(f856(x42381,x42381))),f775(f775(f20(x42381,x42381,f856(x42381,x42381)),f241(x42381,x42381)),f7(x42381)))),f180(f857(f856(x42381,x42381),a844)))),f260(x42381,x42382)) % 186.05/186.61 [4246]E(f198(x42461,f775(f775(f241(a1,a1),f775(f81(a1),f775(f775(f75(f856(a1,a1),a1,x42461,f240(a1,a1)),f207(x42461)),x42462))),f775(f775(f75(f856(a1,a1),a1,x42461,f250(a1,a1)),f207(x42461)),x42462))),f221(x42461,x42462)) % 186.05/186.61 [4326]E(f775(f256(f857(x43261,a844)),f775(f775(f10(f857(f857(x43261,a844),a844),a844,f857(x43261,a844)),f89(f857(x43261,a844))),f775(f775(f9(f857(x43261,a844),f857(f857(x43261,a844),a844),f857(f857(x43261,a844),a844)),f775(f775(f10(f857(f857(x43261,a844),f857(a844,a844)),f857(f857(f857(x43261,a844),a844),f857(f857(x43261,a844),a844)),f857(x43261,a844)),f20(f857(x43261,a844),a844,a844)),f775(f775(f10(f857(f857(x43261,a844),a844),f857(f857(x43261,a844),f857(a844,a844)),f857(x43261,a844)),f775(f10(a844,f857(a844,a844),f857(x43261,a844)),a331)),f775(f775(f9(f857(x43261,a844),f857(f857(x43261,a844),f857(x43261,a844)),f857(f857(x43261,a844),a844)),f775(f775(f10(f857(f857(x43261,a844),a844),f857(f857(f857(x43261,a844),f857(x43261,a844)),f857(f857(x43261,a844),a844)),f857(x43261,a844)),f10(f857(x43261,a844),a844,f857(x43261,a844))),a330)),f81(f857(x43261,a844)))))),f775(f775(f10(f857(f857(x43261,a844),a844),a844,f857(x43261,a844)),f775(f334(f857(x43261,a844)),x43262)),f301(x43261))))),f775(f301(x43261),f775(f81(f857(x43261,a844)),x43262))) % 186.05/186.61 [4470]~E(f775(f775(f82(a1),x44701),x44701),f775(f775(f3(a1),f775(f775(f82(a1),x44702),x44702)),a99)) % 186.05/186.61 [4475]~P1(f775(f775(f233(a850),f775(f775(f82(a850),x44751),x44752)),x44752)) % 186.05/186.61 [4476]~P1(f775(f775(f233(a850),f775(f775(f82(a850),x44761),x44762)),x44761)) % 186.05/186.61 [3663]E(f775(f775(f3(a850),x36631),f775(f775(f83(a850),f775(f775(f43(a850),x36631),x36632)),x36632)),f52(a850,x36631,x36632)) % 186.05/186.61 [3664]E(f775(f775(f3(a1),x36641),f775(f775(f83(a1),f775(f775(f43(a1),x36641),x36642)),x36642)),f52(a1,x36641,x36642)) % 186.05/186.61 [3699]E(f775(f775(f143(a850,x36991),f775(f153(x36991),x36992)),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(x36991)),x36992)))),x36992) % 186.05/186.61 [3760]E(f775(f277(x37601,x37601,f300(x37601,f180(f857(f856(x37601,x37601),a844)))),x37602),x37602) % 186.05/186.61 [3880]E(f300(x38801,f775(f775(f3(f857(f856(x38801,x38801),a844)),x38802),f300(x38801,f180(f857(f856(x38801,x38801),a844))))),f300(x38801,x38802)) % 186.05/186.61 [3881]E(f300(x38811,f775(f775(f103(f857(f856(x38811,x38811),a844)),x38812),f300(x38811,f180(f857(f856(x38811,x38811),a844))))),f300(x38811,x38812)) % 186.05/186.61 [3937]E(f775(f775(f3(a1),f775(f775(f3(a1),f775(f775(f82(a1),x39371),x39371)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x39372),x39372)),a99)),f775(f775(f82(a1),f775(f775(f3(a1),x39371),x39372)),f775(f775(f3(a1),x39371),x39372))) % 186.05/186.61 [3979]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f82(a1),x39791),x39792)),f775(f775(f82(a1),x39791),x39792))),a99),f775(f775(f82(a1),f775(f775(f82(a1),x39791),x39791)),f775(f775(f3(a1),f775(f775(f82(a1),x39792),x39792)),a99))) % 186.05/186.61 [4005]E(f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),x40051),x40051)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x40052),x40052)),a99)),f775(f775(f82(a1),f775(f775(f82(a1),x40051),f775(f775(f3(a1),x40052),a99))),f775(f775(f82(a1),x40051),f775(f775(f3(a1),x40052),a99)))) % 186.05/186.61 [4016]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f82(a1),x40161),x40162)),f775(f775(f82(a1),x40161),x40162))),a99),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),x40161),x40161)),a99)),f775(f775(f82(a1),x40162),x40162))) % 186.05/186.61 [4017]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),x40171),x40172)),f775(f775(f3(a1),x40171),x40172))),a99),f775(f775(f3(a1),f775(f775(f3(a1),f775(f775(f82(a1),x40171),x40171)),a99)),f775(f775(f82(a1),x40172),x40172))) % 186.05/186.61 [4070]E(f775(f102(a1),f775(f775(f43(a850),f775(f775(f83(a850),f775(a107,f775(f77(a1),x40701))),f775(a107,f775(f77(a1),x40702)))),f211(f775(a107,f775(f77(a1),x40701)),f775(a107,f775(f77(a1),x40702))))),f213(x40701,x40702)) % 186.05/186.61 [4115]E(f775(f775(f253(f856(a101,a101),a101,f856(a101,a101),f856(x41151,f856(a101,a101))),f264(f775(a5,f775(f181(f851(x41151)),x41152)))),f775(f775(f10(x41151,f857(f856(a101,a101),f856(x41151,f856(a101,a101))),a101),f241(x41151,f856(a101,a101))),f775(f775(f10(a850,x41151,a101),f775(f153(x41151),x41152)),a22))),f270(x41151,x41152)) % 186.05/186.61 [4198]E(f775(f132(a850,f851(x41981),f775(f9(f851(x41981),a850,a850),f775(f775(f10(a850,f857(a850,a850),f851(x41981)),f179(a850)),f181(f851(x41981)))),f2(a850)),f775(f142(f851(x41981)),f164(x41981,x41982))),f775(f181(f851(f851(x41981))),f775(f126(f851(x41981),f775(f775(f10(a844,a844,f851(x41981)),a328),f775(f775(f9(f851(x41981),f851(x41981),a844),a330),f115(x41981)))),x41982))) % 186.05/186.61 [4204]E(f775(f775(f46(a850,f857(x42041,a844)),f239(f857(a850,a844))),f775(f775(f9(a850,f857(a850,f857(x42041,a844)),f857(x42041,a844)),f775(f775(f10(f857(a850,a844),f857(f857(a850,f857(x42041,a844)),f857(x42041,a844)),a850),f46(a850,f857(x42041,a844))),f294(a850,f2(a850)))),x42042)),f775(f775(f46(a850,f857(x42041,a844)),f239(f857(a850,a844))),x42042)) % 186.05/186.61 [4223]P1(f775(f63(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),x42231)),f775(f775(f9(a850,a850,a844),f233(a850)),x42232))))) % 186.05/186.61 [4336]E(f775(f256(f856(f851(x43361),f851(x43361))),f775(f251(f851(x43361),f851(x43361),a844),f775(f775(f20(f851(x43361),f857(f851(x43361),a844),f857(f851(x43361),a844)),f775(f775(f10(f857(f851(x43361),f857(a844,a844)),f857(f857(f851(x43361),a844),f857(f851(x43361),a844)),f851(x43361)),f20(f851(x43361),a844,a844)),f775(f775(f10(f857(f851(x43361),a844),f857(f851(x43361),f857(a844,a844)),f851(x43361)),f775(f10(a844,f857(a844,a844),f851(x43361)),a332)),f775(f775(f9(f851(x43361),f857(f851(x43361),a850),f857(f851(x43361),a844)),f775(f775(f10(f857(a850,a844),f857(f857(f851(x43361),a850),f857(f851(x43361),a844)),f851(x43361)),f10(a850,a844,f851(x43361))),f775(f775(f10(a850,f857(a850,a844),f851(x43361)),f233(a850)),f181(f851(x43361))))),f181(f851(x43361)))))),f775(f775(f20(f851(x43361),f857(f851(x43361),a844),f857(f851(x43361),a844)),f775(f775(f10(f857(f851(x43361),f857(a844,a844)),f857(f857(f851(x43361),a844),f857(f851(x43361),a844)),f851(x43361)),f20(f851(x43361),a844,a844)),f775(f775(f10(f857(f851(x43361),a844),f857(f851(x43361),f857(a844,a844)),f851(x43361)),f775(f10(a844,f857(a844,a844),f851(x43361)),a331)),f775(f775(f9(f851(x43361),f857(f851(x43361),a850),f857(f851(x43361),a844)),f775(f775(f10(f857(a850,a844),f857(f857(f851(x43361),a850),f857(f851(x43361),a844)),f851(x43361)),f10(a850,a844,f851(x43361))),f775(f775(f10(a850,f857(a850,a844),f851(x43361)),a330),f181(f851(x43361))))),f181(f851(x43361)))))),f775(f775(f9(f851(x43361),f857(f856(f851(x43361),f851(x43361)),a844),f857(f851(x43361),a844)),f775(f775(f10(f857(f851(x43361),f857(f857(f856(f851(x43361),f851(x43361)),a844),a844)),f857(f857(f856(f851(x43361),f851(x43361)),a844),f857(f851(x43361),a844)),f851(x43361)),f9(f851(x43361),f857(f856(f851(x43361),f851(x43361)),a844),a844)),f775(f775(f10(f857(f851(x43361),f856(f851(x43361),f851(x43361))),f857(f851(x43361),f857(f857(f856(f851(x43361),f851(x43361)),a844),a844)),f851(x43361)),f775(f10(f856(f851(x43361),f851(x43361)),f857(f857(f856(f851(x43361),f851(x43361)),a844),a844),f851(x43361)),f334(f856(f851(x43361),f851(x43361))))),f241(f851(x43361),f851(x43361))))),f135(x43361,x43362)))))),f136(x43361,x43362)) % 186.05/186.61 [4008]E(f775(f775(f82(a1),f775(f775(f82(a1),f775(f775(f83(a1),x40081),x40082)),f775(f775(f83(a1),x40081),x40082))),x40082),f775(f775(f83(a1),f775(f775(f3(a1),f775(f775(f82(a1),x40081),x40081)),a99)),x40082)) % 186.05/186.61 [4113]E(f775(a107,f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x41131),x41132)),f180(f857(f856(a850,a850),a844)))))),f775(f775(f3(a850),x41131),x41132)) % 186.05/186.61 [4119]E(f775(f775(f281(x41191,x41191,x41191),f775(f775(f103(f857(f856(x41191,x41191),a844)),x41192),f300(x41191,f180(f857(f856(x41191,x41191),a844))))),f300(x41191,f775(f775(f103(f857(f856(x41191,x41191),a844)),x41192),f300(x41191,f180(f857(f856(x41191,x41191),a844)))))),f300(x41191,x41192)) % 186.05/186.61 [4158]E(f265(x41581,f775(f126(f856(a101,x41581),f775(f251(a101,x41581,a844),f775(f775(f10(a844,f857(x41581,a844),a101),f18(a844,x41581)),f775(f233(a101),f2(a101))))),x41582)),f265(x41581,x41582)) % 186.05/186.61 [4159]E(f263(x41591,f775(f126(f856(a101,x41591),f775(f251(a101,x41591,a844),f775(f775(f10(a844,f857(x41591,a844),a101),f18(a844,x41591)),f775(f233(a101),f2(a101))))),x41592)),f263(x41591,x41592)) % 186.05/186.61 [4161]E(f775(f81(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x41611),x41612)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x41612),x41611)),f180(f857(f856(a850,a850),a844)))))) % 186.05/186.61 [4235]E(f775(f775(f88(a1,a850),f775(f106(a1),f775(f775(f82(a1),x42351),a99))),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f2(a850))),f775(f775(f10(a850,a850,a1),a114),f775(f775(f10(a850,a850,a1),f775(f236(a850),x42352)),a107)))),f775(f775(f236(a850),f775(a114,x42352)),f775(f106(a850),x42351))) % 186.05/186.61 [4236]E(f775(f775(f88(a1,a850),f775(f106(a1),f775(f775(f82(a1),x42361),a99))),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f775(a114,x42362))),f775(f775(f10(a850,a850,a1),a114),f775(f775(f10(a850,a850,a1),f775(f179(a850),x42362)),a107)))),f775(f775(f179(a850),f775(a114,x42362)),f775(f106(a850),x42361))) % 186.05/186.61 [4256]E(f775(f132(f851(x42561),f851(x42561),f125(x42561),f115(x42561)),f775(f775(f143(f851(x42561),f851(x42561)),f145(f851(x42561),x42561,f115(x42561),f775(f775(f10(f851(x42561),f857(f851(x42561),f851(x42561)),x42561),f18(f851(x42561),f851(x42561))),f775(f775(f9(x42561,f851(x42561),f851(x42561)),f140(x42561)),f115(x42561))))),x42562)),f775(f775(f143(f851(x42561),x42561),f131(x42561)),f775(f126(f851(x42561),f775(f775(f10(a844,a844,f851(x42561)),a328),f775(f775(f9(f851(x42561),f851(x42561),a844),a330),f115(x42561)))),x42562))) % 186.05/186.61 [4316]E(f775(f251(a1,a1,a844),f775(f775(f9(a1,f857(a1,a844),f857(a1,a844)),f775(f775(f10(f857(a1,f857(a844,a844)),f857(f857(a1,a844),f857(a1,a844)),a1),f20(a1,a844,a844)),f775(f775(f10(f857(a1,a844),f857(a1,f857(a844,a844)),a1),f775(f10(a844,f857(a844,a844),a1),a331)),f775(f775(f10(f857(a1,a1),f857(a1,a844),a1),f775(f10(a1,a844,a1),f775(a330,x43161))),f775(f775(f10(a1,f857(a1,a1),a1),f82(a1)),f775(f83(a1),x43162)))))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),f775(a335,f775(f775(f233(a1),f2(a1)),x43162))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),f775(f775(f9(a1,a1,a844),f233(a1)),x43162))))),f775(f775(f10(a844,a844,a1),f775(a335,f775(a328,f775(f775(f233(a1),f2(a1)),x43162)))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f233(a1),x43162))),f775(f775(f9(a1,a1,a844),f232(a1)),f2(a1))))))),f56(x43161,x43162)) % 186.05/186.61 [4318]E(f775(f256(x43181),f775(f775(f10(f857(a850,a844),a844,x43181),f89(a850)),f775(f775(f9(x43181,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),x43181),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),x43181),f775(f10(a844,f857(a844,a844),a850),a331)),f775(f775(f9(x43181,f857(a850,x43181),f857(a850,a844)),f775(f775(f10(f857(x43181,a844),f857(f857(a850,x43181),f857(a850,a844)),x43181),f10(x43181,a844,a850)),a330)),f775(f153(x43181),x43182))))),f775(f775(f9(a850,a850,a844),f233(a850)),f775(f181(f851(x43181)),x43182))))),f775(f158(x43181),x43182)) % 186.05/186.61 [4131]E(f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),x41311),a99)),x41312)),f775(f775(f3(a1),f775(f775(f82(a1),x41311),a99)),x41312))),a99),f775(f775(f3(a1),f775(f775(f82(a1),x41311),x41311)),f775(f775(f3(a1),f775(f775(f82(a1),x41312),x41312)),a99))) % 186.05/186.61 [4251]E(f775(f132(f851(f851(x42511)),f851(f851(x42511)),f125(f851(x42511)),f115(f851(x42511))),f775(f775(f143(f851(x42511),f851(f851(x42511))),f145(f851(f851(x42511)),x42511,f115(f851(x42511)),f775(f18(f857(f851(x42511),f851(f851(x42511))),x42511),f775(f775(f9(f851(x42511),f851(f851(x42511)),f851(f851(x42511))),f140(f851(x42511))),f115(f851(x42511)))))),x42512)),f775(f775(f143(f851(x42511),f851(x42511)),f157(x42511)),f775(f126(f851(x42511),f775(f775(f10(a844,a844,f851(x42511)),a328),f775(f775(f9(f851(x42511),f851(x42511),a844),a330),f115(x42511)))),x42512))) % 186.05/186.61 [4261]E(f775(f775(f88(a1,a850),f775(f106(a1),f775(f775(f82(a1),x42611),a99))),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f2(a850))),f775(f775(f10(a850,a850,a1),a114),f775(f775(f9(a1,a850,a850),f775(f775(f10(a850,f857(a850,a850),a1),f236(a850)),a107)),x42612)))),f775(f775(f236(a850),f775(f106(a850),x42611)),f775(a114,x42612))) % 186.05/186.61 [4262]E(f775(f775(f88(a1,a850),f775(f106(a1),f775(f775(f82(a1),x42621),a99))),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f775(a114,x42622))),f775(f775(f10(a850,a850,a1),a114),f775(f775(f9(a1,a850,a850),f775(f775(f10(a850,f857(a850,a850),a1),f179(a850)),a107)),x42622)))),f775(f775(f179(a850),f775(f106(a850),x42621)),f775(a114,x42622))) % 186.05/186.61 [4250]E(f775(f251(x42501,x42501,a844),f775(f775(f20(x42501,a844,f857(x42501,a844)),f775(f775(f10(f857(x42501,f857(a844,a844)),f857(a844,f857(x42501,a844)),x42501),f9(x42501,a844,a844)),f775(f775(f10(f857(x42501,a844),f857(x42501,f857(a844,a844)),x42501),f775(f10(a844,f857(a844,a844),x42501),a331)),a330))),x42502)),f260(x42501,x42502)) % 186.05/186.61 [4294]E(f775(f775(f43(a850),x42941),f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x42942)),f775(f775(f43(a850),x42941),f775(a114,f775(a114,f775(a114,x42942))))) % 186.05/186.61 [4295]E(f52(a850,x42951,f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x42952)),f52(a850,x42951,f775(a114,f775(a114,f775(a114,x42952))))) % 186.05/186.61 [4296]E(f52(a850,f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x42961),x42962),f52(a850,f775(a114,f775(a114,f775(a114,x42961))),x42962)) % 186.05/186.61 [4309]E(f122(f775(x43091,f775(f775(f83(a101),f775(f106(a101),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x43092))),f775(f195(x43091),x43092)) % 186.05/186.61 [4310]E(f775(f775(f43(a850),f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),x43101)),x43102),f775(f775(f43(a850),f775(a114,f775(a114,f775(a114,x43101)))),x43102)) % 186.05/186.61 [3484]P29(x34841,f858(x34842,x34841),f313(x34841,x34842),x34843) % 186.05/186.61 [3485]P29(x34851,f858(x34851,x34852),f304(x34851,x34852),x34853) % 186.05/186.61 [4378]~E(f35(x43781,x43782),f775(a27,x43783)) % 186.05/186.61 [4379]~E(f36(x43791,x43792),f775(a27,x43793)) % 186.05/186.61 [4380]~E(f28(x43801,x43802),f775(a27,x43803)) % 186.05/186.61 [4381]~E(f775(a27,x43811),f35(x43812,x43813)) % 186.05/186.61 [4382]~E(f775(a27,x43821),f36(x43822,x43823)) % 186.05/186.61 [4383]~E(f775(a27,x43831),f28(x43832,x43833)) % 186.05/186.61 [4402]~E(f33(x44021,x44022,x44023),a25) % 186.05/186.61 [4403]~E(f32(x44031,x44032,x44033),a25) % 186.05/186.61 [4404]~E(f31(x44041,x44042,x44043),a25) % 186.05/186.61 [3098]E(f775(f185(x30981,x30982),x30983),f120(x30981,x30982)) % 186.05/186.61 [3099]E(f775(f194(x30991,x30992),x30993),f123(x30991,x30992)) % 186.05/186.61 [3193]E(f775(f775(f143(x31931,x31932),x31933),f115(x31931)),f115(x31932)) % 186.05/186.61 [3194]E(f775(f775(f196(x31941,x31942),x31943),f183(x31941)),f183(x31942)) % 186.05/186.61 [3214]E(f34(f31(x32141,x32142,x32143)),f2(a850)) % 186.05/186.61 [3233]E(f775(f174(x32331,x32332,x32333),f2(a850)),x32332) % 186.05/186.61 [3234]E(f775(f181(a845),f31(x32341,x32342,x32343)),f2(a850)) % 186.05/186.61 [3235]E(f775(f775(f167(x32351,x32352),x32353),f115(x32352)),f115(f856(x32351,x32352))) % 186.05/186.61 [3272]E(f87(x32721,f64(x32721,x32722,x32723)),f775(f65(x32721,x32722),x32723)) % 186.05/186.61 [3341]E(f775(f240(f851(x33411),f851(x33411)),f156(x33411,x33412,x33413)),f775(f126(x33411,x33412),x33413)) % 186.05/186.61 [3418]E(f175(x34181,x34182,x34183,f2(a850)),x34182) % 186.05/186.61 [3419]E(f19(x34191,x34192,x34193,f2(a101)),x34192) % 186.05/186.61 [3420]E(f21(x34201,x34202,x34203,f2(a101)),x34202) % 186.05/186.61 [3427]E(f154(x34271,x34272,x34273,f115(x34271)),f115(x34272)) % 186.05/186.61 [3434]E(f775(f775(f153(x34341),f775(f775(f140(x34341),x34342),x34343)),f2(a850)),x34342) % 186.05/186.61 [3483]P29(x34831,x34832,x34833,f180(f857(x34831,a844))) % 186.05/186.61 [3579]E(f262(x35791,x35792,x35793),f775(f241(f857(a101,f857(a844,f854(f852(x35791)))),f856(a101,a101)),f48(x35791))) % 186.05/186.61 [3638]E(f775(f75(x36381,x36382,x36381,x36383),f39(x36381)),x36383) % 186.05/186.61 [3814]P1(f775(f775(f334(f856(x38141,x38141)),f775(f775(f241(x38141,x38141),x38142),x38142)),f300(x38141,x38143))) % 186.05/186.61 [4479]~P1(f775(f775(f334(f856(f851(x44791),f851(x44791))),f775(f775(f241(f851(x44791),f851(x44791)),x44792),f115(x44791))),f135(x44791,x44793))) % 186.05/186.61 [4480]~P1(f775(f775(f334(f856(f851(x44801),f851(x44801))),f775(f775(f241(f851(x44801),f851(x44801)),x44802),f115(x44801))),f137(x44801,x44803))) % 186.05/186.61 [4481]~P1(f775(f775(f334(f856(f851(x44811),f851(x44811))),f775(f775(f241(f851(x44811),f851(x44811)),x44812),f115(x44811))),f146(x44811,x44813))) % 186.05/186.61 [4482]~P1(f775(f775(f334(f856(f851(x44821),f851(x44821))),f775(f775(f241(f851(x44821),f851(x44821)),f115(x44821)),x44822)),f135(x44821,x44823))) % 186.05/186.61 [4483]~P1(f775(f775(f334(f856(f851(x44831),f851(x44831))),f775(f775(f241(f851(x44831),f851(x44831)),f115(x44831)),x44832)),f146(x44831,x44833))) % 186.05/186.61 [3168]E(f775(f775(f197(x31681),x31682),x31683),f198(x31681,f210(x31682,x31683))) % 186.05/186.61 [3223]E(f775(f278(x32231,x32232),f775(f278(x32232,x32231),x32233)),x32233) % 186.05/186.61 [3240]E(f312(x32401,x32402,f775(f304(x32401,x32402),x32403)),x32403) % 186.05/186.61 [3241]E(f315(x32411,x32412,f775(f313(x32412,x32411),x32413)),x32413) % 186.05/186.61 [3247]E(f775(f775(f167(x32471,x32472),f115(x32471)),x32473),f115(f856(x32471,x32472))) % 186.05/186.61 [3250]E(f160(x32501,x32502,f775(f257(a850),x32503)),f775(f775(f159(x32501),x32503),x32502)) % 186.05/186.61 [3264]E(f775(f181(f858(x32641,x32642)),f775(f304(x32641,x32642),x32643)),f2(a850)) % 186.05/186.61 [3265]E(f775(f181(f858(x32651,x32652)),f775(f313(x32652,x32651),x32653)),f2(a850)) % 186.05/186.61 [3270]E(f775(f259(x32701,x32702),f775(f278(x32702,x32701),x32703)),f775(f261(x32702,x32701),x32703)) % 186.05/186.61 [3271]E(f775(f261(x32711,x32712),f775(f278(x32712,x32711),x32713)),f775(f259(x32712,x32711),x32713)) % 186.05/186.61 [3286]E(f775(f126(x32861,x32862),f775(f142(x32861),x32863)),f775(f142(x32861),f775(f126(x32861,x32862),x32863))) % 186.05/186.61 [3299]E(f775(f775(f128(x32991),x32992),f775(f157(x32991),x32993)),f775(f775(f128(x32991),f775(a114,x32992)),x32993)) % 186.05/186.61 [3317]E(f34(f32(x33171,x33172,x33173)),f775(f775(f82(a850),f34(x33173)),f775(a114,f2(a850)))) % 186.05/186.61 [3318]E(f775(f303(x33181,x33182,x33183),f180(f857(x33181,a844))),f180(f857(x33182,a844))) % 186.05/186.61 [3319]E(f775(f277(x33191,x33192,x33193),f180(f857(x33191,a844))),f180(f857(x33192,a844))) % 186.05/186.61 [3320]E(f775(f305(x33201,x33202,x33203),f239(f857(x33202,a844))),f239(f857(x33201,a844))) % 186.05/186.61 [3321]E(f775(f305(x33211,x33212,x33213),f180(f857(x33212,a844))),f180(f857(x33211,a844))) % 186.05/186.61 [3358]E(f228(x33581,x33582,f775(f227(x33581),x33583)),f775(f775(f82(a850),f775(x33582,x33583)),f775(a114,f2(a850)))) % 186.05/186.61 [3439]E(f775(f181(a845),f32(x34391,x34392,x34393)),f775(f775(f82(a850),f775(f181(a845),x34393)),f775(a114,f2(a850)))) % 186.05/186.61 [3440]E(f775(f303(f856(x34401,x34402),x34402,f250(x34401,x34402)),x34403),f775(f259(x34401,x34402),x34403)) % 186.05/186.61 [3441]E(f775(f303(f856(x34411,x34412),x34411,f240(x34411,x34412)),x34413),f775(f261(x34411,x34412),x34413)) % 186.05/186.61 [3510]E(f775(f775(f241(x35101,x35102),f775(f240(x35101,x35102),x35103)),f775(f250(x35101,x35102),x35103)),x35103) % 186.05/186.61 [3517]E(f775(f775(f251(x35171,x35172,x35171),f18(x35171,x35172)),x35173),f775(f240(x35171,x35172),x35173)) % 186.05/186.61 [3536]E(f170(x35361,x35362,x35363,f775(f18(f854(x35362),x35361),f183(x35362))),x35363) % 186.05/186.61 [3537]E(f170(x35371,x35372,f775(f18(f854(x35372),x35371),f183(x35372)),x35373),x35373) % 186.05/186.61 [3592]E(f34(f33(x35921,x35922,x35923)),f775(f775(f82(a850),f775(f775(f82(a850),f34(x35922)),f34(x35923))),f775(a114,f2(a850)))) % 186.05/186.61 [3642]E(f775(f75(x36421,x36421,x36422,f39(x36421)),x36423),x36423) % 186.05/186.61 [3728]P1(f775(f63(x37281),f169(x37281,x37282,f166(x37281,x37282,x37283)))) % 186.05/186.61 [3751]P1(f775(f775(f187(f28(x37511,x37512)),x37513),f775(f775(f775(a189,x37513),x37511),f775(x37512,x37513)))) % 186.05/186.61 [3753]E(f775(f181(a845),f33(x37531,x37532,x37533)),f775(f775(f82(a850),f775(f775(f82(a850),f775(f181(a845),x37532)),f775(f181(a845),x37533))),f775(a114,f2(a850)))) % 186.05/186.61 [3824]P1(f775(f775(f232(f857(x38241,a844)),f775(f158(x38241),f775(f126(x38241,x38242),x38243))),f775(f158(x38241),x38243))) % 186.05/186.61 [3867]P1(f775(f775(f232(f857(x38671,a844)),f775(f158(x38671),f775(f775(f159(x38671),x38672),x38673))),f775(f158(x38671),x38673))) % 186.05/186.61 [3868]P1(f775(f775(f232(f857(x38681,a844)),f775(f158(x38681),f775(f775(f128(x38681),x38682),x38683))),f775(f158(x38681),x38683))) % 186.05/186.61 [3872]P1(f775(f775(f232(f857(x38721,a844)),f775(f158(x38721),f151(x38721,x38722,x38723))),f775(f158(x38721),x38723))) % 186.05/186.61 [3873]P1(f775(f775(f232(f857(x38731,a844)),f775(f158(x38731),f160(x38731,x38732,x38733))),f775(f158(x38731),x38732))) % 186.05/186.61 [3897]P29(f856(x38971,x38972),f856(x38972,x38971),f775(f251(x38971,x38972,f856(x38972,x38971)),f775(f9(x38972,x38971,f856(x38972,x38971)),f241(x38972,x38971))),x38973) % 186.05/186.61 [3909]E(f775(f775(f775(f173(f851(x39091),f851(x39091)),f52(a850,x39092,f775(f181(f851(x39091)),x39093))),f141(x39091)),x39093),f775(f775(f775(f173(f851(x39091),f851(x39091)),x39092),f141(x39091)),x39093)) % 186.05/186.61 [3954]P1(f775(f775(f334(f856(f851(x39541),f851(x39541))),f775(f775(f241(f851(x39541),f851(x39541)),x39542),x39542)),f147(x39541,f300(x39541,x39543)))) % 186.05/186.61 [4098]E(f87(f856(x40981,x40982),f775(f775(f20(f856(x40981,x40982),x40982,a844),f775(f775(f10(x40981,f857(x40982,a844),f856(x40981,x40982)),x40983),f240(x40981,x40982))),f250(x40981,x40982))),f87(f856(x40981,x40982),f775(f251(x40981,x40982,a844),x40983))) % 186.05/186.61 [4099]E(f92(f856(x40991,x40992),f775(f775(f20(f856(x40991,x40992),x40992,a844),f775(f775(f10(x40991,f857(x40992,a844),f856(x40991,x40992)),x40993),f240(x40991,x40992))),f250(x40991,x40992))),f92(f856(x40991,x40992),f775(f251(x40991,x40992,a844),x40993))) % 186.05/186.61 [4138]E(f775(f775(f280(f856(a850,x41381),x41381),f325(a850,x41381,a237,x41382)),f775(f775(f20(x41381,x41381,f856(a850,x41381)),f775(f775(f10(a850,f857(x41381,f856(a850,x41381)),x41381),f241(a850,x41381)),x41383)),f7(x41381))),f327(x41381,x41383,x41382)) % 186.05/186.61 [4200]E(f775(f252(x42001,x42001,x42002,x42002,f7(x42001),f7(x42002)),x42003),x42003) % 186.05/186.61 [4335]E(f775(f775(f88(a1,x43351),f213(f775(f775(f75(f856(a1,a1),a1,x43351,f250(a1,a1)),f207(x43351)),x43352),f775(f775(f75(f856(a1,a1),a1,x43351,f250(a1,a1)),f207(x43351)),x43353))),f775(f775(f20(a1,a1,x43351),f775(f775(f10(a1,f857(a1,x43351),a1),f197(x43351)),f775(f775(f20(a1,a1,a1),f775(f775(f10(a1,f857(a1,a1),a1),f82(a1)),f775(f775(f10(a1,a1,a1),f775(f83(a1),f775(f775(f75(f856(a1,a1),a1,x43351,f240(a1,a1)),f207(x43351)),x43352))),f775(f775(f9(a1,a1,a1),f43(a1)),f775(f775(f75(f856(a1,a1),a1,x43351,f250(a1,a1)),f207(x43351)),x43352))))),f775(f775(f10(a1,a1,a1),f775(f83(a1),f775(f775(f75(f856(a1,a1),a1,x43351,f240(a1,a1)),f207(x43351)),x43353))),f775(f775(f9(a1,a1,a1),f43(a1)),f775(f775(f75(f856(a1,a1),a1,x43351,f250(a1,a1)),f207(x43351)),x43353)))))),f7(a1))),f224(x43351,x43352,x43353)) % 186.05/186.61 [4397]~E(f775(f775(f140(x43971),x43972),x43973),x43973) % 186.05/186.61 [4406]~E(f775(f775(f140(x44061),x44062),x44063),f115(x44061)) % 186.05/186.61 [4432]~E(f775(f775(f302(x44321),x44322),x44323),f180(f857(x44321,a844))) % 186.05/186.61 [4461]~E(f775(f303(x44611,f857(x44611,a844),x44612),x44613),f775(f301(x44611),x44613)) % 186.05/186.61 [3227]E(f775(f775(f148(x32271,f115(x32271)),x32272),x32273),f115(x32271)) % 186.05/186.61 [3228]E(f775(f131(x32281),f775(f775(f140(x32281),x32282),x32283)),x32282) % 186.05/186.61 [3229]E(f775(f157(x32291),f775(f775(f140(x32291),x32292),x32293)),x32293) % 186.05/186.61 [3275]E(f775(f775(f128(x32751),f80(a850)),f775(f775(f140(x32751),x32752),x32753)),x32753) % 186.05/186.61 [3306]E(f116(x33061,f775(f775(f128(x33061),x33062),x33063)),f775(f775(f128(x33061),x33062),f116(x33061,x33063))) % 186.05/186.61 [3308]E(f775(f775(f148(x33081,x33082),x33083),f775(f775(f153(x33081),x33082),x33083)),x33082) % 186.05/186.61 [3331]E(f775(f775(f302(x33311),x33312),f775(f775(f302(x33311),x33312),x33313)),f775(f775(f302(x33311),x33312),x33313)) % 186.05/186.61 [3344]E(f775(f775(f302(x33441),x33442),f775(f158(x33441),x33443)),f775(f158(x33441),f775(f775(f140(x33441),x33442),x33443))) % 186.05/186.62 [3346]E(f775(f775(f128(x33461),x33462),f775(f157(x33461),x33463)),f775(f157(x33461),f775(f775(f128(x33461),x33462),x33463))) % 186.05/186.62 [3355]E(f775(f775(f159(x33551),f80(a850)),f775(f775(f140(x33551),x33552),x33553)),f775(f775(f140(x33551),x33552),f115(x33551))) % 186.05/186.62 [3388]E(f775(f166(x33881,x33882,f115(f856(x33881,x33882))),x33883),f183(x33882)) % 186.05/186.62 [3403]E(f775(f65(x34031,x34032),f775(f775(f302(x34031),x34033),f180(f857(x34031,a844)))),x34033) % 186.05/186.62 [3447]E(f775(f775(f82(a850),x34471),f775(f775(f82(a850),x34472),x34473)),f775(f775(f82(a850),x34472),f775(f775(f82(a850),x34471),x34473))) % 186.05/186.62 [3448]E(f775(f775(f82(a1),x34481),f775(f775(f82(a1),x34482),x34483)),f775(f775(f82(a1),x34482),f775(f775(f82(a1),x34481),x34483))) % 186.05/186.62 [3453]E(f775(f775(f248(x34531,x34532),f180(f857(x34531,a844))),x34533),f180(f857(f856(x34531,x34532),a844))) % 186.05/186.62 [3475]E(f775(f775(f103(f857(x34751,a844)),x34752),x34753),f775(f775(f103(f857(x34751,a844)),x34753),x34752)) % 186.05/186.62 [3476]E(f775(f775(f104(f857(x34761,a844)),x34762),x34763),f775(f775(f104(f857(x34761,a844)),x34763),x34762)) % 186.05/186.62 [3478]E(f775(f775(f125(x34781),x34782),f775(f775(f140(x34781),x34783),f115(x34781))),f775(f141(x34781),f775(f775(f140(x34781),x34783),x34782))) % 186.05/186.62 [3479]E(f775(f775(f125(x34791),f775(f142(x34791),x34792)),f775(f142(x34791),x34793)),f775(f142(x34791),f775(f775(f125(x34791),x34793),x34792))) % 186.05/186.62 [3489]E(f775(f157(x34891),f775(f775(f159(x34891),f775(a114,x34892)),x34893)),f775(f775(f159(x34891),x34892),f775(f157(x34891),x34893))) % 186.05/186.62 [3496]P1(f775(f775(f334(x34961),x34962),f775(f775(f302(x34961),x34962),x34963))) % 186.05/186.62 [3500]E(f775(f775(f47(x35001,f857(x35002,a844)),f180(f857(x35001,a844))),x35003),f239(f857(x35002,a844))) % 186.05/186.62 [3503]E(f775(f277(x35031,x35031,f260(x35031,x35032)),x35033),f775(f775(f104(f857(x35031,a844)),x35032),x35033)) % 186.05/186.62 [3515]E(f775(f181(f851(x35151)),f775(f775(f140(x35151),x35152),x35153)),f775(f775(f82(a850),f775(f181(f851(x35151)),x35153)),f775(a114,f2(a850)))) % 186.05/186.62 [3519]E(f134(x35191,f775(f775(f125(x35191),x35192),f775(f775(f140(x35191),x35193),f115(x35191)))),x35193) % 186.05/186.62 [3520]E(f116(x35201,f775(f775(f125(x35201),x35202),f775(f775(f140(x35201),x35203),f115(x35201)))),x35202) % 186.05/186.62 [3525]E(f775(f775(f125(x35251),f775(f775(f159(x35251),x35252),x35253)),f775(f775(f128(x35251),x35252),x35253)),x35253) % 186.05/186.62 [3534]E(f775(f775(f3(a850),f775(f775(f82(a850),x35341),x35342)),f775(f775(f82(a850),x35343),x35342)),f775(f775(f3(a850),x35341),x35343)) % 186.05/186.62 [3535]E(f775(f775(f3(a850),f775(f775(f82(a850),x35351),x35352)),f775(f775(f82(a850),x35351),x35353)),f775(f775(f3(a850),x35352),x35353)) % 186.05/186.62 [3541]E(f775(f775(f125(x35411),f775(f142(x35411),x35412)),f775(f775(f140(x35411),x35413),f115(x35411))),f775(f142(x35411),f775(f775(f140(x35411),x35413),x35412))) % 186.05/186.62 [3543]E(f775(f775(f82(a850),f775(f181(f851(x35431)),x35432)),f775(f181(f851(x35431)),x35433)),f775(f181(f851(x35431)),f775(f775(f125(x35431),x35432),x35433))) % 186.05/186.62 [3553]E(f775(f775(f103(f857(x35531,a844)),f775(f158(x35531),x35532)),f775(f158(x35531),x35533)),f775(f158(x35531),f775(f775(f125(x35531),x35532),x35533))) % 186.05/186.62 [3554]E(f52(a850,f775(f775(f83(a850),x35541),x35542),f775(f775(f83(a850),x35541),x35543)),f775(f775(f83(a850),x35541),f52(a850,x35542,x35543))) % 186.05/186.62 [3567]E(f775(f775(f159(x35671),f775(f775(f3(a850),x35672),f80(a850))),f775(f157(x35671),x35673)),f775(f157(x35671),f775(f775(f159(x35671),x35672),x35673))) % 186.05/186.62 [3572]E(f775(f775(f104(f857(x35721,a844)),x35722),f775(f81(f857(x35721,a844)),x35723)),f775(f775(f3(f857(x35721,a844)),x35722),x35723)) % 186.05/186.62 [3573]E(f775(f775(f3(f857(x35731,a844)),x35732),f775(f81(f857(x35731,a844)),x35733)),f775(f775(f104(f857(x35731,a844)),x35732),x35733)) % 186.05/186.62 [3595]E(f775(f775(f248(x35951,x35952),x35953),f775(f18(f857(x35952,a844),x35951),f180(f857(x35952,a844)))),f180(f857(f856(x35951,x35952),a844))) % 186.05/186.62 [3597]E(f775(f775(f82(a850),f775(f775(f83(a850),x35971),x35972)),f775(f775(f83(a850),x35971),x35973)),f775(f775(f83(a850),x35971),f775(f775(f82(a850),x35972),x35973))) % 186.05/186.62 [3598]E(f775(f775(f3(a850),f775(f775(f83(a850),x35981),x35982)),f775(f775(f83(a850),x35981),x35983)),f775(f775(f83(a850),x35981),f775(f775(f3(a850),x35982),x35983))) % 186.05/186.62 [3599]E(f775(f775(f82(a1),f775(f775(f83(a1),x35991),x35992)),f775(f775(f83(a1),x35991),x35993)),f775(f775(f83(a1),x35991),f775(f775(f82(a1),x35992),x35993))) % 186.05/186.62 [3600]E(f775(f775(f3(a1),f775(f775(f83(a1),x36001),x36002)),f775(f775(f83(a1),x36001),x36003)),f775(f775(f83(a1),x36001),f775(f775(f3(a1),x36002),x36003))) % 186.05/186.62 [3601]E(f775(f775(f83(a1),f775(f775(f242(a1),x36011),x36012)),f775(f775(f242(a1),x36011),x36013)),f775(f775(f242(a1),x36011),f775(f775(f82(a850),x36012),x36013))) % 186.05/186.62 [3614]E(f775(f775(f46(x36141,f857(x36142,a844)),x36143),f775(f18(f857(x36142,a844),x36141),f180(f857(x36142,a844)))),f180(f857(x36142,a844))) % 186.05/186.62 [3616]E(f52(a850,f775(f775(f83(a850),x36161),x36162),f775(f775(f83(a850),x36163),x36162)),f775(f775(f83(a850),f52(a850,x36161,x36163)),x36162)) % 186.05/186.62 [3621]E(f52(a1,f775(f775(f83(a1),x36211),f52(a1,x36212,x36213)),x36213),f52(a1,f775(f775(f83(a1),x36211),x36212),x36213)) % 186.05/186.62 [3622]E(f52(a1,f775(f775(f3(a1),x36221),f52(a1,x36222,x36223)),x36223),f52(a1,f775(f775(f3(a1),x36221),x36222),x36223)) % 186.05/186.62 [3623]P1(f775(f775(f232(f857(x36231,a844)),x36232),f775(f775(f302(x36231),x36233),x36232))) % 186.05/186.62 [3647]E(f775(f303(f856(x36471,x36472),x36471,f240(x36471,x36472)),f775(f158(f856(x36471,x36472)),x36473)),f169(x36471,x36472,f166(x36471,x36472,x36473))) % 186.05/186.62 [3704]E(f775(f775(f47(f857(x37041,a844),f857(x37041,a844)),x37042),f775(f103(f857(x37041,a844)),x37043)),f775(f775(f103(f857(x37041,a844)),x37043),f45(f857(x37041,a844),x37042))) % 186.05/186.62 [3705]E(f775(f775(f46(f857(x37051,a844),f857(x37051,a844)),x37052),f775(f104(f857(x37051,a844)),x37053)),f775(f775(f104(f857(x37051,a844)),x37053),f44(f857(x37051,a844),x37052))) % 186.05/186.62 [3715]E(f775(f158(x37151),f775(f775(f775(f173(f851(x37151),f851(x37151)),x37152),f141(x37151)),x37153)),f775(f158(x37151),x37153)) % 186.05/186.62 [3719]E(f775(f775(f159(x37191),f775(f181(f851(x37191)),f162(x37191,x37192,x37193))),x37193),f162(x37191,x37192,x37193)) % 186.05/186.62 [3720]E(f169(x37201,x37202,f775(f775(f10(x37202,f854(x37202),x37201),f227(x37202)),x37203)),f239(f857(x37201,a844))) % 186.05/186.62 [3723]E(f775(f181(f851(x37231)),f775(f775(f775(f173(f851(x37231),f851(x37231)),x37232),f141(x37231)),x37233)),f775(f181(f851(x37231)),x37233)) % 186.05/186.62 [3726]E(f775(f775(f251(x37261,x37262,x37262),f775(f18(f857(x37262,x37262),x37261),f7(x37262))),x37263),f775(f250(x37261,x37262),x37263)) % 186.05/186.62 [3733]E(f52(a1,f775(f775(f3(a1),f52(a1,x37331,x37332)),x37333),x37332),f52(a1,f775(f775(f3(a1),x37331),x37333),x37332)) % 186.05/186.62 [3734]E(f52(a1,f775(f775(f242(a1),f52(a1,x37341,x37342)),x37343),x37342),f52(a1,f775(f775(f242(a1),x37341),x37343),x37342)) % 186.05/186.62 [3737]E(f775(f775(f46(f857(f856(x37371,x37372),a844),f857(x37372,a844)),x37373),f259(x37371,x37372)),f775(f259(x37371,x37372),f44(f857(f856(x37371,x37372),a844),x37373))) % 186.05/186.62 [3738]E(f775(f775(f46(f857(f856(x37381,x37382),a844),f857(x37381,a844)),x37383),f261(x37381,x37382)),f775(f261(x37381,x37382),f44(f857(f856(x37381,x37382),a844),x37383))) % 186.05/186.62 [3766]E(f775(f75(x37661,x37661,x37661,x37662),f775(f775(f173(x37661,x37661),x37663),x37662)),f775(f775(f173(x37661,x37661),f775(a114,x37663)),x37662)) % 186.05/186.62 [3776]E(f229(f854(x37761),x37762,f183(x37761),f775(f775(f10(x37761,f854(x37761),x37762),f227(x37761)),x37763)),f775(f196(x37762,x37761),x37763)) % 186.05/186.62 [3783]E(f775(f775(f128(x37831),f775(f775(f3(a850),f775(f181(f851(x37831)),x37832)),x37833)),f775(f142(x37831),x37832)),f775(f142(x37831),f775(f775(f159(x37831),x37833),x37832))) % 186.05/186.62 [3784]E(f775(f775(f159(x37841),f775(f775(f3(a850),f775(f181(f851(x37841)),x37842)),x37843)),f775(f142(x37841),x37842)),f775(f142(x37841),f775(f775(f128(x37841),x37843),x37842))) % 186.05/186.62 [3787]E(f775(f775(f82(a850),f775(f155(a850),f775(f775(f143(x37871,a850),x37872),x37873))),f775(f181(f851(x37871)),x37873)),f144(x37871,x37872,x37873)) % 186.05/186.62 [3803]E(f775(f141(x38031),f775(f775(f775(f173(f851(x38031),f851(x38031)),x38032),f141(x38031)),x38033)),f775(f775(f775(f173(f851(x38031),f851(x38031)),f775(a114,x38032)),f141(x38031)),x38033)) % 186.05/186.62 [3815]P1(f775(f775(f232(a850),f775(f181(f851(x38151)),f775(f126(x38151,x38152),x38153))),f775(f181(f851(x38151)),x38153))) % 186.05/186.62 [3832]E(f775(f775(f103(f857(f857(x38321,a844),a844)),f775(f301(x38321),x38322)),f775(f303(f857(x38321,a844),f857(x38321,a844),f775(f302(x38321),x38323)),f775(f301(x38321),x38322))),f775(f301(x38321),f775(f775(f302(x38321),x38323),x38322))) % 186.05/186.62 [3848]P28(x38481,x38482,f775(f775(f302(f849(x38481)),f775(f775(f775(f93(x38481),x38483),a25),x38483)),f180(f857(f849(x38481),a844)))) % 186.05/186.62 [3864]P1(f775(f775(f232(a850),f775(f181(f851(x38641)),f162(x38641,x38642,x38643))),f775(f181(f851(x38641)),x38643))) % 186.05/186.62 [3871]E(f775(f261(x38711,x38712),f775(f256(f856(x38711,x38712)),f775(f251(x38711,x38712,a844),x38713))),f775(f256(x38711),f775(f775(f10(f857(x38712,a844),a844,x38711),f89(x38712)),x38713))) % 186.05/186.62 [3884]E(f775(f303(a850,a850,f775(f775(f9(a850,a850,a850),f82(a850)),x38841)),f295(a850,x38842,x38843)),f295(a850,f775(f775(f82(a850),x38842),x38841),f775(f775(f82(a850),x38843),x38841))) % 186.05/186.62 [3900]E(f775(f303(a850,a850,f775(f775(f9(a850,a850,a850),f82(a850)),x39001)),f775(f294(a850,x39002),x39003)),f775(f294(a850,f775(f775(f82(a850),x39002),x39001)),f775(f775(f82(a850),x39003),x39001))) % 186.05/186.62 [3918]E(f775(f775(f167(x39181,x39182),f775(f775(f143(f856(x39181,x39182),x39181),f240(x39181,x39182)),x39183)),f775(f775(f143(f856(x39181,x39182),x39182),f250(x39181,x39182)),x39183)),x39183) % 186.05/186.62 [3923]E(f775(f775(f82(a850),f775(f775(f83(a850),x39231),f52(a850,f775(f775(f43(a850),x39232),x39231),x39233))),f52(a850,x39232,x39231)),f52(a850,x39232,f775(f775(f83(a850),x39231),x39233))) % 186.05/186.62 [3934]P1(f775(f63(f854(x39341)),f775(f303(x39342,f854(x39341),f166(x39342,x39341,x39343)),f239(f857(x39342,a844))))) % 186.05/186.62 [3938]E(f775(f775(f125(x39381),x39382),f775(f132(f851(x39381),f851(x39381),f125(x39381),f115(x39381)),x39383)),f775(f132(f851(x39381),f851(x39381),f125(x39381),x39382),x39383)) % 186.05/186.62 [3958]P1(f775(f775(f334(f856(x39581,x39581)),f775(f775(f241(x39581,x39581),x39582),x39582)),f775(f775(f173(f856(x39581,x39581),a844),f2(a850)),x39583))) % 186.05/186.62 [3964]E(f775(f256(x39641),f775(f775(f10(f857(x39642,a844),a844,x39641),f89(x39642)),f775(f9(x39642,x39641,a844),x39643))),f775(f259(x39642,x39641),f775(f256(f856(x39642,x39641)),f775(f251(x39642,x39641,a844),x39643)))) % 186.05/186.62 [3983]E(f775(f775(f103(f857(x39831,a844)),f775(f775(f46(a850,f857(x39831,a844)),f295(a850,f80(a850),x39832)),x39833)),f775(x39833,f2(a850))),f775(f775(f46(a850,f857(x39831,a844)),f775(f293(a850),x39832)),x39833)) % 186.05/186.62 [3998]E(f775(f132(f851(x39981),f851(x39981),f125(x39981),f115(x39981)),f775(f775(f143(f851(x39981),f851(x39981)),f126(x39981,x39982)),x39983)),f775(f126(x39981,x39982),f775(f132(f851(x39981),f851(x39981),f125(x39981),f115(x39981)),x39983))) % 186.05/186.62 [4003]E(f775(f250(f851(x40031),f851(x40031)),f156(x40031,x40032,x40033)),f775(f126(x40031,f775(f75(a844,a844,x40031,a328),x40032)),x40033)) % 186.05/186.62 [4052]E(f775(f775(f82(a1),f775(f775(f82(a1),f775(f775(f83(a1),x40521),f775(f775(f43(a1),x40522),x40521))),f52(a1,x40522,x40521))),x40523),f775(f775(f82(a1),x40522),x40523)) % 186.05/186.62 [4086]E(f775(f775(f82(a1),f775(f775(f82(a1),f775(f775(f83(a1),f775(f775(f43(a1),x40861),x40862)),x40862)),f52(a1,x40861,x40862))),x40863),f775(f775(f82(a1),x40861),x40863)) % 186.05/186.62 [4116]E(f87(f856(x41161,x41162),f775(f251(x41161,x41162,a844),f775(f775(f10(f857(x41162,f856(x41161,x41162)),f857(x41162,a844),x41161),f775(f10(f856(x41161,x41162),a844,x41162),x41163)),f241(x41161,x41162)))),f87(f856(x41161,x41162),x41163)) % 186.05/186.62 [4117]E(f92(f856(x41171,x41172),f775(f251(x41171,x41172,a844),f775(f775(f10(f857(x41172,f856(x41171,x41172)),f857(x41172,a844),x41171),f775(f10(f856(x41171,x41172),a844,x41172),x41173)),f241(x41171,x41172)))),f92(f856(x41171,x41172),x41173)) % 186.05/186.62 [4149]P1(f775(f775(f232(f857(x41491,a844)),f44(f857(x41491,a844),f775(f775(f104(f857(f857(x41491,a844),a844)),x41492),x41493))),f775(f775(f104(f857(x41491,a844)),f44(f857(x41491,a844),x41492)),f44(f857(x41491,a844),x41493)))) % 186.05/186.62 [4150]E(f775(f142(x41501),f775(f775(f775(f173(f851(x41501),f851(x41501)),f775(f775(f3(a850),f775(f181(f851(x41501)),x41502)),f52(a850,x41503,f775(f181(f851(x41501)),x41502)))),f141(x41501)),x41502)),f775(f775(f775(f173(f851(x41501),f851(x41501)),x41503),f141(x41501)),f775(f142(x41501),x41502))) % 186.05/186.62 [4162]E(f775(f256(x41621),f775(f775(f10(a844,a844,x41621),a328),f775(f775(f9(x41621,f854(x41622),a844),f775(f775(f10(f854(x41622),f857(f854(x41622),a844),x41621),a330),x41623)),f183(x41622)))),f169(x41621,x41622,x41623)) % 186.05/186.62 [4225]E(f775(f256(x42251),f775(f775(f10(f857(x42252,a844),a844,x42251),f89(x42252)),f775(f775(f10(f854(x42251),f857(x42252,a844),x42251),f775(f9(x42252,f854(x42251),a844),f775(f775(f10(f854(x42251),f857(f854(x42251),a844),x42252),a330),x42253))),f227(x42251)))),f171(x42252,x42251,x42253)) % 186.05/186.62 [4474]~P1(f775(f64(x44741,x44742,f180(f857(x44741,a844))),x44743)) % 186.05/186.62 [3490]E(f775(f181(f851(x34901)),f775(f775(f159(x34901),x34902),x34903)),f775(f775(f236(a850),f775(f181(f851(x34901)),x34903)),x34902)) % 186.05/186.62 [3491]E(f775(f181(f851(x34911)),f775(f775(f128(x34911),x34912),x34913)),f775(f775(f3(a850),f775(f181(f851(x34911)),x34913)),x34912)) % 186.05/186.62 [3527]E(f775(f775(f43(a850),f775(f775(f43(a850),x35271),x35272)),x35273),f775(f775(f43(a850),x35271),f775(f775(f83(a850),x35272),x35273))) % 186.05/186.62 [3528]E(f775(f775(f82(a850),f775(f775(f82(a850),x35281),x35282)),x35283),f775(f775(f82(a850),x35281),f775(f775(f82(a850),x35282),x35283))) % 186.05/186.62 [3529]E(f775(f775(f82(a1),f775(f775(f82(a1),x35291),x35292)),x35293),f775(f775(f82(a1),x35291),f775(f775(f82(a1),x35292),x35293))) % 186.05/186.62 [3530]E(f775(f775(f83(a850),f775(f775(f83(a850),x35301),x35302)),x35303),f775(f775(f83(a850),x35301),f775(f775(f83(a850),x35302),x35303))) % 186.05/186.62 [3531]E(f775(f775(f83(a1),f775(f775(f83(a1),x35311),x35312)),x35313),f775(f775(f83(a1),x35311),f775(f775(f83(a1),x35312),x35313))) % 186.05/186.62 [3532]E(f775(f775(f3(a850),f775(f775(f3(a850),x35321),x35322)),x35323),f775(f775(f3(a850),x35321),f775(f775(f82(a850),x35322),x35323))) % 186.05/186.62 [3533]E(f775(f775(f242(a1),f775(f775(f242(a1),x35331),x35332)),x35333),f775(f775(f242(a1),x35331),f775(f775(f83(a850),x35332),x35333))) % 186.05/186.62 [3551]E(f150(x35511,f775(f775(f140(f857(x35511,a844)),x35512),x35513)),f161(x35511,x35512,f150(x35511,x35513))) % 186.05/186.62 [3596]E(f775(f775(f3(a850),f775(f775(f3(a850),x35961),x35962)),x35963),f775(f775(f3(a850),f775(f775(f3(a850),x35961),x35963)),x35962)) % 186.05/186.62 [3604]E(f775(f775(f104(f857(x36041,a844)),x36042),f775(f775(f3(f857(x36041,a844)),x36043),x36042)),f180(f857(x36041,a844))) % 186.05/186.62 [3649]E(f45(f857(x36491,a844),f775(f775(f302(f857(x36491,a844)),x36492),x36493)),f775(f775(f104(f857(x36491,a844)),x36492),f45(f857(x36491,a844),x36493))) % 186.05/186.62 [3650]E(f44(f857(x36501,a844),f775(f775(f302(f857(x36501,a844)),x36502),x36503)),f775(f775(f103(f857(x36501,a844)),x36502),f44(f857(x36501,a844),x36503))) % 186.05/186.62 [3652]E(f775(f775(f82(a850),f775(f775(f83(a850),x36521),x36522)),f775(f775(f83(a850),x36523),x36522)),f775(f775(f83(a850),f775(f775(f82(a850),x36521),x36523)),x36522)) % 186.05/186.62 [3653]E(f775(f775(f3(a850),f775(f775(f83(a850),x36531),x36532)),f775(f775(f83(a850),x36533),x36532)),f775(f775(f83(a850),f775(f775(f3(a850),x36531),x36533)),x36532)) % 186.05/186.62 [3654]E(f775(f775(f82(a1),f775(f775(f83(a1),x36541),x36542)),f775(f775(f83(a1),x36543),x36542)),f775(f775(f83(a1),f775(f775(f82(a1),x36541),x36543)),x36542)) % 186.05/186.62 [3656]E(f775(f775(f3(a1),f775(f775(f83(a1),x36561),x36562)),f775(f775(f83(a1),x36563),x36562)),f775(f775(f83(a1),f775(f775(f3(a1),x36561),x36563)),x36562)) % 186.05/186.62 [3657]E(f775(f775(f236(a850),f775(f775(f3(a850),x36571),x36572)),f775(f775(f3(a850),x36573),x36572)),f775(f775(f3(a850),f775(f775(f236(a850),x36571),x36573)),x36572)) % 186.05/186.62 [3681]E(f775(f775(f103(f857(x36811,a844)),x36812),f775(f775(f3(f857(x36811,a844)),x36813),x36812)),f775(f775(f103(f857(x36811,a844)),x36812),x36813)) % 186.05/186.62 [3682]E(f775(f775(f103(f857(x36821,a844)),x36822),f775(f775(f103(f857(x36821,a844)),x36822),x36823)),f775(f775(f103(f857(x36821,a844)),x36822),x36823)) % 186.05/186.62 [3683]E(f775(f775(f104(f857(x36831,a844)),x36832),f775(f775(f104(f857(x36831,a844)),x36832),x36833)),f775(f775(f104(f857(x36831,a844)),x36832),x36833)) % 186.05/186.62 [3695]E(f775(f775(f281(x36951,x36952,x36952),x36953),f300(x36952,f180(f857(f856(x36952,x36952),a844)))),x36953) % 186.05/186.62 [3700]E(f775(f775(f103(f857(x37001,a844)),f775(f775(f302(x37001),x37002),f180(f857(x37001,a844)))),x37003),f775(f775(f302(x37001),x37002),x37003)) % 186.05/186.62 [3718]E(f775(f775(f3(a850),f775(f775(f3(a850),f775(a114,x37181)),x37182)),f775(a114,x37183)),f775(f775(f3(a850),f775(f775(f3(a850),x37181),x37182)),x37183)) % 186.05/186.62 [3746]E(f775(f775(f104(f857(f857(x37461,a844),a844)),f775(f301(x37461),x37462)),f775(f301(x37461),x37463)),f775(f301(x37461),f775(f775(f104(f857(x37461,a844)),x37462),x37463))) % 186.05/186.62 [3749]E(f775(f775(f103(f857(x37491,a844)),f775(f81(f857(x37491,a844)),x37492)),x37493),f775(f81(f857(x37491,a844)),f775(f775(f3(f857(x37491,a844)),x37492),x37493))) % 186.05/186.62 [3762]E(f775(f775(f302(x37621),x37622),f775(f775(f3(f857(x37621,a844)),x37623),f775(f775(f302(x37621),x37622),f180(f857(x37621,a844))))),f775(f775(f302(x37621),x37622),x37623)) % 186.05/186.62 [3773]P1(f775(f775(f232(f857(x37731,a844)),x37732),f775(f775(f103(f857(x37731,a844)),x37733),x37732))) % 186.05/186.62 [3774]P1(f775(f775(f232(f857(x37741,a844)),x37742),f775(f775(f103(f857(x37741,a844)),x37742),x37743))) % 186.05/186.62 [3777]E(f775(f775(f104(f857(x37771,a844)),f775(f81(f857(x37771,a844)),x37772)),f775(f81(f857(x37771,a844)),x37773)),f775(f81(f857(x37771,a844)),f775(f775(f103(f857(x37771,a844)),x37772),x37773))) % 186.05/186.62 [3778]E(f775(f775(f103(f857(x37781,a844)),f775(f81(f857(x37781,a844)),x37782)),f775(f81(f857(x37781,a844)),x37783)),f775(f81(f857(x37781,a844)),f775(f775(f104(f857(x37781,a844)),x37782),x37783))) % 186.05/186.62 [3791]P1(f775(f775(f232(f857(x37911,a844)),f775(f158(x37911),x37912)),f775(f158(x37911),f775(f775(f140(x37911),x37913),x37912)))) % 186.05/186.62 [3800]E(f775(f775(f103(f857(x38001,a844)),f775(f775(f3(f857(x38001,a844)),x38002),x38003)),f775(f775(f104(f857(x38001,a844)),x38002),x38003)),x38002) % 186.05/186.62 [3850]E(f775(f775(f8(x38501,a1),f775(f775(f10(a850,a1,x38501),f102(a1)),x38502)),x38503),f775(f102(a1),f775(f775(f8(x38501,a850),x38502),x38503))) % 186.05/186.62 [3851]E(f775(f775(f11(x38511,a1),f775(f775(f10(a850,a1,x38511),f102(a1)),x38512)),x38513),f775(f102(a1),f775(f775(f11(x38511,a850),x38512),x38513))) % 186.05/186.62 [3907]E(f775(f81(f857(f856(x39071,x39072),a844)),f775(f775(f248(x39071,x39072),x39073),f775(f18(f857(x39072,a844),x39071),f239(f857(x39072,a844))))),f775(f775(f248(x39071,x39072),f775(f81(f857(x39071,a844)),x39073)),f775(f18(f857(x39072,a844),x39071),f239(f857(x39072,a844))))) % 186.05/186.62 [3908]E(f775(f81(f857(f856(x39081,x39082),a844)),f775(f775(f248(x39081,x39082),f239(f857(x39081,a844))),f775(f18(f857(x39082,a844),x39081),x39083))),f775(f775(f248(x39081,x39082),f239(f857(x39081,a844))),f775(f18(f857(x39082,a844),x39081),f775(f81(f857(x39082,a844)),x39083)))) % 186.05/186.62 [3959]E(f775(f775(f46(f857(x39591,a844),f857(x39591,a844)),x39592),f775(f775(f9(f857(x39591,a844),f857(x39591,a844),f857(x39591,a844)),f104(f857(x39591,a844))),x39593)),f775(f775(f104(f857(x39591,a844)),f44(f857(x39591,a844),x39592)),x39593)) % 186.05/186.62 [3966]E(f775(f132(f851(x39661),f851(x39661),f125(x39661),f115(x39661)),f775(f775(f140(f851(x39661)),x39662),x39663)),f775(f775(f125(x39661),x39662),f775(f132(f851(x39661),f851(x39661),f125(x39661),f115(x39661)),x39663))) % 186.05/186.62 [3989]E(f775(f775(f302(f857(x39891,a844)),f775(f277(x39891,x39891,x39892),f775(f775(f302(x39891),x39893),f180(f857(x39891,a844))))),f180(f857(f857(x39891,a844),a844))),f775(f775(f61(x39891),f775(f775(f302(x39891),x39893),f180(f857(x39891,a844)))),x39892)) % 186.05/186.62 [3999]E(f775(f775(f82(a850),f775(f775(f83(a850),x39991),f775(f775(f43(a850),x39992),x39993))),f775(f775(f43(a850),f775(f775(f83(a850),x39991),f52(a850,x39992,x39993))),x39993)),f775(f775(f43(a850),f775(f775(f83(a850),x39991),x39992)),x39993)) % 186.05/186.62 [4000]E(f775(f775(f82(a1),f775(f775(f83(a1),x40001),f775(f775(f43(a1),x40002),x40003))),f775(f775(f43(a1),f775(f775(f83(a1),x40001),f52(a1,x40002,x40003))),x40003)),f775(f775(f43(a1),f775(f775(f83(a1),x40001),x40002)),x40003)) % 186.05/186.62 [4084]E(f775(f775(f125(x40841),f775(f132(f851(x40841),f851(x40841),f125(x40841),f115(x40841)),x40842)),f775(f132(f851(x40841),f851(x40841),f125(x40841),f115(x40841)),x40843)),f775(f132(f851(x40841),f851(x40841),f125(x40841),f115(x40841)),f775(f775(f125(f851(x40841)),x40842),x40843))) % 186.05/186.62 [4087]E(f775(f775(f241(f851(x40871),f851(x40871)),f775(f126(x40871,x40872),x40873)),f775(f126(x40871,f775(f75(a844,a844,x40871,a328),x40872)),x40873)),f156(x40871,x40872,x40873)) % 186.05/186.62 [4090]E(f775(f775(f82(a850),f775(f775(f82(a850),f775(f775(f43(a850),x40901),x40902)),f775(f775(f43(a850),x40903),x40902))),f775(f775(f43(a850),f775(f775(f82(a850),f52(a850,x40901,x40902)),f52(a850,x40903,x40902))),x40902)),f775(f775(f43(a850),f775(f775(f82(a850),x40901),x40903)),x40902)) % 186.05/186.62 [4091]E(f775(f775(f82(a1),f775(f775(f82(a1),f775(f775(f43(a1),x40911),x40912)),f775(f775(f43(a1),x40913),x40912))),f775(f775(f43(a1),f775(f775(f82(a1),f52(a1,x40911,x40912)),f52(a1,x40913,x40912))),x40912)),f775(f775(f43(a1),f775(f775(f82(a1),x40911),x40913)),x40912)) % 186.05/186.62 [4164]E(f775(f256(x41641),f775(f775(f20(x41641,a844,a844),f775(f775(f10(a844,f857(a844,a844),x41641),a332),f775(f775(f9(x41641,x41641,a844),a330),x41642))),f775(f775(f9(x41641,f857(x41641,a844),a844),f334(x41641)),x41643))),f775(f775(f302(x41641),x41642),x41643)) % 186.05/186.62 [4186]E(f775(f256(x41861),f775(f775(f20(x41861,a844,a844),f775(f775(f10(a844,f857(a844,a844),x41861),a332),f775(f775(f9(x41861,f857(x41861,a844),a844),f334(x41861)),x41862))),f775(f775(f9(x41861,f857(x41861,a844),a844),f334(x41861)),x41863))),f775(f775(f103(f857(x41861,a844)),x41862),x41863)) % 186.05/186.62 [4187]E(f775(f256(x41871),f775(f775(f20(x41871,a844,a844),f775(f775(f10(a844,f857(a844,a844),x41871),a331),f775(f775(f9(x41871,f857(x41871,a844),a844),f334(x41871)),x41872))),f775(f775(f9(x41871,f857(x41871,a844),a844),f334(x41871)),x41873))),f775(f775(f104(f857(x41871,a844)),x41872),x41873)) % 186.05/186.62 [4274]E(f775(f775(f46(x42741,f857(f857(x42741,a844),a844)),x42742),f775(f775(f9(x42741,f857(f857(x42741,a844),a844),f857(f857(x42741,a844),a844)),f775(f775(f10(f857(x42741,a844),f857(f857(f857(x42741,a844),a844),f857(f857(x42741,a844),a844)),x42741),f302(f857(x42741,a844))),f775(f775(f10(f857(x42741,a844),f857(x42741,a844),x42741),f277(x42741,x42741,x42743)),f775(f775(f9(x42741,f857(x42741,a844),f857(x42741,a844)),f302(x42741)),f180(f857(x42741,a844)))))),f180(f857(f857(x42741,a844),a844)))),f775(f775(f61(x42741),x42742),x42743)) % 186.05/186.62 [4276]E(f775(f775(f197(x42761),f775(f775(f83(a1),f775(f775(f75(f856(a1,a1),a1,x42761,f240(a1,a1)),f207(x42761)),x42762)),f775(f775(f75(f856(a1,a1),a1,x42761,f240(a1,a1)),f207(x42761)),x42763))),f775(f775(f83(a1),f775(f775(f75(f856(a1,a1),a1,x42761,f250(a1,a1)),f207(x42761)),x42762)),f775(f775(f75(f856(a1,a1),a1,x42761,f250(a1,a1)),f207(x42761)),x42763))),f222(x42761,x42762,x42763)) % 186.05/186.62 [3670]E(f52(a850,f775(f775(f82(a850),f775(f775(f83(a850),x36701),x36702)),x36703),x36702),f52(a850,x36703,x36702)) % 186.05/186.62 [3717]E(f130(a850,f775(f294(a850,f775(f775(f82(a850),x37171),x37172)),x37173)),f775(f775(f128(a850),x37172),f130(a850,f775(f294(a850,x37171),x37173)))) % 186.05/186.62 [3761]E(f775(f775(f82(a1),f775(f102(a1),x37611)),f775(f775(f82(a1),f775(f102(a1),x37612)),x37613)),f775(f775(f82(a1),f775(f102(a1),f775(f775(f82(a850),x37611),x37612))),x37613)) % 186.05/186.62 [3769]E(f775(f775(f3(f857(x37691,a844)),f775(f775(f3(f857(x37691,a844)),x37692),x37693)),x37693),f775(f775(f3(f857(x37691,a844)),x37692),x37693)) % 186.05/186.62 [3770]E(f775(f775(f103(f857(x37701,a844)),f775(f775(f3(f857(x37701,a844)),x37702),x37703)),x37703),f775(f775(f103(f857(x37701,a844)),x37702),x37703)) % 186.05/186.62 [3792]E(f775(f775(f281(x37921,x37921,x37922),f300(x37921,f180(f857(f856(x37921,x37921),a844)))),x37923),x37923) % 186.05/186.62 [3797]E(f775(f775(f103(f857(x37971,a844)),f775(f276(x37971),x37972)),f775(f276(x37971),x37973)),f775(f276(x37971),f775(f775(f103(f857(f856(x37971,x37971),a844)),x37972),x37973))) % 186.05/186.62 [3806]E(f263(x38061,f775(f775(f140(f856(a101,x38061)),f775(f775(f241(a101,x38061),f2(a101)),x38062)),x38063)),f263(x38061,x38063)) % 186.05/186.62 [3809]E(f775(f775(f104(f857(x38091,a844)),f45(f857(x38091,a844),x38092)),f45(f857(x38091,a844),x38093)),f45(f857(x38091,a844),f775(f775(f103(f857(f857(x38091,a844),a844)),x38092),x38093))) % 186.05/186.62 [3810]E(f775(f775(f103(f857(x38101,a844)),f44(f857(x38101,a844),x38102)),f44(f857(x38101,a844),x38103)),f44(f857(x38101,a844),f775(f775(f103(f857(f857(x38101,a844),a844)),x38102),x38103))) % 186.05/186.62 [3843]E(f775(f775(f281(x38431,x38431,x38431),f775(f775(f173(f856(x38431,x38431),a844),x38432),x38433)),x38433),f775(f775(f173(f856(x38431,x38431),a844),f775(a114,x38432)),x38433)) % 186.05/186.62 [3893]P1(f775(f775(f232(f857(x38931,a844)),f775(f775(f3(f857(x38931,a844)),x38932),x38933)),x38932)) % 186.05/186.62 [3894]P1(f775(f775(f232(f857(x38941,a844)),f775(f775(f104(f857(x38941,a844)),x38942),x38943)),x38943)) % 186.05/186.62 [3895]P1(f775(f775(f232(f857(x38951,a844)),f775(f775(f104(f857(x38951,a844)),x38952),x38953)),x38952)) % 186.05/186.62 [3920]E(f300(x39201,f775(f775(f103(f857(f856(x39201,x39201),a844)),f300(x39201,x39202)),f300(x39201,x39203))),f300(x39201,f775(f775(f103(f857(f856(x39201,x39201),a844)),x39202),x39203))) % 186.05/186.62 [3924]E(f44(f857(x39241,a844),f775(f775(f302(f857(x39241,a844)),x39242),f775(f775(f302(f857(x39241,a844)),x39243),f180(f857(f857(x39241,a844),a844))))),f775(f775(f103(f857(x39241,a844)),x39242),x39243)) % 186.05/186.62 [3925]E(f45(f857(x39251,a844),f775(f775(f302(f857(x39251,a844)),x39252),f775(f775(f302(f857(x39251,a844)),x39253),f180(f857(f857(x39251,a844),a844))))),f775(f775(f104(f857(x39251,a844)),x39252),x39253)) % 186.05/186.62 [3931]E(f775(f775(f281(x39311,x39311,x39311),f775(f775(f173(f856(x39311,x39311),a844),x39312),x39313)),x39313),f775(f775(f281(x39311,x39311,x39311),x39313),f775(f775(f173(f856(x39311,x39311),a844),x39312),x39313))) % 186.05/186.62 [4004]E(f775(f775(f103(f857(x40041,a844)),f775(f256(x40041),f775(f775(f9(x40041,x40041,a844),a330),x40042))),x40043),f775(f775(f302(x40041),x40042),x40043)) % 186.05/186.62 [4006]E(f775(a107,f775(f775(f8(x40061,a1),f775(f775(f10(a850,a1,x40061),f102(a1)),x40062)),x40063)),f775(f775(f8(x40061,a850),x40062),x40063)) % 186.05/186.62 [4007]E(f775(a107,f775(f775(f11(x40071,a1),f775(f775(f10(a850,a1,x40071),f102(a1)),x40072)),x40073)),f775(f775(f11(x40071,a850),x40072),x40073)) % 186.05/186.62 [4081]E(f775(f145(f851(x40811),x40811,f775(f157(x40811),x40812),f775(f18(f857(f851(x40811),f851(x40811)),x40811),f775(f775(f9(f851(x40811),f851(x40811),f851(x40811)),f125(x40811)),x40812))),x40813),f775(f157(x40811),f775(f775(f125(x40811),x40813),x40812))) % 186.05/186.62 [4112]P1(f775(f775(f232(f857(f857(x41121,a844),a844)),f775(f775(f103(f857(f857(x41121,a844),a844)),f775(f301(x41121),x41122)),f775(f301(x41121),x41123))),f775(f301(x41121),f775(f775(f103(f857(x41121,a844)),x41122),x41123)))) % 186.05/186.62 [4205]E(f775(f256(x42051),f775(f775(f20(x42051,a844,a844),f775(f775(f10(a844,f857(a844,a844),x42051),a331),f775(f775(f9(x42051,f857(x42051,a844),a844),f334(x42051)),x42052))),f775(f775(f10(a844,a844,x42051),a328),f775(f775(f9(x42051,f857(x42051,a844),a844),f334(x42051)),x42053)))),f775(f775(f3(f857(x42051,a844)),x42052),x42053)) % 186.05/186.62 [4226]E(f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,a850,a844),f233(a850)),f775(f181(f851(x42261)),x42262)))),f775(f775(f10(x42261,a844,a850),x42263),f775(f153(x42261),x42262))))),f775(f181(f851(x42261)),f775(f126(x42261,x42263),x42262))) % 186.05/186.62 [4228]E(f775(f181(f851(x42281)),f160(x42281,x42282,x42283)),f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,a850,a844),f233(a850)),f775(f181(f851(x42281)),x42282)))),f775(f775(f9(a850,f857(a850,a844),a844),f334(a850)),x42283))))) % 186.05/186.62 [4321]E(f775(f775(f104(f857(f856(f851(x43211),f851(x43211)),a844)),f775(f303(f856(f856(x43211,f851(x43211)),f856(x43211,f851(x43211))),f856(f851(x43211),f851(x43211)),f252(f856(x43211,f851(x43211)),f851(x43211),f856(x43211,f851(x43211)),f851(x43211),f775(f251(x43211,f851(x43211),f851(x43211)),f140(x43211)),f775(f251(x43211,f851(x43211),f851(x43211)),f140(x43211)))),f325(x43211,f851(x43211),x43212,f775(f133(x43211,x43212),x43213)))),f775(f256(f856(f851(x43211),f851(x43211))),f775(f251(f851(x43211),f851(x43211),a844),f775(f775(f9(f851(x43211),f857(f851(x43211),a844),f857(f851(x43211),a844)),f775(f775(f10(f857(a844,a844),f857(f857(f851(x43211),a844),f857(f851(x43211),a844)),f851(x43211)),f10(a844,a844,f851(x43211))),f775(f775(f10(a844,f857(a844,a844),f851(x43211)),a331),f775(f775(f9(f851(x43211),a850,a844),f775(f775(f10(a850,f857(a850,a844),f851(x43211)),a330),f181(f851(x43211)))),f775(a114,x43213))))),f775(f775(f9(f851(x43211),a850,a844),f775(f775(f10(a850,f857(a850,a844),f851(x43211)),a330),f181(f851(x43211)))),f775(a114,x43213)))))),f775(f133(x43211,x43212),f775(a114,x43213))) % 186.05/186.62 [3811]E(f52(a850,f775(a114,f775(f775(f82(a850),f775(f775(f83(a850),x38111),x38112)),x38113)),x38112),f52(a850,f775(a114,x38113),x38112)) % 186.05/186.62 [4071]E(f775(f256(x40711),f775(f775(f20(x40711,a844,a844),f775(f775(f10(a844,f857(a844,a844),x40711),a331),x40712)),x40713)),f775(f775(f104(f857(x40711,a844)),f775(f256(x40711),x40712)),f775(f256(x40711),x40713))) % 186.05/186.62 [4072]E(f775(f256(x40721),f775(f775(f20(x40721,a844,a844),f775(f775(f10(a844,f857(a844,a844),x40721),a332),x40722)),x40723)),f775(f775(f103(f857(x40721,a844)),f775(f256(x40721),x40722)),f775(f256(x40721),x40723))) % 186.05/186.62 [4074]E(f775(f775(f125(x40741),f775(f775(f128(x40741),f52(a850,x40742,f775(f181(f851(x40741)),x40743))),x40743)),f775(f775(f159(x40741),f52(a850,x40742,f775(f181(f851(x40741)),x40743))),x40743)),f775(f775(f775(f173(f851(x40741),f851(x40741)),x40742),f141(x40741)),x40743)) % 186.05/186.62 [4079]E(f775(f256(x40791),f775(f775(f20(x40791,a844,a844),f775(f775(f10(a844,f857(a844,a844),x40791),a335),x40792)),x40793)),f775(f775(f103(f857(x40791,a844)),f775(f81(f857(x40791,a844)),f775(f256(x40791),x40792))),f775(f256(x40791),x40793))) % 186.05/186.62 [4093]E(f775(f775(f82(a850),f775(f181(f851(x40931)),f775(f126(x40931,x40932),x40933))),f775(f181(f851(x40931)),f775(f126(x40931,f775(f775(f10(a844,a844,x40931),a328),x40932)),x40933))),f775(f181(f851(x40931)),x40933)) % 186.05/186.62 [4120]P1(f775(f775(f232(f857(x41201,a844)),f775(f775(f103(f857(x41201,a844)),f45(f857(x41201,a844),x41202)),f45(f857(x41201,a844),x41203))),f45(f857(x41201,a844),f775(f775(f104(f857(f857(x41201,a844),a844)),x41202),x41203)))) % 186.05/186.62 [4136]E(f775(f158(x41361),f775(f126(x41361,f775(f775(f10(a844,a844,x41361),a328),f775(f775(f9(x41361,x41361,a844),a330),x41362))),x41363)),f775(f775(f3(f857(x41361,a844)),f775(f158(x41361),x41363)),f775(f775(f302(x41361),x41362),f180(f857(x41361,a844))))) % 186.05/186.62 [4145]P1(f775(f775(f232(f857(f856(x41451,x41451),a844)),f775(f775(f103(f857(f856(x41451,x41451),a844)),f300(x41451,x41452)),f300(x41451,x41453))),f300(x41451,f775(f775(f103(f857(f856(x41451,x41451),a844)),x41452),x41453)))) % 186.05/186.62 [4169]E(f775(f775(f83(a850),f775(a114,f775(a114,f2(a850)))),f775(f775(f8(a850,a850),f775(f775(f10(a850,a850,a850),f775(f82(a850),x41691)),f775(f775(f9(a850,a850,a850),f83(a850)),x41692))),f775(f257(a850),x41693))),f775(f775(f83(a850),x41693),f775(f775(f82(a850),x41691),f775(f775(f82(a850),x41691),f775(f775(f83(a850),f775(f775(f3(a850),x41693),f80(a850))),x41692))))) % 186.05/186.62 [4179]E(f775(f256(x41791),f775(f775(f20(x41791,a844,a844),f775(f775(f10(a844,f857(a844,a844),x41791),a331),f775(f775(f9(x41791,f857(x41791,a844),a844),f334(x41791)),f775(f158(x41791),x41792)))),x41793)),f775(f158(x41791),f775(f126(x41791,x41793),x41792))) % 186.05/186.62 [4320]E(f775(f256(x43201),f775(f775(f10(f857(a850,a844),a844,x43201),f89(a850)),f775(f775(f9(x43201,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),x43201),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),x43201),f775(f10(a844,f857(a844,a844),a850),a331)),f775(f775(f9(x43201,f857(a850,x43201),f857(a850,a844)),f775(f775(f10(f857(x43201,a844),f857(f857(a850,x43201),f857(a850,a844)),x43201),f10(x43201,a844,a850)),a330)),f775(f153(x43201),x43202))))),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,a850,a844),f233(a850)),f775(f181(f851(x43201)),x43202)))),f775(f775(f9(a850,f857(a850,a844),a844),f334(a850)),x43203))))),f775(f158(x43201),f160(x43201,x43202,x43203))) % 186.05/186.62 [4216]E(f775(f256(x42161),f775(f775(f20(x42161,a844,a844),f775(f775(f10(a844,f857(a844,a844),x42161),a335),f775(f775(f10(a844,a844,x42161),a328),f775(f775(f9(x42161,x42161,a844),a330),x42162)))),x42163)),f775(f775(f302(x42161),x42162),f775(f256(x42161),x42163))) % 186.05/186.62 [4247]E(f775(f775(f143(f856(x42471,a850),x42471),f240(x42471,a850)),f775(f126(f856(x42471,a850),f775(f775(f9(f856(x42471,a850),f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),f856(x42471,a850)),f334(a850)),f250(x42471,a850))),x42472)),f775(f775(f167(x42471,a850),x42473),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(x42471)),x42473)))))),f160(x42471,x42473,x42472)) % 186.05/186.62 [4275]E(f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f8(a850,a1),f775(f775(f10(a1,a1,a850),f775(f82(a1),x42751)),f775(f775(f9(a850,a1,a1),f775(f775(f10(a1,f857(a1,a1),a850),f83(a1)),f102(a1))),x42752))),f775(f257(a850),x42753))),f775(f775(f83(a1),f775(f102(a1),x42753)),f775(f775(f82(a1),x42751),f775(f775(f82(a1),x42751),f775(f775(f83(a1),f775(f102(a1),f775(f775(f3(a850),x42753),f80(a850)))),x42752))))) % 186.05/186.62 [4314]E(f775(f256(f856(x43141,x43142)),f775(f251(x43141,x43142,a844),f775(f775(f9(x43141,f857(f856(x43142,x43141),a844),f857(x43142,a844)),f775(f775(f10(f857(x43142,f857(f857(f856(x43142,x43141),a844),a844)),f857(f857(f856(x43142,x43141),a844),f857(x43142,a844)),x43141),f9(x43142,f857(f856(x43142,x43141),a844),a844)),f775(f775(f10(f857(x43142,f856(x43142,x43141)),f857(x43142,f857(f857(f856(x43142,x43141),a844),a844)),x43141),f775(f10(f856(x43142,x43141),f857(f857(f856(x43142,x43141),a844),a844),x43142),f334(f856(x43142,x43141)))),f775(f9(x43142,x43141,f856(x43142,x43141)),f241(x43142,x43141))))),x43143))),f775(f278(x43142,x43141),x43143)) % 186.05/186.62 [4349]E(f775(f256(f851(x43491)),f775(f775(f10(f857(x43491,a844),a844,f851(x43491)),f89(x43491)),f775(f775(f10(f857(x43491,f857(f851(x43491),a844)),f857(x43491,a844),f851(x43491)),f775(f10(f857(f851(x43491),a844),a844,x43491),f89(f851(x43491)))),f775(f775(f9(f851(x43491),f857(x43491,f857(f851(x43491),a844)),f857(x43491,f857(f851(x43491),a844))),f775(f775(f10(f857(x43491,f857(f857(f851(x43491),a844),f857(f851(x43491),a844))),f857(f857(x43491,f857(f851(x43491),a844)),f857(x43491,f857(f851(x43491),a844))),f851(x43491)),f20(x43491,f857(f851(x43491),a844),f857(f851(x43491),a844))),f775(f775(f10(f857(x43491,f857(f851(x43491),f857(a844,a844))),f857(x43491,f857(f857(f851(x43491),a844),f857(f851(x43491),a844))),f851(x43491)),f775(f10(f857(f851(x43491),f857(a844,a844)),f857(f857(f851(x43491),a844),f857(f851(x43491),a844)),x43491),f20(f851(x43491),a844,a844))),f775(f775(f10(f857(x43491,f857(f851(x43491),a844)),f857(x43491,f857(f851(x43491),f857(a844,a844))),f851(x43491)),f775(f10(f857(f851(x43491),a844),f857(f851(x43491),f857(a844,a844)),x43491),f775(f10(a844,f857(a844,a844),f851(x43491)),a331))),f775(f775(f9(f851(x43491),f857(x43491,f857(f851(x43491),f851(x43491))),f857(x43491,f857(f851(x43491),a844))),f775(f775(f10(f857(f857(f851(x43491),f851(x43491)),f857(f851(x43491),a844)),f857(f857(x43491,f857(f851(x43491),f851(x43491))),f857(x43491,f857(f851(x43491),a844))),f851(x43491)),f10(f857(f851(x43491),f851(x43491)),f857(f851(x43491),a844),x43491)),f775(f775(f10(f857(f851(x43491),a844),f857(f857(f851(x43491),f851(x43491)),f857(f851(x43491),a844)),f851(x43491)),f10(f851(x43491),a844,f851(x43491))),a330))),f140(x43491)))))),f775(f775(f9(x43491,f857(f851(x43491),a844),f857(f851(x43491),a844)),f775(f775(f10(f857(a844,a844),f857(f857(f851(x43491),a844),f857(f851(x43491),a844)),x43491),f10(a844,a844,f851(x43491))),f775(f775(f10(a844,f857(a844,a844),x43491),a331),f775(f775(f9(x43491,f857(x43491,a844),a844),f334(x43491)),x43492)))),f775(f775(f9(f851(x43491),f857(f851(x43491),a844),a844),f334(f851(x43491))),x43493)))))),f161(x43491,x43492,x43493)) % 186.05/186.62 [4334]E(f775(f775(f88(a1,f856(a1,a1)),f775(f775(f3(a1),x43341),x43342)),f775(f775(f9(a1,f856(a1,a1),f856(a1,a1)),f775(f775(f20(a1,f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),f775(f775(f10(a844,f857(f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),a1),f98(f856(a1,a1))),f775(f232(a1),f2(a1)))),f775(f241(a1,a1),f775(f775(f82(a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x43343)),f80(a1))))),f775(f775(f241(a1,a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x43343)),x43341))),f775(f50(x43342),f775(f775(f241(a1,a1),x43343),x43341))) % 186.05/186.62 [4385]~E(f36(x43851,x43852),f35(x43853,x43854)) % 186.05/186.62 [4388]~E(f28(x43881,x43882),f35(x43883,x43884)) % 186.05/186.62 [4389]~E(f28(x43891,x43892),f36(x43893,x43894)) % 186.05/186.62 [4407]~E(f775(a27,x44071),f33(x44072,x44073,x44074)) % 186.05/186.62 [4408]~E(f775(a27,x44081),f32(x44082,x44083,x44084)) % 186.05/186.62 [4409]~E(f775(a27,x44091),f31(x44092,x44093,x44094)) % 186.05/186.62 [4410]~E(f33(x44101,x44102,x44103),f775(a27,x44104)) % 186.05/186.62 [4411]~E(f32(x44111,x44112,x44113),f775(a27,x44114)) % 186.05/186.62 [4412]~E(f31(x44121,x44122,x44123),f775(a27,x44124)) % 186.05/186.62 [3365]E(f775(f775(f775(f74(x33651,x33652),x33653),x33654),f775(x33653,x33654)),x33653) % 186.05/186.62 [3428]E(f775(f775(f243(x34281,x34282,x34283),x34284),f2(a850)),x34282) % 186.05/186.62 [3467]E(f175(x34671,x34672,x34673,f775(a114,x34674)),f775(x34673,x34674)) % 186.05/186.62 [3508]E(f151(x35081,x35082,f151(x35081,x35083,x35084)),f151(x35081,x35083,f151(x35081,x35082,x35084))) % 186.05/186.62 [3625]P39(f28(x36251,x36252),x36253,x36254,f775(f775(f775(a189,x36253),x36251),f775(x36252,x36253))) % 186.05/186.62 [3637]E(f775(f229(x36371,x36372,x36373,x36374),f183(x36372)),x36373) % 186.05/186.62 [3639]E(f775(f145(x36391,x36392,x36393,x36394),f115(x36392)),x36393) % 186.05/186.62 [3640]E(f775(f132(x36401,x36402,x36403,x36404),f115(x36402)),x36404) % 186.05/186.62 [3677]E(f775(f181(f855(x36771,x36772)),f215(x36771,x36772,x36773,x36774)),f2(a850)) % 186.05/186.62 [3702]E(f775(f251(x37021,x37022,x37023),f249(x37021,x37022,x37023,x37024)),x37024) % 186.05/186.62 [3758]E(f775(f229(f854(x37581),x37582,f183(x37581),f775(f18(f854(x37581),x37582),f183(x37581))),f775(x37583,x37584)),f183(x37581)) % 186.05/186.62 [3801]E(f775(f775(f103(f857(x38011,a844)),f169(x38011,x38012,x38013)),f169(x38011,x38012,x38014)),f169(x38011,x38012,f170(x38011,x38012,x38014,x38013))) % 186.05/186.62 [3830]E(f775(f775(f253(x38301,x38302,x38303,f856(x38302,x38303)),x38304),f241(x38302,x38303)),x38304) % 186.05/186.62 [3839]E(f230(x38391,x38392,x38393,x38394,f183(x38392)),x38393) % 186.05/186.62 [4127]P41(x41271,x41272,x41273,x41274,f180(f857(x41271,a844)),x41274) % 186.05/186.62 [4436]~E(f775(f313(x44361,x44362),x44363),f775(f304(x44362,x44361),x44364)) % 186.05/186.62 [3174]E(f775(f775(f18(x31741,x31742),x31743),x31744),x31743) % 186.05/186.62 [3287]E(f775(f775(f196(x32871,x32872),x32873),f775(f227(x32871),x32874)),f775(f227(x32872),f775(x32873,x32874))) % 186.05/186.62 [3459]E(f151(x34591,x34592,f775(f126(x34591,x34593),x34594)),f775(f126(x34591,x34593),f151(x34591,x34592,x34594))) % 186.05/186.62 [3492]E(f775(f775(f66(x34921,x34922,x34923),x34924),f180(f857(x34921,a844))),x34924) % 186.05/186.62 [3514]E(f775(f775(f153(x35141),f775(f775(f140(x35141),x35142),x35143)),f775(a114,x35144)),f775(f775(f153(x35141),x35143),x35144)) % 186.05/186.62 [3552]P31(x35521,f2(a850),f775(f775(f775(f93(x35521),x35522),f775(a27,x35523)),x35524)) % 186.05/186.62 [3577]E(f775(f775(x35771,x35772),f775(f174(x35773,x35774,x35771),x35772)),f775(f174(x35773,x35774,x35771),f775(a114,x35772))) % 186.05/186.62 [3617]E(f249(x36171,x36172,x36173,f775(f251(x36171,x36172,x36173),x36174)),x36174) % 186.05/186.62 [3675]E(f775(f775(f148(x36751,f775(f775(f140(x36751),x36752),x36753)),f2(a850)),x36754),f775(f775(f140(x36751),x36754),x36753)) % 186.05/186.62 [3685]E(f775(f775(f46(f857(x36851,a844),f857(x36852,a844)),x36853),f303(x36851,x36852,x36854)),f775(f303(x36851,x36852,x36854),f44(f857(x36851,a844),x36853))) % 186.05/186.62 [3686]E(f775(f775(f46(f857(x36861,a844),f857(x36862,a844)),x36863),f305(x36862,x36861,x36864)),f775(f305(x36862,x36861,x36864),f44(f857(x36861,a844),x36863))) % 186.05/186.62 [3786]E(f169(x37861,x37862,f172(x37861,x37862,x37863,x37864)),f775(f775(f104(f857(x37861,a844)),f169(x37861,x37862,x37863)),x37864)) % 186.05/186.62 [3805]E(f775(f132(x38051,x38052,f775(f9(x38052,x38051,x38051),x38053),x38054),f775(f142(x38052),f115(x38052))),x38054) % 186.05/186.62 [3849]E(f78(x38491,x38492,x38493,x38494,f180(f857(x38491,a844))),x38493) % 186.05/186.62 [3896]E(f775(f775(f775(f775(f74(x38961,f854(x38962)),f775(f18(f854(x38962),x38961),f183(x38962))),x38963),f183(x38962)),x38964),f183(x38962)) % 186.05/186.62 [4045]E(f319(x40451,x40452,x40453,f775(f775(f10(f858(x40451,x40453),x40452,x40451),x40454),f304(x40451,x40453)),f775(f775(f10(f858(x40451,x40453),x40452,x40453),x40454),f313(x40453,x40451))),x40454) % 186.05/186.62 [4055]E(f775(f251(x40551,x40552,x40553),f775(f775(f10(f857(x40552,f856(x40551,x40552)),f857(x40552,x40553),x40551),f775(f10(f856(x40551,x40552),x40553,x40552),x40554)),f241(x40551,x40552))),x40554) % 186.05/186.62 [3363]E(f775(f250(x33631,x33632),f775(f775(f241(x33631,x33632),x33633),x33634)),x33634) % 186.05/186.62 [3364]E(f775(f240(x33641,x33642),f775(f775(f241(x33641,x33642),x33643),x33644)),x33643) % 186.05/186.62 [3401]E(f775(f181(f851(x34011)),f775(f775(f143(x34012,x34011),x34013),x34014)),f775(f181(f851(x34012)),x34014)) % 186.05/186.62 [3402]E(f775(f181(f851(x34021)),f775(f775(f148(x34021,x34022),x34023),x34024)),f775(f181(f851(x34021)),x34022)) % 186.05/186.62 [3423]E(f775(f775(f128(x34231),f775(a114,x34232)),f775(f775(f140(x34231),x34233),x34234)),f775(f775(f128(x34231),x34232),x34234)) % 186.05/186.62 [3494]E(f775(f775(f302(x34941),x34942),f775(f775(f302(x34941),x34943),x34944)),f775(f775(f302(x34941),x34943),f775(f775(f302(x34941),x34942),x34944))) % 186.05/186.62 [3497]E(f775(f775(f143(x34971,x34972),x34973),f116(x34971,x34974)),f116(x34972,f775(f775(f143(x34971,x34972),x34973),x34974))) % 186.05/186.62 [3512]E(f775(f142(x35121),f775(f775(f143(x35122,x35121),x35123),x35124)),f775(f775(f143(x35122,x35121),x35123),f775(f142(x35122),x35124))) % 186.05/186.62 [3513]E(f775(f775(f143(x35131,x35132),x35133),f775(f157(x35131),x35134)),f775(f157(x35132),f775(f775(f143(x35131,x35132),x35133),x35134))) % 186.05/186.62 [3522]E(f775(f775(f159(x35221),f775(a114,x35222)),f775(f775(f140(x35221),x35223),x35224)),f775(f775(f140(x35221),x35223),f775(f775(f159(x35221),x35222),x35224))) % 186.05/186.62 [3526]E(f775(f158(x35261),f775(f775(f143(x35262,x35261),x35263),x35264)),f775(f303(x35262,x35261,x35263),f775(f158(x35262),x35264))) % 186.05/186.62 [3576]E(f19(x35761,x35762,x35763,f775(a5,f775(a114,f775(a22,x35764)))),f775(x35763,x35764)) % 186.05/186.62 [3580]E(f775(f775(f125(x35801),f775(f126(x35801,x35802),x35803)),f775(f126(x35801,x35802),x35804)),f775(f126(x35801,x35802),f775(f775(f125(x35801),x35803),x35804))) % 186.05/186.62 [3607]E(f775(f278(x36071,x36071),f775(f775(f280(x36072,x36071),x36073),x36074)),f775(f775(f280(x36072,x36071),f775(f278(x36072,x36072),x36073)),x36074)) % 186.05/186.62 [3618]E(f775(f775(f281(x36181,x36182,x36183),x36184),f180(f857(f856(x36182,x36183),a844))),f180(f857(f856(x36181,x36183),a844))) % 186.05/186.62 [3619]E(f775(f775(f159(x36191),f775(f775(f3(a850),x36192),x36193)),f775(f775(f128(x36191),x36193),x36194)),f775(f775(f128(x36191),x36193),f775(f775(f159(x36191),x36192),x36194))) % 186.05/186.62 [3641]E(f775(f775(f775(f273(x36411),x36412),x36413),x36414),f775(f241(f857(a101,f857(a844,f854(f852(x36411)))),f856(a101,a101)),f775(f49(x36411),x36412))) % 186.05/186.62 [3667]E(f45(f857(x36671,a844),f775(f303(x36672,f857(x36671,a844),x36673),x36674)),f775(f775(f47(x36672,f857(x36671,a844)),x36674),x36673)) % 186.05/186.62 [3668]E(f44(f857(x36681,a844),f775(f303(x36682,f857(x36681,a844),x36683),x36684)),f775(f775(f46(x36682,f857(x36681,a844)),x36684),x36683)) % 186.05/186.62 [3669]E(f775(f181(f851(f856(x36691,x36692))),f775(f775(f167(x36691,x36692),x36693),x36694)),f775(f775(f236(a850),f775(f181(f851(x36691)),x36693)),f775(f181(f851(x36692)),x36694))) % 186.05/186.62 [3671]E(f775(f305(x36711,x36712,x36713),f775(f81(f857(x36712,a844)),x36714)),f775(f81(f857(x36711,a844)),f775(f305(x36711,x36712,x36713),x36714))) % 186.05/186.62 [3703]E(f775(f172(x37031,x37032,x37033,f180(f857(x37031,a844))),x37034),f183(x37032)) % 186.05/186.62 [3722]E(f775(f305(x37221,x37222,x37223),f775(f256(x37222),x37224)),f775(f256(x37221),f775(f775(f10(x37222,a844,x37221),x37224),x37223))) % 186.05/186.62 [3740]E(f775(f775(f153(x37401),f775(f775(f125(x37401),x37402),f775(f775(f140(x37401),x37403),x37404))),f775(f181(f851(x37401)),x37402)),x37403) % 186.05/186.62 [3745]E(f775(f172(x37451,x37452,f775(f18(f854(x37452),x37451),f183(x37452)),x37453),x37454),f183(x37452)) % 186.05/186.62 [3767]E(f775(f303(x37671,x37672,x37673),f775(f305(x37671,x37672,x37673),x37674)),f775(f775(f104(f857(x37672,a844)),x37674),f775(f303(x37671,x37672,x37673),f239(f857(x37671,a844))))) % 186.05/186.62 [3785]P1(f775(f775(f334(x37851),f775(x37852,x37853)),f775(f303(x37854,x37851,x37852),f239(f857(x37854,a844))))) % 186.05/186.62 [3793]E(f21(x37931,x37932,x37933,f775(a5,f775(a114,f775(a22,x37934)))),f775(f775(x37933,x37934),f21(x37931,x37932,x37933,x37934))) % 186.05/186.62 [3808]E(f144(x38081,x38082,f775(f775(f140(x38081),x38083),x38084)),f775(f775(f82(a850),f775(f775(f82(a850),f775(x38082,x38083)),f144(x38081,x38082,x38084))),f775(a114,f2(a850)))) % 186.05/186.62 [3821]E(f175(f851(x38211),f775(f775(f140(x38211),x38212),x38213),f775(f775(f9(a850,f851(x38211),f851(x38211)),f128(x38211)),x38213),x38214),f775(f775(f128(x38211),x38214),f775(f775(f140(x38211),x38212),x38213))) % 186.05/186.62 [3822]P29(x38221,f856(x38222,x38221),f336(x38223,x38224,x38222,x38221),f775(f775(f46(x38222,f857(x38221,a844)),x38224),x38223)) % 186.05/186.62 [3831]E(f775(f775(f3(f857(x38311,a844)),f775(f775(f3(f857(x38311,a844)),x38312),x38313)),f775(f775(f302(x38311),x38314),f180(f857(x38311,a844)))),f775(f775(f3(f857(x38311,a844)),x38312),f775(f775(f302(x38311),x38314),x38313))) % 186.05/186.62 [3842]E(f775(f775(f173(f857(x38421,x38422),f857(x38421,x38422)),x38423),f75(x38422,x38422,x38421,x38424)),f75(x38422,x38422,x38421,f775(f775(f173(x38422,x38422),x38423),x38424))) % 186.05/186.62 [3919]E(f775(f775(f775(f173(f851(x39191),f851(x39191)),x39192),f141(x39191)),f775(f775(f775(f173(f851(x39191),f851(x39191)),x39193),f141(x39191)),x39194)),f775(f775(f775(f173(f851(x39191),f851(x39191)),f775(f775(f82(a850),x39192),x39193)),f141(x39191)),x39194)) % 186.05/186.62 [3968]E(f775(f775(f103(f857(f858(x39681,x39682),a844)),f775(f303(x39681,f858(x39681,x39682),f304(x39681,x39682)),x39683)),f775(f303(x39682,f858(x39681,x39682),f313(x39682,x39681)),x39684)),f314(x39681,x39682,x39683,x39684)) % 186.05/186.62 [4009]P1(f775(f775(f232(f857(x40091,a844)),f775(f158(x40091),f775(f775(f148(x40091,x40092),x40093),x40094))),f775(f775(f302(x40091),x40094),f775(f158(x40091),x40092)))) % 186.05/186.62 [4043]E(f775(f775(f46(f857(x40431,a844),f857(f856(x40431,x40432),a844)),x40433),f775(f775(f9(f857(x40431,a844),f857(x40431,f857(x40432,a844)),f857(f856(x40431,x40432),a844)),f248(x40431,x40432)),x40434)),f775(f775(f248(x40431,x40432),f44(f857(x40431,a844),x40433)),x40434)) % 186.05/186.62 [4080]E(f204(x40801,x40802,x40803,f775(f75(x40802,f857(a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(x40802))))),x40801,f203(x40802)),x40804)),f205(x40801,x40802,x40804,x40803)) % 186.05/186.62 [4096]E(f200(x40961,x40962,x40963,f775(f75(x40962,f857(a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(f854(x40962)))))),x40961,f199(x40962)),x40964)),f201(x40961,x40962,x40964,x40963)) % 186.05/186.62 [4101]P1(f775(f68(x41011,x41012,x41013,x41014,f180(f857(x41011,a844))),x41014)) % 186.05/186.62 [4148]E(f775(f775(f46(x41481,f857(x41482,a844)),x41483),f775(f775(f9(x41481,f857(x41482,a844),f857(x41482,a844)),f775(f775(f10(x41482,f857(f857(x41482,a844),f857(x41482,a844)),x41481),f302(x41482)),x41484)),f180(f857(x41482,a844)))),f775(f303(x41481,x41482,x41484),x41483)) % 186.05/186.62 [4154]P1(f775(f775(f232(f857(x41541,a844)),f775(f259(x41542,x41541),f775(f775(f104(f857(f856(x41542,x41541),a844)),x41543),x41544))),f775(f775(f104(f857(x41541,a844)),f775(f259(x41542,x41541),x41543)),f775(f259(x41542,x41541),x41544)))) % 186.05/186.62 [4155]P1(f775(f775(f232(f857(x41551,a844)),f775(f261(x41551,x41552),f775(f775(f104(f857(f856(x41551,x41552),a844)),x41553),x41554))),f775(f775(f104(f857(x41551,a844)),f775(f261(x41551,x41552),x41553)),f775(f261(x41551,x41552),x41554)))) % 186.05/186.62 [4214]P1(f775(f775(f232(f857(f856(x42141,x42142),a844)),f775(f303(x42142,f856(x42141,x42142),f336(x42143,x42144,x42141,x42142)),f775(f775(f46(x42141,f857(x42142,a844)),x42144),x42143))),f775(f775(f248(x42141,x42142),x42144),x42143))) % 186.05/186.62 [4215]E(f271(x42151,x42152,x42153,f775(f75(x42152,f857(a101,f857(a101,f857(f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x42152)))),f856(a101,a101))))),x42151,f273(x42152)),x42154)),f274(x42151,x42152,x42154,x42153)) % 186.05/186.62 [4253]E(f87(f856(x42531,x42532),f775(f251(x42531,x42532,a844),f775(f775(f9(x42531,f857(x42532,a844),f857(x42532,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x42532,a844),f857(x42532,a844)),x42531),f10(a844,a844,x42532)),f775(f775(f10(a844,f857(a844,a844),x42531),a331),f775(a330,x42533)))),f775(a330,x42534)))),f775(f775(f241(x42531,x42532),x42533),x42534)) % 186.05/186.62 [4254]E(f92(f856(x42541,x42542),f775(f251(x42541,x42542,a844),f775(f775(f9(x42541,f857(x42542,a844),f857(x42542,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x42542,a844),f857(x42542,a844)),x42541),f10(a844,a844,x42542)),f775(f775(f10(a844,f857(a844,a844),x42541),a331),f775(a330,x42543)))),f775(a330,x42544)))),f775(f775(f241(x42541,x42542),x42543),x42544)) % 186.05/186.62 [4324]E(f775(f775(f251(f851(x43241),f851(x43241),f856(f851(x43241),f851(x43241))),f775(f775(f20(f851(x43241),f857(f851(x43241),f856(f851(x43241),f851(x43241))),f857(f851(x43241),f856(f851(x43241),f851(x43241)))),f775(f775(f10(f857(f851(x43241),f857(f856(f851(x43241),f851(x43241)),f856(f851(x43241),f851(x43241)))),f857(f857(f851(x43241),f856(f851(x43241),f851(x43241))),f857(f851(x43241),f856(f851(x43241),f851(x43241)))),f851(x43241)),f20(f851(x43241),f856(f851(x43241),f851(x43241)),f856(f851(x43241),f851(x43241)))),f775(f775(f10(f857(f851(x43241),f856(f851(x43241),f851(x43241))),f857(f851(x43241),f857(f856(f851(x43241),f851(x43241)),f856(f851(x43241),f851(x43241)))),f851(x43241)),f775(f10(f856(f851(x43241),f851(x43241)),f857(f856(f851(x43241),f851(x43241)),f856(f851(x43241),f851(x43241))),f851(x43241)),f775(f98(f856(f851(x43241),f851(x43241))),f775(x43242,x43243)))),f775(f775(f10(f851(x43241),f857(f851(x43241),f856(f851(x43241),f851(x43241))),f851(x43241)),f241(f851(x43241),f851(x43241))),f775(f140(x43241),x43243))))),f775(f775(f9(f851(x43241),f857(f851(x43241),f851(x43241)),f857(f851(x43241),f856(f851(x43241),f851(x43241)))),f775(f775(f10(f857(f851(x43241),f856(f851(x43241),f851(x43241))),f857(f857(f851(x43241),f851(x43241)),f857(f851(x43241),f856(f851(x43241),f851(x43241)))),f851(x43241)),f10(f851(x43241),f856(f851(x43241),f851(x43241)),f851(x43241))),f241(f851(x43241),f851(x43241)))),f775(f140(x43241),x43243)))),f156(x43241,x43242,x43244)),f156(x43241,x43242,f775(f775(f140(x43241),x43243),x43244))) % 186.05/186.62 [4330]E(f775(f132(f857(x43301,f854(x43302)),f856(x43301,x43302),f775(f9(f856(x43301,x43302),f857(x43301,f854(x43302)),f857(x43301,f854(x43302))),f775(f251(x43301,x43302,f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302)))),f775(f775(f9(x43301,f857(x43302,f854(x43302)),f857(x43302,f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302))))),f775(f775(f10(f857(f854(x43302),f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302)))),f857(f857(x43302,f854(x43302)),f857(x43302,f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302))))),x43301),f10(f854(x43302),f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302))),x43302)),f775(f775(f10(f857(f857(x43301,f854(x43302)),f857(f854(x43302),f857(x43301,f854(x43302)))),f857(f854(x43302),f857(f857(x43301,f854(x43302)),f857(x43301,f854(x43302)))),x43301),f9(f857(x43301,f854(x43302)),f854(x43302),f857(x43301,f854(x43302)))),f775(f9(f857(x43301,f854(x43302)),x43301,f857(f854(x43302),f857(x43301,f854(x43302)))),f74(x43301,f854(x43302)))))),f227(x43302)))),x43303),f775(f142(f856(x43301,x43302)),x43304)),f170(x43301,x43302,x43303,f166(x43301,x43302,x43304))) % 186.05/186.62 [3442]E(f775(f181(f849(x34421)),f775(f775(f775(f93(x34421),x34422),x34423),x34424)),f2(a850)) % 186.05/186.62 [3555]E(f775(f775(f159(x35551),x35552),f775(f775(f159(x35551),x35553),x35554)),f775(f775(f159(x35551),f775(f775(f236(a850),x35552),x35553)),x35554)) % 186.05/186.62 [3556]E(f775(f775(f128(x35561),x35562),f775(f775(f128(x35561),x35563),x35564)),f775(f775(f128(x35561),f775(f775(f82(a850),x35562),x35563)),x35564)) % 186.05/186.62 [3568]E(f775(f775(f125(x35681),f775(f775(f140(x35681),x35682),x35683)),x35684),f775(f775(f140(x35681),x35682),f775(f775(f125(x35681),x35683),x35684))) % 186.05/186.62 [3569]E(f775(f775(f125(x35691),f775(f775(f125(x35691),x35692),x35693)),x35694),f775(f775(f125(x35691),x35692),f775(f775(f125(x35691),x35693),x35694))) % 186.05/186.62 [3651]E(f775(f775(f153(x36511),f775(f775(f140(x36511),x36512),x36513)),x36514),f175(x36511,x36512,f775(f153(x36511),x36513),x36514)) % 186.05/186.62 [3660]E(f775(f775(f173(x36601,x36601),x36602),f775(f775(f173(x36601,x36601),x36603),x36604)),f775(f775(f173(x36601,x36601),f775(f775(f83(a850),x36603),x36602)),x36604)) % 186.05/186.62 [3688]E(f775(f775(f103(f857(x36881,a844)),x36882),f775(f775(f302(x36881),x36883),x36884)),f775(f775(f302(x36881),x36883),f775(f775(f103(f857(x36881,a844)),x36882),x36884))) % 186.05/186.62 [3706]E(f775(f775(f775(f173(x37061,x37061),x37062),x37063),f775(x37063,x37064)),f775(x37063,f775(f775(f775(f173(x37061,x37061),x37062),x37063),x37064))) % 186.05/186.62 [3713]E(f775(f775(f281(x37131,x37132,x37133),f180(f857(f856(x37131,x37132),a844))),x37134),f180(f857(f856(x37131,x37133),a844))) % 186.05/186.62 [3729]E(f775(f775(f103(f857(x37291,a844)),f775(f775(f302(x37291),x37292),x37293)),x37294),f775(f775(f302(x37291),x37292),f775(f775(f103(f857(x37291,a844)),x37293),x37294))) % 186.05/186.62 [3747]E(f775(f42(f856(x37471,x37472)),f775(f775(f248(x37471,x37472),x37473),f775(f18(f857(x37472,a844),x37471),x37474))),f775(f775(f83(a850),f775(f42(x37471),x37473)),f775(f42(x37472),x37474))) % 186.05/186.62 [3755]E(f775(f775(f104(f857(x37551,a844)),f775(f775(f302(x37551),x37552),x37553)),f775(f775(f302(x37551),x37552),x37554)),f775(f775(f302(x37551),x37552),f775(f775(f104(f857(x37551,a844)),x37553),x37554))) % 186.05/186.62 [3765]E(f170(x37651,x37652,f166(x37651,x37652,x37653),f166(x37651,x37652,x37654)),f166(x37651,x37652,f775(f775(f125(f856(x37651,x37652)),x37654),x37653))) % 186.05/186.62 [3771]E(f775(f775(f103(f857(x37711,a844)),x37712),f775(f775(f103(f857(x37711,a844)),x37713),x37714)),f775(f775(f103(f857(x37711,a844)),x37713),f775(f775(f103(f857(x37711,a844)),x37712),x37714))) % 186.05/186.62 [3772]E(f775(f775(f104(f857(x37721,a844)),x37722),f775(f775(f104(f857(x37721,a844)),x37723),x37724)),f775(f775(f104(f857(x37721,a844)),x37723),f775(f775(f104(f857(x37721,a844)),x37722),x37724))) % 186.05/186.62 [3781]E(f66(x37811,x37812,f775(f775(f10(x37812,f857(x37812,x37812),x37811),x37813),x37814)),f775(f67(x37812,x37811,x37813),x37814)) % 186.05/186.62 [3790]E(f164(x37901,f775(f775(f143(f851(x37902),f851(x37901)),f775(f143(x37902,x37901),x37903)),x37904)),f775(f775(f143(f851(x37902),f851(x37901)),f775(f143(x37902,x37901),x37903)),f164(x37902,x37904))) % 186.05/186.62 [3807]E(f172(x38071,x38072,x38073,f775(f81(f857(x38071,a844)),f775(f775(f302(x38071),x38074),f180(f857(x38071,a844))))),f775(f775(f775(f74(x38071,f854(x38072)),x38073),x38074),f183(x38072))) % 186.05/186.62 [3863]E(f775(f75(x38631,x38631,x38631,f775(f775(f173(x38631,x38631),x38632),x38633)),f775(f775(f173(x38631,x38631),x38634),x38633)),f775(f775(f173(x38631,x38631),f775(f775(f82(a850),x38632),x38634)),x38633)) % 186.05/186.62 [3878]E(f775(f775(f775(f74(x38781,f854(x38782)),f166(x38781,x38782,x38783)),f775(f240(x38781,x38782),x38784)),f775(f227(x38782),f775(f250(x38781,x38782),x38784))),f166(x38781,x38782,f775(f775(f140(f856(x38781,x38782)),x38784),x38783))) % 186.05/186.62 [3885]E(f170(x38851,x38852,x38853,f166(x38851,x38852,f775(f142(f856(x38851,x38852)),f775(f775(f167(x38851,x38852),x38854),f115(x38852))))),x38853) % 186.05/186.62 [3888]E(f775(f775(f104(f857(x38881,a844)),f775(f775(f3(f857(x38881,a844)),x38882),x38883)),f775(f775(f3(f857(x38881,a844)),x38882),x38884)),f775(f775(f3(f857(x38881,a844)),x38882),f775(f775(f103(f857(x38881,a844)),x38883),x38884))) % 186.05/186.62 [3889]E(f775(f775(f103(f857(x38891,a844)),f775(f775(f3(f857(x38891,a844)),x38892),x38893)),f775(f775(f3(f857(x38891,a844)),x38892),x38894)),f775(f775(f3(f857(x38891,a844)),x38892),f775(f775(f104(f857(x38891,a844)),x38893),x38894))) % 186.05/186.62 [3890]E(f775(f775(f104(f857(x38901,a844)),f775(f775(f103(f857(x38901,a844)),x38902),x38903)),f775(f775(f103(f857(x38901,a844)),x38902),x38904)),f775(f775(f103(f857(x38901,a844)),x38902),f775(f775(f104(f857(x38901,a844)),x38903),x38904))) % 186.05/186.62 [3891]E(f775(f775(f3(f857(x38911,a844)),f775(f775(f104(f857(x38911,a844)),x38912),x38913)),f775(f775(f104(f857(x38911,a844)),x38912),x38914)),f775(f775(f104(f857(x38911,a844)),x38912),f775(f775(f3(f857(x38911,a844)),x38913),x38914))) % 186.05/186.62 [3892]E(f775(f775(f103(f857(x38921,a844)),f775(f775(f104(f857(x38921,a844)),x38922),x38923)),f775(f775(f104(f857(x38921,a844)),x38922),x38924)),f775(f775(f104(f857(x38921,a844)),x38922),f775(f775(f103(f857(x38921,a844)),x38923),x38924))) % 186.05/186.62 [3898]E(f775(f42(f856(x38981,x38982)),f775(f775(f248(x38981,x38982),f775(f775(f302(x38981),x38983),f180(f857(x38981,a844)))),f775(f18(f857(x38982,a844),x38981),x38984))),f775(f42(x38982),x38984)) % 186.05/186.62 [3935]E(f775(f775(f47(x39351,f857(x39352,a844)),x39353),f775(f775(f10(f857(x39352,a844),f857(x39352,a844),x39351),f81(f857(x39352,a844))),x39354)),f775(f81(f857(x39352,a844)),f775(f775(f46(x39351,f857(x39352,a844)),x39353),x39354))) % 186.05/186.62 [3936]E(f775(f775(f46(x39361,f857(x39362,a844)),x39363),f775(f775(f10(f857(x39362,a844),f857(x39362,a844),x39361),f81(f857(x39362,a844))),x39364)),f775(f81(f857(x39362,a844)),f775(f775(f47(x39361,f857(x39362,a844)),x39363),x39364))) % 186.05/186.62 [3952]E(f775(f775(f281(x39521,x39521,x39521),f775(f775(f173(f856(x39521,x39521),a844),x39522),x39523)),f775(f775(f173(f856(x39521,x39521),a844),x39524),x39523)),f775(f775(f173(f856(x39521,x39521),a844),f775(f775(f82(a850),x39522),x39524)),x39523)) % 186.05/186.62 [3984]E(f775(f775(f47(x39841,f857(f857(x39842,a844),a844)),x39843),f775(f775(f10(f857(x39842,a844),f857(f857(x39842,a844),a844),x39841),f301(x39842)),x39844)),f775(f301(x39842),f775(f775(f47(x39841,f857(x39842,a844)),x39843),x39844))) % 186.05/186.62 [4014]E(f775(f775(f46(f857(x40141,a844),f857(x40142,a844)),x40143),f775(f775(f9(f857(x40141,a844),f857(x40141,f857(x40142,a844)),f857(x40142,a844)),f46(x40141,f857(x40142,a844))),x40144)),f775(f775(f46(x40141,f857(x40142,a844)),f44(f857(x40141,a844),x40143)),x40144)) % 186.05/186.62 [4015]E(f775(f775(f47(f857(x40151,a844),f857(x40152,a844)),x40153),f775(f775(f9(f857(x40151,a844),f857(x40151,f857(x40152,a844)),f857(x40152,a844)),f47(x40151,f857(x40152,a844))),x40154)),f775(f775(f47(x40151,f857(x40152,a844)),f44(f857(x40151,a844),x40153)),x40154)) % 186.05/186.62 [4020]E(f775(f775(f143(x40201,x40202),x40203),f775(f132(f851(x40201),f851(x40201),f125(x40201),f115(x40201)),x40204)),f775(f132(f851(x40202),f851(x40202),f125(x40202),f115(x40202)),f775(f775(f143(f851(x40201),f851(x40202)),f775(f143(x40201,x40202),x40203)),x40204))) % 186.05/186.62 [4022]E(f175(f851(x40221),f115(x40221),f775(f775(f10(f851(x40221),f851(x40221),a850),f775(f140(x40221),x40222)),f775(f775(f9(a850,f851(x40221),f851(x40221)),f159(x40221)),x40223)),x40224),f775(f775(f159(x40221),x40224),f775(f775(f140(x40221),x40222),x40223))) % 186.05/186.62 [4065]P1(f775(f775(f232(f857(x40651,a844)),f775(f303(x40652,x40651,x40653),f775(f305(x40652,x40651,x40653),x40654))),x40654)) % 186.05/186.62 [4067]E(f775(f303(f856(x40671,x40672),f856(x40672,x40671),f775(f251(x40671,x40672,f856(x40672,x40671)),f775(f9(x40672,x40671,f856(x40672,x40671)),f241(x40672,x40671)))),f775(f775(f248(x40671,x40672),x40673),f775(f18(f857(x40672,a844),x40671),x40674))),f775(f775(f248(x40672,x40671),x40674),f775(f18(f857(x40671,a844),x40672),x40673))) % 186.05/186.62 [4076]E(f775(f775(f46(x40761,f857(x40762,a844)),x40763),f775(f775(f10(f857(x40761,a844),f857(x40762,a844),x40761),f277(x40761,x40762,x40764)),f775(f775(f9(x40761,f857(x40761,a844),f857(x40761,a844)),f302(x40761)),f180(f857(x40761,a844))))),f775(f277(x40761,x40762,x40764),x40763)) % 186.05/186.62 [4077]E(f775(f775(f46(x40771,f857(x40772,a844)),x40773),f775(f775(f10(f857(x40771,a844),f857(x40772,a844),x40771),f305(x40772,x40771,x40774)),f775(f775(f9(x40771,f857(x40771,a844),f857(x40771,a844)),f302(x40771)),f180(f857(x40771,a844))))),f775(f305(x40772,x40771,x40774),x40773)) % 186.05/186.62 [4168]E(f775(f775(f104(f857(x41681,a844)),f775(f775(f104(f857(x41681,a844)),f775(f775(f103(f857(x41681,a844)),x41682),x41683)),f775(f775(f103(f857(x41681,a844)),x41683),x41684))),f775(f775(f103(f857(x41681,a844)),x41684),x41682)),f775(f775(f103(f857(x41681,a844)),f775(f775(f103(f857(x41681,a844)),f775(f775(f104(f857(x41681,a844)),x41682),x41683)),f775(f775(f104(f857(x41681,a844)),x41683),x41684))),f775(f775(f104(f857(x41681,a844)),x41684),x41682))) % 186.05/186.62 [4227]E(f775(f132(f851(x42271),f851(x42271),f125(x42271),f115(x42271)),f775(f775(f143(x42272,f851(x42271)),f775(f775(f9(x42272,f851(x42271),f851(x42271)),f775(f775(f10(x42271,f857(f851(x42271),f851(x42271)),x42272),f140(x42271)),x42273)),f115(x42271))),x42274)),f775(f775(f143(x42272,x42271),x42273),x42274)) % 186.05/186.62 [4237]E(f775(f775(f88(a1,x42371),f775(f106(a1),f775(f775(f82(a1),x42372),a99))),f775(f775(f20(a1,x42371,x42371),f775(f775(f9(a1,x42371,f857(x42371,x42371)),f775(f775(f10(a844,f857(x42371,f857(x42371,x42371)),a1),f98(x42371)),a186)),x42373)),f775(f775(f10(a850,x42371,a1),x42374),a107))),f175(x42371,x42373,x42374,f775(f106(a850),x42372))) % 186.05/186.62 [4478]~P1(f775(f775(f180(f857(x44781,f857(x44782,a844))),x44783),x44784)) % 186.05/186.62 [3716]E(f775(f775(f153(x37161),f775(f775(f125(x37161),x37162),x37163)),f775(f775(f82(a850),f775(f181(f851(x37161)),x37162)),x37164)),f775(f775(f153(x37161),x37163),x37164)) % 186.05/186.62 [3721]E(f775(f775(f128(x37211),x37212),f775(f775(f159(x37211),f775(f775(f82(a850),x37213),x37212)),x37214)),f775(f775(f159(x37211),x37213),f775(f775(f128(x37211),x37212),x37214))) % 186.05/186.62 [3819]E(f775(f775(f103(f857(x38191,a844)),f775(f259(x38192,x38191),x38193)),f775(f259(x38192,x38191),x38194)),f775(f259(x38192,x38191),f775(f775(f103(f857(f856(x38192,x38191),a844)),x38193),x38194))) % 186.05/186.62 [3820]E(f775(f775(f103(f857(x38201,a844)),f775(f261(x38201,x38202),x38203)),f775(f261(x38201,x38202),x38204)),f775(f261(x38201,x38202),f775(f775(f103(f857(f856(x38201,x38202),a844)),x38203),x38204))) % 186.05/186.62 [3825]E(f775(f775(f3(f857(x38251,a844)),f775(f775(f104(f857(x38251,a844)),x38252),x38253)),x38254),f775(f775(f104(f857(x38251,a844)),x38252),f775(f775(f3(f857(x38251,a844)),x38253),x38254))) % 186.05/186.62 [3826]E(f775(f775(f103(f857(x38261,a844)),f775(f775(f103(f857(x38261,a844)),x38262),x38263)),x38264),f775(f775(f103(f857(x38261,a844)),x38262),f775(f775(f103(f857(x38261,a844)),x38263),x38264))) % 186.05/186.62 [3827]E(f775(f775(f104(f857(x38271,a844)),f775(f775(f104(f857(x38271,a844)),x38272),x38273)),x38274),f775(f775(f104(f857(x38271,a844)),x38272),f775(f775(f104(f857(x38271,a844)),x38273),x38274))) % 186.05/186.62 [3865]E(f775(f775(f103(f857(f856(x38651,x38652),a844)),f775(f278(x38652,x38651),x38653)),f775(f278(x38652,x38651),x38654)),f775(f278(x38652,x38651),f775(f775(f103(f857(f856(x38652,x38651),a844)),x38653),x38654))) % 186.05/186.62 [3866]E(f775(f775(f104(f857(f856(x38661,x38662),a844)),f775(f278(x38662,x38661),x38663)),f775(f278(x38662,x38661),x38664)),f775(f278(x38662,x38661),f775(f775(f104(f857(f856(x38662,x38661),a844)),x38663),x38664))) % 186.05/186.62 [3901]E(f170(x39011,x39012,x39013,f166(x39011,x39012,f775(f142(f856(x39011,x39012)),f775(f775(f167(x39011,x39012),f115(x39011)),x39014)))),x39013) % 186.05/186.62 [3939]E(f775(f775(f103(f857(x39391,a844)),f775(f775(f3(f857(x39391,a844)),x39392),x39393)),f775(f775(f3(f857(x39391,a844)),x39394),x39393)),f775(f775(f3(f857(x39391,a844)),f775(f775(f103(f857(x39391,a844)),x39392),x39394)),x39393)) % 186.05/186.62 [3940]E(f775(f775(f104(f857(x39401,a844)),f775(f775(f103(f857(x39401,a844)),x39402),x39403)),f775(f775(f103(f857(x39401,a844)),x39404),x39403)),f775(f775(f103(f857(x39401,a844)),f775(f775(f104(f857(x39401,a844)),x39402),x39404)),x39403)) % 186.05/186.62 [3941]E(f775(f775(f3(f857(x39411,a844)),f775(f775(f104(f857(x39411,a844)),x39412),x39413)),f775(f775(f104(f857(x39411,a844)),x39414),x39413)),f775(f775(f104(f857(x39411,a844)),f775(f775(f3(f857(x39411,a844)),x39412),x39414)),x39413)) % 186.05/186.62 [3942]E(f775(f775(f103(f857(x39421,a844)),f775(f775(f104(f857(x39421,a844)),x39422),x39423)),f775(f775(f104(f857(x39421,a844)),x39424),x39423)),f775(f775(f104(f857(x39421,a844)),f775(f775(f103(f857(x39421,a844)),x39422),x39424)),x39423)) % 186.05/186.62 [3943]E(f775(f775(f3(f857(x39431,a844)),f775(f775(f104(f857(x39431,a844)),x39432),x39433)),f775(f775(f104(f857(x39431,a844)),x39434),x39433)),f775(f775(f3(f857(x39431,a844)),f775(f775(f104(f857(x39431,a844)),x39432),x39433)),x39434)) % 186.05/186.62 [3955]E(f775(f775(f3(f857(x39551,a844)),f775(f775(f3(f857(x39551,a844)),x39552),f775(f775(f302(x39551),x39553),f180(f857(x39551,a844))))),x39554),f775(f775(f3(f857(x39551,a844)),x39552),f775(f775(f302(x39551),x39553),x39554))) % 186.05/186.62 [4011]E(f775(f775(f103(f857(x40111,a844)),f775(f775(f302(x40111),x40112),f775(f775(f302(x40111),x40113),f180(f857(x40111,a844))))),f775(f276(x40111),x40114)),f775(f276(x40111),f775(f775(f302(f856(x40111,x40111)),f775(f775(f241(x40111,x40111),x40112),x40113)),x40114))) % 186.05/186.62 [4038]E(f775(f775(f46(a850,f857(x40381,a844)),f775(f293(a850),x40382)),f775(f775(f10(a850,f857(x40381,a844),a850),x40383),f775(f775(f9(a850,a850,a850),f82(a850)),x40384))),f775(f775(f46(a850,f857(x40381,a844)),f295(a850,x40384,f775(f775(f82(a850),x40382),x40384))),x40383)) % 186.05/186.62 [4039]E(f161(x40391,f775(f277(x40391,x40391,x40392),f775(f775(f302(x40391),x40393),f180(f857(x40391,a844)))),f775(f277(f851(x40391),f851(x40391),f147(x40391,x40392)),f775(f775(f302(f851(x40391)),x40394),f180(f857(f851(x40391),a844))))),f775(f277(f851(x40391),f851(x40391),f147(x40391,x40392)),f775(f775(f302(f851(x40391)),f775(f775(f140(x40391),x40393),x40394)),f180(f857(f851(x40391),a844))))) % 186.05/186.62 [4102]E(f166(x41021,x41022,f775(f775(f143(x41021,f856(x41021,x41022)),f775(f775(f20(x41021,x41022,f856(x41021,x41022)),f241(x41021,x41022)),x41023)),x41024)),f172(x41021,x41022,f775(f75(x41022,f854(x41022),x41021,f227(x41022)),x41023),f775(f158(x41021),x41024))) % 186.05/186.62 [4105]E(f775(f256(x41051),f775(f775(f9(x41051,f857(x41052,a844),a844),f775(f775(f10(x41052,f857(f857(x41052,a844),a844),x41051),f334(x41052)),x41053)),x41054)),f775(f305(x41051,x41052,x41053),x41054)) % 186.05/186.62 [4199]E(f775(f256(x41991),f775(f775(f9(x41991,f857(f856(x41992,x41991),a844),a844),f775(f775(f10(f856(x41992,x41991),f857(f857(f856(x41992,x41991),a844),a844),x41991),f334(f856(x41992,x41991))),f775(f241(x41992,x41991),x41993))),x41994)),f775(f277(x41992,x41991,x41994),f775(f775(f302(x41992),x41993),f180(f857(x41992,a844))))) % 186.05/186.62 [4213]E(f775(f775(f143(f856(x42131,a850),x42131),f240(x42131,a850)),f775(f126(f856(x42131,a850),f775(f775(f10(a850,a844,f856(x42131,a850)),x42132),f775(f775(f10(a850,a850,f856(x42131,a850)),a114),f250(x42131,a850)))),f775(f775(f167(x42131,a850),x42133),x42134))),f775(f775(f143(f856(x42131,a850),x42131),f240(x42131,a850)),f775(f126(f856(x42131,a850),f775(f775(f10(a850,a844,f856(x42131,a850)),x42132),f250(x42131,a850))),f775(f775(f167(x42131,a850),x42133),f775(f775(f143(a850,a850),a114),x42134))))) % 186.05/186.62 [4220]P1(f775(f775(f232(f857(f857(x42201,a844),a844)),f775(f775(f46(x42202,f857(f857(x42201,a844),a844)),x42203),f775(f775(f10(f857(x42201,a844),f857(f857(x42201,a844),a844),x42202),f301(x42201)),x42204))),f775(f301(x42201),f775(f775(f46(x42202,f857(x42201,a844)),x42203),x42204)))) % 186.05/186.62 [4260]E(f775(f775(f88(a1,x42601),f775(f106(a1),f775(f775(f82(a1),x42602),a99))),f775(f775(f20(a1,x42601,x42601),f775(f775(f9(a1,x42601,f857(x42601,x42601)),f775(f775(f10(a844,f857(x42601,f857(x42601,x42601)),a1),f98(x42601)),a186)),x42603)),f775(f775(f20(a1,x42601,x42601),f775(f775(f10(a850,f857(x42601,x42601),a1),x42604),a107)),f775(f775(f10(a850,x42601,a1),f174(x42601,x42603,x42604)),a107)))),f775(f174(x42601,x42603,x42604),f775(f106(a850),x42602))) % 186.05/186.62 [4263]E(f775(f775(f143(x42631,x42632),f775(f75(f854(x42632),x42632,x42631,f231(x42632)),x42633)),f775(f126(x42631,f775(f775(f10(a844,a844,x42631),a328),f775(f775(f9(x42631,f854(x42632),a844),f775(f775(f10(f854(x42632),f857(f854(x42632),a844),x42631),a330),x42633)),f183(x42632)))),x42634)),f154(x42631,x42632,x42633,x42634)) % 186.05/186.62 [4284]E(f775(f256(f856(x42841,x42842)),f775(f251(x42841,x42842,a844),f775(f775(f9(x42841,f857(x42842,a844),f857(x42842,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x42842,a844),f857(x42842,a844)),x42841),f10(a844,a844,x42842)),f775(f775(f10(a844,f857(a844,a844),x42841),a331),f775(f775(f9(x42841,f857(x42841,a844),a844),f334(x42841)),x42843)))),f775(f775(f9(x42842,f857(x42842,a844),a844),f334(x42842)),x42844)))),f223(x42841,x42842,x42843,x42844)) % 186.05/186.62 [4317]E(f775(f775(f46(x43171,f857(f856(x43171,x43172),a844)),x43173),f775(f775(f20(x43171,f857(x43172,f857(f856(x43171,x43172),a844)),f857(f856(x43171,x43172),a844)),f775(f775(f10(f857(x43172,a844),f857(f857(x43172,f857(f856(x43171,x43172),a844)),f857(f856(x43171,x43172),a844)),x43171),f46(x43172,f857(f856(x43171,x43172),a844))),x43174)),f775(f775(f9(x43171,f857(f856(x43171,x43172),a844),f857(x43172,f857(f856(x43171,x43172),a844))),f775(f775(f10(f857(x43172,f857(f857(f856(x43171,x43172),a844),f857(f856(x43171,x43172),a844))),f857(f857(f856(x43171,x43172),a844),f857(x43172,f857(f856(x43171,x43172),a844))),x43171),f9(x43172,f857(f856(x43171,x43172),a844),f857(f856(x43171,x43172),a844))),f775(f775(f10(f857(x43172,f856(x43171,x43172)),f857(x43172,f857(f857(f856(x43171,x43172),a844),f857(f856(x43171,x43172),a844))),x43171),f775(f10(f856(x43171,x43172),f857(f857(f856(x43171,x43172),a844),f857(f856(x43171,x43172),a844)),x43172),f302(f856(x43171,x43172)))),f241(x43171,x43172)))),f180(f857(f856(x43171,x43172),a844))))),f775(f775(f248(x43171,x43172),x43173),x43174)) % 186.05/186.62 [3874]E(f775(f775(f125(x38741),f775(f775(f159(x38741),x38742),x38743)),f775(f775(f159(x38741),f775(f775(f3(a850),x38742),f775(f181(f851(x38741)),x38743))),x38744)),f775(f775(f159(x38741),x38742),f775(f775(f125(x38741),x38743),x38744))) % 186.05/186.62 [3875]E(f775(f775(f125(x38751),f775(f775(f128(x38751),x38752),x38753)),f775(f775(f128(x38751),f775(f775(f3(a850),x38752),f775(f181(f851(x38751)),x38753))),x38754)),f775(f775(f128(x38751),x38752),f775(f775(f125(x38751),x38753),x38754))) % 186.05/186.62 [3928]E(f775(f775(f82(a850),f775(f775(f83(a850),x39281),x39282)),f775(f775(f82(a850),f775(f775(f83(a850),x39283),x39282)),x39284)),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f82(a850),x39281),x39283)),x39282)),x39284)) % 186.05/186.62 [4133]P1(f775(f775(f232(f857(x41331,a844)),f775(f775(f3(f857(x41331,a844)),f775(f259(x41332,x41331),x41333)),f775(f259(x41332,x41331),x41334))),f775(f259(x41332,x41331),f775(f775(f3(f857(f856(x41332,x41331),a844)),x41333),x41334)))) % 186.05/186.62 [4134]P1(f775(f775(f232(f857(x41341,a844)),f775(f775(f3(f857(x41341,a844)),f775(f261(x41341,x41342),x41343)),f775(f261(x41341,x41342),x41344))),f775(f261(x41341,x41342),f775(f775(f3(f857(f856(x41341,x41342),a844)),x41343),x41344)))) % 186.05/186.62 [4239]E(f775(f775(f82(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x42391),x42392)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x42393),x42394)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),f775(f775(f82(a850),x42391),x42393)),f775(f775(f82(a850),x42392),x42394))),f180(f857(f856(a850,a850),a844)))))) % 186.05/186.62 [4279]E(f775(f775(f83(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x42791),x42792)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x42793),x42794)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),f775(f775(f82(a850),f775(f775(f83(a850),x42791),x42793)),f775(f775(f83(a850),x42792),x42794))),f775(f775(f82(a850),f775(f775(f83(a850),x42791),x42794)),f775(f775(f83(a850),x42792),x42793)))),f180(f857(f856(a850,a850),a844)))))) % 186.05/186.62 [4299]E(f775(f256(x42991),f775(f775(f10(f857(x42992,a844),a844,x42991),f90(x42992)),f775(f775(f10(f857(x42992,a844),f857(x42992,a844),x42991),f775(f20(x42992,a844,a844),f775(f775(f10(a844,f857(a844,a844),x42992),a335),f775(f775(f9(x42992,f857(x42992,a844),a844),f334(x42992)),x42993)))),f775(f775(f9(x42991,f857(x42992,f857(x42991,a844)),f857(x42992,a844)),f775(f775(f10(f857(f857(x42991,a844),a844),f857(f857(x42992,f857(x42991,a844)),f857(x42992,a844)),x42991),f10(f857(x42991,a844),a844,x42992)),f334(x42991))),x42994)))),f775(f775(f47(x42992,f857(x42991,a844)),x42993),x42994)) % 186.05/186.62 [4333]E(f775(f775(f281(x43331,x43331,x43331),f775(f775(f302(f856(x43331,x43331)),f775(f775(f241(x43331,x43331),x43332),x43333)),x43334)),f300(x43331,f775(f775(f302(f856(x43331,x43331)),f775(f775(f241(x43331,x43331),x43332),x43333)),x43334))),f775(f775(f103(f857(f856(x43331,x43331),a844)),f775(f775(f281(x43331,x43331,x43331),x43334),f300(x43331,x43334))),f775(f256(f856(x43331,x43331)),f775(f251(x43331,x43331,a844),f775(f775(f9(x43331,f857(x43331,a844),f857(x43331,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x43331,a844),f857(x43331,a844)),x43331),f10(a844,a844,x43331)),f775(f775(f10(a844,f857(a844,a844),x43331),a331),f775(f775(f9(x43331,f857(f856(x43331,x43331),a844),a844),f775(f775(f10(f856(x43331,x43331),f857(f857(f856(x43331,x43331),a844),a844),x43331),f334(f856(x43331,x43331))),f775(f775(f9(x43331,x43331,f856(x43331,x43331)),f241(x43331,x43331)),x43332))),f300(x43331,x43334))))),f775(f775(f9(x43331,f857(f856(x43331,x43331),a844),a844),f775(f775(f10(f856(x43331,x43331),f857(f857(f856(x43331,x43331),a844),a844),x43331),f334(f856(x43331,x43331))),f775(f241(x43331,x43331),x43333))),f300(x43331,x43334))))))) % 186.05/186.62 [4135]E(f775(f126(x41351,f775(f775(f20(x41351,a844,a844),f775(f775(f10(a844,f857(a844,a844),x41351),a331),x41352)),x41353)),x41354),f775(f126(x41351,x41353),f775(f126(x41351,x41352),x41354))) % 186.05/186.62 [4233]E(f775(f775(f125(x42331),f775(f775(f775(f98(f851(x42331)),f775(f775(f334(a850),f2(a850)),x42332)),f775(f775(f140(x42331),x42333),f115(x42331))),f115(x42331))),f160(x42331,x42334,f775(f256(a850),f775(f775(f9(a850,f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),a850),f334(a850)),a114)),x42332)))),f160(x42331,f775(f775(f140(x42331),x42333),x42334),x42332)) % 186.05/186.62 [4328]E(f775(f256(f856(x43281,x43282)),f775(f775(f10(f857(a850,a844),a844,f856(x43281,x43282)),f89(a850)),f775(f775(f9(f856(x43281,x43282),f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),f856(x43281,x43282)),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),f856(x43281,x43282)),f775(f10(a844,f857(a844,a844),a850),a331)),f775(f775(f9(f856(x43281,x43282),f857(a850,f856(x43281,x43282)),f857(a850,a844)),f775(f775(f10(f857(f856(x43281,x43282),a844),f857(f857(a850,f856(x43281,x43282)),f857(a850,a844)),f856(x43281,x43282)),f10(f856(x43281,x43282),a844,a850)),a330)),f775(f775(f20(a850,x43282,f856(x43281,x43282)),f775(f775(f10(x43281,f857(x43282,f856(x43281,x43282)),a850),f241(x43281,x43282)),f775(f153(x43281),x43283))),f775(f153(x43282),x43284)))))),f775(f775(f9(a850,a850,a844),f233(a850)),f775(f775(f236(a850),f775(f181(f851(x43281)),x43283)),f775(f181(f851(x43282)),x43284)))))),f775(f158(f856(x43281,x43282)),f775(f775(f167(x43281,x43282),x43283),x43284))) % 186.05/186.62 [4252]E(f775(f256(f856(x42521,x42522)),f775(f251(x42521,x42522,a844),f775(f775(f9(x42521,f857(x42522,a844),f857(x42522,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x42522,a844),f857(x42522,a844)),x42521),f10(a844,a844,x42522)),f775(f775(f10(a844,f857(a844,a844),x42521),a331),x42523))),x42524))),f775(f775(f248(x42521,x42522),f775(f256(x42521),x42523)),f775(f18(f857(x42522,a844),x42521),f775(f256(x42522),x42524)))) % 186.05/186.62 [4255]E(f775(f256(f856(x42551,x42552)),f775(f251(x42551,x42552,a844),f775(f775(f20(x42551,f857(x42552,a844),f857(x42552,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x42552,a844),f857(x42552,a844)),x42551),f10(a844,a844,x42552)),f775(f775(f10(a844,f857(a844,a844),x42551),a331),x42553))),x42554))),f775(f775(f248(x42551,x42552),f775(f256(x42551),x42553)),f775(f775(f10(f857(x42552,a844),f857(x42552,a844),x42551),f256(x42552)),x42554))) % 186.05/186.62 [4270]E(f775(f256(x42701),f775(f775(f10(f857(x42702,a844),a844,x42701),f90(x42702)),f775(f775(f10(f857(x42702,a844),f857(x42702,a844),x42701),f775(f20(x42702,a844,a844),f775(f775(f10(a844,f857(a844,a844),x42702),a335),f775(f775(f9(x42702,f857(x42702,a844),a844),f334(x42702)),x42703)))),x42704))),f775(f775(f47(x42702,f857(x42701,a844)),x42703),f775(f775(f10(f857(x42701,a844),f857(x42701,a844),x42702),f256(x42701)),f775(f9(x42701,x42702,a844),x42704)))) % 186.05/186.62 [4312]E(f775(f775(f143(f856(x43121,a850),x43121),f240(x43121,a850)),f775(f126(f856(x43121,a850),f775(f775(f9(f856(x43121,a850),f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),f856(x43121,a850)),f334(a850)),f250(x43121,a850))),x43122)),f775(f775(f167(x43121,a850),x43123),f130(a850,f775(f294(a850,x43124),f775(f775(f82(a850),x43124),f775(f181(f851(x43121)),x43123))))))),f775(f775(f143(f856(x43121,a850),x43121),f240(x43121,a850)),f775(f126(f856(x43121,a850),f775(f775(f9(f856(x43121,a850),f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),f856(x43121,a850)),f334(a850)),f775(f775(f9(f856(x43121,a850),a850,a850),f775(f775(f10(a850,f857(a850,a850),f856(x43121,a850)),f82(a850)),f250(x43121,a850))),x43124))),x43122)),f775(f775(f167(x43121,a850),x43123),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(x43121)),x43123))))))) % 186.05/186.62 [4313]E(f775(a114,f775(f775(f179(a850),f775(f181(f851(x43131)),x43132)),f775(f132(a850,f851(x43133),f775(f9(f851(x43133),a850,a850),f775(f775(f10(a850,f857(a850,a850),f851(x43133)),f179(a850)),f775(f775(f9(f851(x43133),a850,a850),f775(f775(f10(a850,f857(a850,a850),f851(x43133)),f3(a850)),f181(f851(x43133)))),f775(a114,f2(a850))))),f2(a850)),f775(f142(f851(x43133)),f775(f126(f851(x43133),f775(f775(f10(a844,a844,f851(x43133)),a328),f775(f775(f9(f851(x43133),f851(x43133),a844),a330),f115(x43133)))),x43134))))),f775(f775(f179(a850),f775(a114,f775(f181(f851(x43131)),x43132))),f775(f132(a850,f851(x43133),f775(f9(f851(x43133),a850,a850),f775(f775(f10(a850,f857(a850,a850),f851(x43133)),f179(a850)),f181(f851(x43133)))),f2(a850)),f775(f142(f851(x43133)),x43134)))) % 186.05/186.62 [4269]E(f775(f775(f125(x42691),f160(x42691,x42692,x42693)),f160(x42691,x42694,f775(f256(a850),f775(f775(f9(a850,f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),a850),f334(a850)),f775(f775(f9(a850,a850,a850),f82(a850)),f775(f181(f851(x42691)),x42692)))),x42693)))),f160(x42691,f775(f775(f125(x42691),x42692),x42694),x42693)) % 186.05/186.62 [4319]E(f775(f775(f140(f851(x43191)),f775(f775(f140(x43191),x43192),f775(f132(f851(x43191),f851(x43191),f125(x43191),f115(x43191)),f775(f775(f143(f851(x43191),f851(x43191)),f145(f851(x43191),x43191,f115(x43191),f775(f775(f10(f851(x43191),f857(f851(x43191),f851(x43191)),x43191),f18(f851(x43191),f851(x43191))),f775(f775(f9(x43191,f851(x43191),f851(x43191)),f140(x43191)),f115(x43191))))),x43193)))),f164(x43191,f775(f775(f140(f851(x43191)),x43194),f775(f132(f851(f851(x43191)),f851(f851(x43191)),f125(f851(x43191)),f115(f851(x43191))),f775(f775(f143(f851(x43191),f851(f851(x43191))),f145(f851(f851(x43191)),x43191,f115(f851(x43191)),f775(f18(f857(f851(x43191),f851(f851(x43191))),x43191),f775(f775(f9(f851(x43191),f851(f851(x43191)),f851(f851(x43191))),f140(f851(x43191))),f115(f851(x43191)))))),x43193))))),f164(x43191,f775(f775(f140(f851(x43191)),f775(f775(f140(x43191),x43192),x43194)),x43193))) % 186.05/186.62 [4329]E(f775(f256(f856(x43291,x43291)),f775(f251(x43291,x43291,a844),f775(f775(f9(x43291,f857(f856(x43292,x43292),a844),f857(x43291,a844)),f775(f775(f10(f857(x43291,f857(f857(f856(x43292,x43292),a844),a844)),f857(f857(f856(x43292,x43292),a844),f857(x43291,a844)),x43291),f9(x43291,f857(f856(x43292,x43292),a844),a844)),f775(f775(f10(f857(x43291,f856(x43292,x43292)),f857(x43291,f857(f857(f856(x43292,x43292),a844),a844)),x43291),f775(f10(f856(x43292,x43292),f857(f857(f856(x43292,x43292),a844),a844),x43291),f334(f856(x43292,x43292)))),f775(f775(f9(x43291,f857(x43291,x43292),f857(x43291,f856(x43292,x43292))),f775(f775(f10(f857(x43292,f856(x43292,x43292)),f857(f857(x43291,x43292),f857(x43291,f856(x43292,x43292))),x43291),f10(x43292,f856(x43292,x43292),x43291)),f775(f775(f10(x43292,f857(x43292,f856(x43292,x43292)),x43291),f241(x43292,x43292)),x43293))),x43293)))),x43294))),f775(f775(f280(x43292,x43291),x43294),x43293)) % 186.05/186.62 [4413]~E(f35(x44131,x44132),f33(x44133,x44134,x44135)) % 186.05/186.62 [4414]~E(f35(x44141,x44142),f32(x44143,x44144,x44145)) % 186.05/186.62 [4415]~E(f35(x44151,x44152),f31(x44153,x44154,x44155)) % 186.05/186.62 [4416]~E(f36(x44161,x44162),f33(x44163,x44164,x44165)) % 186.05/186.62 [4417]~E(f36(x44171,x44172),f32(x44173,x44174,x44175)) % 186.05/186.62 [4418]~E(f36(x44181,x44182),f31(x44183,x44184,x44185)) % 186.05/186.62 [4419]~E(f28(x44191,x44192),f33(x44193,x44194,x44195)) % 186.05/186.62 [4420]~E(f28(x44201,x44202),f32(x44203,x44204,x44205)) % 186.05/186.62 [4421]~E(f28(x44211,x44212),f31(x44213,x44214,x44215)) % 186.05/186.62 [4422]~E(f33(x44221,x44222,x44223),f35(x44224,x44225)) % 186.05/186.62 [4423]~E(f33(x44231,x44232,x44233),f36(x44234,x44235)) % 186.05/186.62 [4424]~E(f33(x44241,x44242,x44243),f28(x44244,x44245)) % 186.05/186.62 [4425]~E(f32(x44251,x44252,x44253),f35(x44254,x44255)) % 186.05/186.62 [4426]~E(f32(x44261,x44262,x44263),f36(x44264,x44265)) % 186.05/186.62 [4427]~E(f32(x44271,x44272,x44273),f28(x44274,x44275)) % 186.05/186.62 [4428]~E(f31(x44281,x44282,x44283),f35(x44284,x44285)) % 186.05/186.62 [4429]~E(f31(x44291,x44292,x44293),f36(x44294,x44295)) % 186.05/186.62 [4430]~E(f31(x44301,x44302,x44303),f28(x44304,x44305)) % 186.05/186.62 [3817]E(f775(f170(x38171,x38172,x38173,x38174),x38175),f775(f229(f854(x38172),x38172,f775(x38173,x38175),f227(x38172)),f775(x38174,x38175))) % 186.05/186.62 [3903]E(f170(x39031,x39032,f170(x39031,x39032,x39033,x39034),x39035),f170(x39031,x39032,x39033,f170(x39031,x39032,x39034,x39035))) % 186.05/186.62 [3646]E(f775(f775(f251(x36461,x36462,x36463),x36464),x36465),f775(f775(x36464,f775(f240(x36461,x36462),x36465)),f775(f250(x36461,x36462),x36465))) % 186.05/186.62 [3672]E(f775(f229(x36721,x36722,x36723,x36724),f775(f227(x36722),x36725)),f775(x36724,x36725)) % 186.05/186.62 [3680]E(f775(f775(f775(f67(x36801,x36802,x36803),x36804),x36805),f180(f857(x36802,a844))),x36805) % 186.05/186.62 [3696]E(f775(f316(x36961,x36962,x36963,x36964),f775(f304(x36961,x36963),x36965)),f775(x36964,x36965)) % 186.05/186.62 [3697]E(f775(f317(x36971,x36972,x36973,x36974),f775(f313(x36971,x36973),x36975)),f775(x36974,x36975)) % 186.05/186.62 [3846]E(f230(x38461,x38462,x38463,x38464,f775(f227(x38462),x38465)),f775(x38464,x38465)) % 186.05/186.62 [3882]E(f318(x38821,x38822,x38823,x38824,f775(f304(x38821,x38822),x38825)),f775(f775(f82(a850),f775(x38823,x38825)),f775(a114,f2(a850)))) % 186.05/186.62 [3883]E(f318(x38831,x38832,x38833,x38834,f775(f313(x38832,x38831),x38835)),f775(f775(f82(a850),f775(x38834,x38835)),f775(a114,f2(a850)))) % 186.05/186.62 [3961]E(f775(f75(f854(x39611),f854(x39612),f854(x39613),f775(f196(x39611,x39612),x39614)),f775(f196(x39613,x39611),x39615)),f775(f196(x39613,x39612),f775(f75(x39611,x39612,x39613,x39614),x39615))) % 186.05/186.62 [3963]E(f775(f75(f851(x39631),f851(x39632),f851(x39633),f775(f143(x39631,x39632),x39634)),f775(f143(x39633,x39631),x39635)),f775(f143(x39633,x39632),f775(f75(x39631,x39632,x39633,x39634),x39635))) % 186.05/186.62 [4042]E(f87(x40421,f68(x40422,x40421,x40423,x40424,x40425)),f775(f775(f66(x40422,x40421,x40423),x40424),x40425)) % 186.05/186.62 [4078]E(f775(f775(f82(a850),f775(f775(f82(a850),f775(x40781,f775(f240(x40782,x40783),x40784))),f775(x40785,f775(f250(x40782,x40783),x40784)))),f775(a114,f2(a850))),f255(x40782,x40783,x40781,x40785,x40784)) % 186.05/186.62 [4265]E(f154(x42651,x42652,f775(f775(f9(x42651,f854(x42652),f854(x42652)),f775(f775(f20(x42651,f854(x42652),f857(f854(x42652),f854(x42652))),f775(f775(f10(a844,f857(f854(x42652),f857(f854(x42652),f854(x42652))),x42651),f98(f854(x42652))),x42653)),f775(f775(f10(x42652,f854(x42652),x42651),f227(x42652)),x42654))),f183(x42652)),x42655),f775(f775(f143(x42651,x42652),x42654),f775(f126(x42651,x42653),x42655))) % 186.05/186.62 [4471]~E(f775(f775(f775(f74(x44711,f854(x44712)),x44713),x44714),f775(f227(x44712),x44715)),f775(f18(f854(x44712),x44711),f183(x44712))) % 186.05/186.62 [3581]E(f775(f775(f159(x35811),x35812),f775(f775(f143(x35813,x35811),x35814),x35815)),f775(f775(f143(x35813,x35811),x35814),f775(f775(f159(x35813),x35812),x35815))) % 186.05/186.62 [3582]E(f775(f775(f128(x35821),x35822),f775(f775(f143(x35823,x35821),x35824),x35825)),f775(f775(f143(x35823,x35821),x35824),f775(f775(f128(x35823),x35822),x35825))) % 186.05/186.62 [3612]E(f775(f775(f143(x36121,x36122),x36123),f775(f775(f140(x36121),x36124),x36125)),f775(f775(f140(x36122),f775(x36123,x36124)),f775(f775(f143(x36121,x36122),x36123),x36125))) % 186.05/186.62 [3676]E(f775(f303(x36761,x36762,x36763),f775(f775(f302(x36761),x36764),x36765)),f775(f775(f302(x36762),f775(x36763,x36764)),f775(f303(x36761,x36762,x36763),x36765))) % 186.05/186.62 [3742]E(f775(f775(f167(x37421,x37422),f775(f775(f159(x37421),x37423),x37424)),f775(f775(f159(x37422),x37423),x37425)),f775(f775(f159(f856(x37421,x37422)),x37423),f775(f775(f167(x37421,x37422),x37424),x37425))) % 186.05/186.62 [3743]E(f775(f775(f167(x37431,x37432),f775(f775(f128(x37431),x37433),x37434)),f775(f775(f128(x37432),x37433),x37435)),f775(f775(f128(f856(x37431,x37432)),x37433),f775(f775(f167(x37431,x37432),x37434),x37435))) % 186.05/186.62 [3754]E(f775(f775(f148(x37541,f775(f775(f140(x37541),x37542),x37543)),f775(a114,x37544)),x37545),f775(f775(f140(x37541),x37542),f775(f775(f148(x37541,x37543),x37544),x37545))) % 186.05/186.62 [3757]E(f775(f229(f854(x37571),x37572,f183(x37571),x37573),f775(f775(f18(f854(x37572),x37574),f183(x37572)),x37575)),f183(x37571)) % 186.05/186.62 [3759]E(f775(f775(f125(x37591),f775(f775(f143(x37592,x37591),x37593),x37594)),f775(f775(f143(x37592,x37591),x37593),x37595)),f775(f775(f143(x37592,x37591),x37593),f775(f775(f125(x37592),x37594),x37595))) % 186.05/186.62 [3763]E(f775(f775(x37631,x37632),f775(f775(f243(x37633,x37634,x37631),x37632),x37635)),f775(f775(f243(x37633,x37634,x37631),x37632),f775(a114,x37635))) % 186.05/186.62 [3804]E(f775(f775(f281(x38041,x38042,x38043),f775(f278(x38042,x38041),x38044)),f775(f278(x38043,x38042),x38045)),f775(f278(x38043,x38041),f775(f775(f281(x38043,x38042,x38041),x38045),x38044))) % 186.05/186.62 [3835]E(f775(f775(f775(f173(f851(x38351),f851(x38351)),x38352),f141(x38351)),f775(f775(f143(x38353,x38351),x38354),x38355)),f775(f775(f143(x38353,x38351),x38354),f775(f775(f775(f173(f851(x38353),f851(x38353)),x38352),f141(x38353)),x38355))) % 186.05/186.62 [3836]E(f775(f775(f253(x38361,x38362,x38361,x38363),f775(f241(x38362,x38361),x38364)),x38365),f775(x38365,x38364)) % 186.05/186.62 [3860]E(f144(x38601,x38602,f775(f775(f143(x38603,x38601),x38604),x38605)),f144(x38603,f775(f75(x38601,a850,x38603,x38602),x38604),x38605)) % 186.05/186.62 [3926]E(f775(f775(f75(f854(x39261),f854(x39262),x39263,f775(f196(x39261,x39262),x39264)),f775(f18(f854(x39261),x39263),f183(x39261))),x39265),f183(x39262)) % 186.05/186.62 [3927]E(f162(f856(x39271,x39272),f775(f75(x39272,a844,f856(x39271,x39272),x39273),f250(x39271,x39272)),f775(f775(f167(x39271,x39272),x39274),x39275)),f775(f775(f167(x39271,x39272),x39274),f162(x39272,x39273,x39275))) % 186.05/186.62 [3932]E(f775(f303(x39321,x39322,f775(f775(f10(x39323,x39322,x39321),x39324),x39325)),f239(f857(x39321,a844))),f775(f303(x39323,x39322,x39324),f775(f303(x39321,x39323,x39325),f239(f857(x39321,a844))))) % 186.05/186.62 [3946]E(f162(f856(x39461,x39462),f775(f75(x39461,a844,f856(x39461,x39462),x39463),f240(x39461,x39462)),f775(f775(f167(x39461,x39462),x39464),x39465)),f775(f775(f167(x39461,x39462),f162(x39461,x39463,x39464)),x39465)) % 186.05/186.62 [3967]E(f775(f775(f103(f857(x39671,a844)),f775(f305(x39671,x39672,x39673),f775(f775(f302(x39672),x39674),f180(f857(x39672,a844))))),f775(f305(x39671,x39672,x39673),x39675)),f775(f305(x39671,x39672,x39673),f775(f775(f302(x39672),x39674),x39675))) % 186.05/186.62 [4027]E(f775(f775(f143(x40271,x40272),x40273),f162(x40271,f775(f75(x40272,a844,x40271,x40274),x40273),x40275)),f162(x40272,x40274,f775(f775(f143(x40271,x40272),x40273),x40275))) % 186.05/186.62 [4034]E(f775(f132(x40341,x40342,f775(f9(x40342,x40341,x40341),f775(f9(x40341,x40342,x40341),x40343)),x40344),f775(f142(x40342),f775(f142(x40342),x40345))),f775(f132(x40341,x40342,x40343,x40344),x40345)) % 186.05/186.62 [4035]E(f775(f775(f775(f74(x40351,f854(x40352)),f172(x40351,x40352,x40353,x40354)),x40355),f775(x40353,x40355)),f172(x40351,x40352,x40353,f775(f775(f302(x40351),x40355),x40354))) % 186.05/186.62 [4044]E(f775(f319(x40441,x40442,x40443,f775(f18(x40442,x40441),x40444),f775(f18(x40442,x40443),x40444)),x40445),x40444) % 186.05/186.62 [4103]E(f775(f229(f851(x41031),x41031,f154(x41032,x41031,x41033,x41034),f775(f775(f9(x41031,f851(x41031),f851(x41031)),f140(x41031)),f154(x41032,x41031,x41033,x41034))),f775(x41033,x41035)),f154(x41032,x41031,x41033,f775(f775(f140(x41032),x41035),x41034))) % 186.05/186.62 [4143]P1(f775(f775(f232(f857(x41431,a844)),f775(f303(x41432,x41431,x41433),f775(f775(f104(f857(x41432,a844)),x41434),x41435))),f775(f775(f104(f857(x41431,a844)),f775(f303(x41432,x41431,x41433),x41434)),f775(f303(x41432,x41431,x41433),x41435)))) % 186.05/186.62 [4144]P1(f775(f775(f232(f857(x41441,a844)),f775(f277(x41442,x41441,x41443),f775(f775(f104(f857(x41442,a844)),x41444),x41445))),f775(f775(f104(f857(x41441,a844)),f775(f277(x41442,x41441,x41443),x41444)),f775(f277(x41442,x41441,x41443),x41445)))) % 186.05/186.62 [4240]E(f775(f250(x42401,x42402),f775(f252(x42403,x42401,x42402,x42402,x42404,f39(x42402)),x42405)),f775(f250(x42403,x42402),x42405)) % 186.05/186.62 [4241]E(f775(f240(x42411,x42412),f775(f252(x42411,x42411,x42413,x42412,f39(x42411),x42414),x42415)),f775(f240(x42411,x42413),x42415)) % 186.05/186.62 [4323]P28(x43231,x43232,f775(f775(f302(f849(x43231)),f775(f775(f775(f93(x43231),f775(f775(f9(x43231,f857(a847,a847),f857(a847,a844)),f775(f775(f10(f857(a847,a844),f857(f857(a847,a847),f857(a847,a844)),x43231),f10(a847,a844,a847)),x43233)),f775(f775(f20(a847,a850,a847),f775(f775(f9(a847,a848,f857(a850,a847)),a189),x43234)),x43235))),f28(x43234,x43235)),x43233)),f180(f857(f849(x43231),a844)))) % 186.05/186.62 [4327]P28(x43271,x43272,f775(f775(f302(f849(x43271)),f775(f775(f775(f93(x43271),f775(f775(f9(x43271,f857(a847,a844),f857(a847,a844)),f775(f775(f10(f857(a847,f857(a844,a844)),f857(f857(a847,a844),f857(a847,a844)),x43271),f20(a847,a844,a844)),f775(f775(f10(f857(a847,a844),f857(a847,f857(a844,a844)),x43271),f775(f10(a844,f857(a844,a844),a847),a331)),x43273))),f775(f775(f10(a844,a844,a847),a328),x43274))),f35(x43274,x43275)),x43273)),f180(f857(f849(x43271),a844)))) % 186.05/186.62 [3429]E(f775(f775(f775(f775(f199(x34291),x34292),x34293),x34294),x34295),f185(x34291,x34292)) % 186.05/186.62 [3430]E(f775(f775(f775(f775(f203(x34301),x34302),x34303),x34304),x34305),f194(x34301,x34302)) % 186.05/186.62 [3474]E(f95(x34741,x34742,f775(f775(f775(f93(x34741),x34743),x34744),x34745)),f2(a850)) % 186.05/186.62 [3564]E(f775(f775(f775(f775(f74(x35641,x35642),x35643),x35644),x35645),x35644),x35645) % 186.05/186.62 [3794]E(f775(f775(f46(x37941,f857(x37942,a844)),f775(f775(f302(x37941),x37943),x37944)),x37945),f775(f775(f103(f857(x37942,a844)),f775(x37945,x37943)),f775(f775(f46(x37941,f857(x37942,a844)),x37944),x37945))) % 186.05/186.62 [3795]E(f775(f775(f47(x37951,f857(x37952,a844)),f775(f775(f302(x37951),x37953),x37954)),x37955),f775(f775(f104(f857(x37952,a844)),f775(x37955,x37953)),f775(f775(f47(x37951,f857(x37952,a844)),x37954),x37955))) % 186.05/186.62 [3853]E(f775(f775(f103(f857(x38531,a844)),f775(f303(x38532,x38531,x38533),x38534)),f775(f303(x38532,x38531,x38533),x38535)),f775(f303(x38532,x38531,x38533),f775(f775(f103(f857(x38532,a844)),x38534),x38535))) % 186.05/186.62 [3854]E(f775(f775(f103(f857(x38541,a844)),f775(f277(x38542,x38541,x38543),x38544)),f775(f277(x38542,x38541,x38543),x38545)),f775(f277(x38542,x38541,x38543),f775(f775(f103(f857(x38542,a844)),x38544),x38545))) % 186.05/186.62 [3855]E(f775(f775(f3(f857(x38551,a844)),f775(f305(x38551,x38552,x38553),x38554)),f775(f305(x38551,x38552,x38553),x38555)),f775(f305(x38551,x38552,x38553),f775(f775(f3(f857(x38552,a844)),x38554),x38555))) % 186.05/186.62 [3856]E(f775(f775(f103(f857(x38561,a844)),f775(f305(x38561,x38562,x38563),x38564)),f775(f305(x38561,x38562,x38563),x38565)),f775(f305(x38561,x38562,x38563),f775(f775(f103(f857(x38562,a844)),x38564),x38565))) % 186.05/186.62 [3857]E(f775(f775(f104(f857(x38571,a844)),f775(f305(x38571,x38572,x38573),x38574)),f775(f305(x38571,x38572,x38573),x38575)),f775(f305(x38571,x38572,x38573),f775(f775(f104(f857(x38572,a844)),x38574),x38575))) % 186.05/186.62 [3859]E(f172(x38591,x38592,f172(x38591,x38592,x38593,x38594),x38595),f172(x38591,x38592,x38593,f775(f775(f104(f857(x38591,a844)),x38594),x38595))) % 186.05/186.62 [3861]E(f118(x38611,x38612,f775(x38613,x38614),f775(f775(f9(x38611,a101,f852(x38612)),x38615),x38614)),f775(f192(x38611,x38612,x38613,x38615),x38614)) % 186.05/186.62 [3922]E(f775(f775(f148(x39221,f775(f775(f125(x39221),x39222),f775(f775(f140(x39221),x39223),x39224))),f775(f181(f851(x39221)),x39222)),x39225),f775(f775(f125(x39221),x39222),f775(f775(f140(x39221),x39225),x39224))) % 186.05/186.62 [3930]E(f775(f775(f47(x39301,f857(x39302,a844)),x39303),f775(f775(f10(f857(x39302,a844),f857(x39302,a844),x39301),f775(f302(x39302),x39304)),x39305)),f775(f775(f302(x39302),x39304),f775(f775(f47(x39301,f857(x39302,a844)),x39303),x39305))) % 186.05/186.62 [4002]E(f172(x40021,x40022,f775(f775(f775(f74(x40021,f854(x40022)),x40023),x40024),f775(f227(x40022),x40025)),f775(f81(f857(x40021,a844)),f775(f775(f302(x40021),x40024),f180(f857(x40021,a844))))),f172(x40021,x40022,x40023,f775(f81(f857(x40021,a844)),f775(f775(f302(x40021),x40024),f180(f857(x40021,a844)))))) % 186.05/186.62 [4088]E(f775(f775(f143(x40881,x40882),x40883),f775(f126(x40881,f775(f75(x40882,a844,x40881,x40884),x40883)),x40885)),f775(f126(x40882,x40884),f775(f775(f143(x40881,x40882),x40883),x40885))) % 186.05/186.62 [4095]E(f775(f181(f851(x40951)),f775(f126(x40951,x40952),f775(f775(f143(x40953,x40951),x40954),x40955))),f775(f181(f851(x40953)),f775(f126(x40953,f775(f75(x40951,a844,x40953,x40952),x40954)),x40955))) % 186.05/186.62 [4232]E(f775(f775(f103(f857(x42321,a844)),f775(f775(f3(f857(x42321,a844)),f169(x42321,x42322,x42323)),f775(f256(x42321),f775(f775(f9(x42321,f857(x42321,a844),a844),f334(x42321)),f775(f775(f3(f857(x42321,a844)),x42324),f169(x42321,x42322,x42325)))))),f775(f256(x42321),f775(f775(f9(x42321,f857(x42321,a844),a844),f334(x42321)),f775(f775(f104(f857(x42321,a844)),x42324),f169(x42321,x42322,x42325))))),f169(x42321,x42322,f78(x42321,f854(x42322),x42323,x42325,x42324))) % 186.05/186.62 [4304]E(f775(f145(f851(f856(x43041,x43042)),x43042,f115(f856(x43041,x43042)),f775(f775(f9(x43042,f857(f851(x43042),f851(f856(x43041,x43042))),f857(f851(x43042),f851(f856(x43041,x43042)))),f775(f775(f10(f857(f851(f856(x43041,x43042)),f851(f856(x43041,x43042))),f857(f857(f851(x43042),f851(f856(x43041,x43042))),f857(f851(x43042),f851(f856(x43041,x43042)))),x43042),f10(f851(f856(x43041,x43042)),f851(f856(x43041,x43042)),f851(x43042))),f775(f775(f10(f856(x43041,x43042),f857(f851(f856(x43041,x43042)),f851(f856(x43041,x43042))),x43042),f140(f856(x43041,x43042))),f775(f241(x43041,x43042),x43043)))),f775(f167(x43041,x43042),x43044))),x43045),f775(f775(f167(x43041,x43042),f775(f775(f140(x43041),x43043),x43044)),x43045)) % 186.05/186.62 [3789]E(f775(f775(f148(x37891,f775(f775(f148(x37891,x37892),x37893),x37894)),x37893),x37895),f775(f775(f148(x37891,x37892),x37893),x37895)) % 186.05/186.62 [3837]E(f775(f259(x38371,x38372),f775(f775(f302(f856(x38371,x38372)),f775(f775(f241(x38371,x38372),x38373),x38374)),x38375)),f775(f775(f302(x38372),x38374),f775(f259(x38371,x38372),x38375))) % 186.05/186.62 [3838]E(f775(f261(x38381,x38382),f775(f775(f302(f856(x38381,x38382)),f775(f775(f241(x38381,x38382),x38383),x38384)),x38385)),f775(f775(f302(x38381),x38383),f775(f261(x38381,x38382),x38385))) % 186.05/186.62 [3886]E(f121(x38861,x38862,f775(x38863,x38864),f775(f775(f9(x38861,a101,f852(f854(x38862))),x38865),x38864)),f775(f190(x38861,x38862,x38863,x38865),x38864)) % 186.05/186.62 [3915]E(f775(f775(f3(f857(f856(x39151,x39152),a844)),f775(f775(f248(x39151,x39152),x39153),x39154)),f775(f775(f248(x39151,x39152),x39155),x39154)),f775(f775(f248(x39151,x39152),f775(f775(f3(f857(x39151,a844)),x39153),x39155)),x39154)) % 186.05/186.62 [3916]E(f775(f775(f103(f857(f856(x39161,x39162),a844)),f775(f775(f248(x39161,x39162),x39163),x39164)),f775(f775(f248(x39161,x39162),x39165),x39164)),f775(f775(f248(x39161,x39162),f775(f775(f103(f857(x39161,a844)),x39163),x39165)),x39164)) % 186.05/186.62 [3917]E(f775(f775(f104(f857(f856(x39171,x39172),a844)),f775(f775(f248(x39171,x39172),x39173),x39174)),f775(f775(f248(x39171,x39172),x39175),x39174)),f775(f775(f248(x39171,x39172),f775(f775(f104(f857(x39171,a844)),x39173),x39175)),x39174)) % 186.05/186.62 [3980]E(f775(f775(f103(f857(x39801,a844)),f775(f775(f46(x39802,f857(x39801,a844)),x39803),x39804)),f775(f775(f46(x39802,f857(x39801,a844)),x39805),x39804)),f775(f775(f46(x39802,f857(x39801,a844)),f775(f775(f103(f857(x39802,a844)),x39803),x39805)),x39804)) % 186.05/186.62 [3981]E(f775(f775(f104(f857(x39811,a844)),f775(f775(f47(x39812,f857(x39811,a844)),x39813),x39814)),f775(f775(f47(x39812,f857(x39811,a844)),x39815),x39814)),f775(f775(f47(x39812,f857(x39811,a844)),f775(f775(f103(f857(x39812,a844)),x39813),x39815)),x39814)) % 186.05/186.62 [3995]E(f775(f775(f46(x39951,f857(x39952,a844)),x39953),f775(f775(f10(f857(x39952,a844),f857(x39952,a844),x39951),f775(f3(f857(x39952,a844)),x39954)),x39955)),f775(f775(f3(f857(x39952,a844)),x39954),f775(f775(f47(x39951,f857(x39952,a844)),x39953),x39955))) % 186.05/186.62 [3996]E(f775(f775(f46(x39961,f857(x39962,a844)),x39963),f775(f775(f10(f857(x39962,a844),f857(x39962,a844),x39961),f775(f104(f857(x39962,a844)),x39964)),x39965)),f775(f775(f104(f857(x39962,a844)),x39964),f775(f775(f46(x39961,f857(x39962,a844)),x39963),x39965))) % 186.05/186.62 [3997]E(f775(f775(f47(x39971,f857(x39972,a844)),x39973),f775(f775(f10(f857(x39972,a844),f857(x39972,a844),x39971),f775(f103(f857(x39972,a844)),x39974)),x39975)),f775(f775(f103(f857(x39972,a844)),x39974),f775(f775(f47(x39971,f857(x39972,a844)),x39973),x39975))) % 186.05/186.62 [4056]E(f175(f851(x40561),f775(f775(f140(x40561),x40562),x40563),f775(f775(f10(f851(x40561),f851(x40561),a850),f775(f140(x40561),x40564)),f775(f775(f9(a850,x40561,f851(x40561)),f148(x40561,x40563)),x40562)),x40565),f775(f775(f148(x40561,f775(f775(f140(x40561),x40564),x40563)),x40565),x40562)) % 186.05/186.62 [4060]E(f775(f775(f46(x40601,f857(f856(x40602,x40603),a844)),x40604),f775(f775(f10(f857(f856(x40603,x40602),a844),f857(f856(x40602,x40603),a844),x40601),f278(x40603,x40602)),x40605)),f775(f278(x40603,x40602),f775(f775(f46(x40601,f857(f856(x40603,x40602),a844)),x40604),x40605))) % 186.05/186.62 [4061]E(f775(f775(f47(x40611,f857(f856(x40612,x40613),a844)),x40614),f775(f775(f10(f857(f856(x40613,x40612),a844),f857(f856(x40612,x40613),a844),x40611),f278(x40613,x40612)),x40615)),f775(f278(x40613,x40612),f775(f775(f47(x40611,f857(f856(x40613,x40612),a844)),x40614),x40615))) % 186.05/186.62 [4114]E(f169(x41141,x41142,f775(f775(f20(x41141,f854(x41143),f854(x41142)),f775(f775(f10(f857(x41143,x41142),f857(f854(x41143),f854(x41142)),x41141),f196(x41143,x41142)),x41144)),x41145)),f169(x41141,x41143,x41145)) % 186.05/186.62 [4167]P1(f775(f775(f232(f857(x41671,a844)),f775(f775(f3(f857(x41671,a844)),f775(f303(x41672,x41671,x41673),x41674)),f775(f303(x41672,x41671,x41673),x41675))),f775(f303(x41672,x41671,x41673),f775(f775(f3(f857(x41672,a844)),x41674),x41675)))) % 186.05/186.62 [4308]E(f775(f145(f851(f856(x43081,x43082)),x43081,f115(f856(x43081,x43082)),f775(f775(f9(x43081,f857(f851(x43081),f851(f856(x43081,x43082))),f857(f851(x43081),f851(f856(x43081,x43082)))),f775(f775(f10(f857(f851(f856(x43081,x43082)),f851(f856(x43081,x43082))),f857(f857(f851(x43081),f851(f856(x43081,x43082))),f857(f851(x43081),f851(f856(x43081,x43082)))),x43081),f10(f851(f856(x43081,x43082)),f851(f856(x43081,x43082)),f851(x43081))),f775(f775(f10(f856(x43081,x43082),f857(f851(f856(x43081,x43082)),f851(f856(x43081,x43082))),x43081),f140(f856(x43081,x43082))),f775(f775(f9(x43081,x43082,f856(x43081,x43082)),f241(x43081,x43082)),x43083)))),f775(f775(f9(f851(x43081),f851(x43082),f851(f856(x43081,x43082))),f167(x43081,x43082)),x43084))),x43085),f775(f775(f167(x43081,x43082),x43085),f775(f775(f140(x43082),x43083),x43084))) % 186.05/186.62 [4325]E(f775(f132(f857(x43251,f854(x43252)),f856(x43251,x43252),f775(f775(f10(f857(x43251,f857(x43252,f857(x43251,f854(x43252)))),f857(f856(x43251,x43252),f857(x43251,f854(x43252))),f857(x43251,f854(x43252))),f251(x43251,x43252,f857(x43251,f854(x43252)))),f775(f775(f9(f857(x43251,f854(x43252)),f857(x43252,f854(x43252)),f857(x43251,f857(x43252,f857(x43251,f854(x43252))))),f775(f775(f10(f857(x43251,f857(f857(x43252,f854(x43252)),f857(x43252,f857(x43251,f854(x43252))))),f857(f857(x43252,f854(x43252)),f857(x43251,f857(x43252,f857(x43251,f854(x43252))))),f857(x43251,f854(x43252))),f9(x43251,f857(x43252,f854(x43252)),f857(x43252,f857(x43251,f854(x43252))))),f775(f775(f10(f857(x43251,f857(f854(x43252),f857(x43251,f854(x43252)))),f857(x43251,f857(f857(x43252,f854(x43252)),f857(x43252,f857(x43251,f854(x43252))))),f857(x43251,f854(x43252))),f775(f10(f857(f854(x43252),f857(x43251,f854(x43252))),f857(f857(x43252,f854(x43252)),f857(x43252,f857(x43251,f854(x43252)))),x43251),f10(f854(x43252),f857(x43251,f854(x43252)),x43252))),f74(x43251,f854(x43252))))),f227(x43252))),x43253),f775(f775(f167(x43251,x43252),x43254),x43255)),f170(x43251,x43252,x43253,f166(x43251,x43252,f775(f142(f856(x43251,x43252)),f775(f775(f167(x43251,x43252),x43254),x43255))))) % 186.05/186.62 [4021]E(f775(f775(f103(f857(x40211,a844)),f775(f277(x40212,x40211,x40213),x40214)),f775(f277(x40212,x40211,x40215),x40214)),f775(f277(x40212,x40211,f775(f775(f103(f857(f856(x40212,x40211),a844)),x40213),x40215)),x40214)) % 186.05/186.62 [4063]E(f775(f775(f125(f856(x40631,x40632)),f775(f775(f167(x40631,x40632),x40633),f775(f775(f159(x40632),f775(f181(f851(x40631)),x40633)),x40634))),f775(f775(f167(x40631,x40632),x40635),f775(f775(f128(x40632),f775(f181(f851(x40631)),x40633)),x40634))),f775(f775(f167(x40631,x40632),f775(f775(f125(x40631),x40633),x40635)),x40634)) % 186.05/186.62 [4092]E(f169(x40921,x40922,f170(x40921,x40922,x40923,f166(x40921,x40922,f775(f142(f856(x40921,x40922)),f775(f775(f167(x40921,x40922),x40924),x40925))))),f775(f775(f103(f857(x40921,a844)),f775(f158(x40921),f775(f775(f159(x40921),f775(f181(f851(x40922)),x40925)),x40924))),f169(x40921,x40922,x40923))) % 186.05/186.62 [4170]E(f775(f775(f248(x41701,x41702),x41703),f775(f775(f20(x41701,f857(x41702,a844),f857(x41702,a844)),f775(f775(f10(f857(x41702,a844),f857(f857(x41702,a844),f857(x41702,a844)),x41701),f3(f857(x41702,a844))),x41704)),x41705)),f775(f775(f3(f857(f856(x41701,x41702),a844)),f775(f775(f248(x41701,x41702),x41703),x41704)),f775(f775(f248(x41701,x41702),x41703),x41705))) % 186.05/186.62 [4171]E(f775(f775(f248(x41711,x41712),x41713),f775(f775(f20(x41711,f857(x41712,a844),f857(x41712,a844)),f775(f775(f10(f857(x41712,a844),f857(f857(x41712,a844),f857(x41712,a844)),x41711),f103(f857(x41712,a844))),x41714)),x41715)),f775(f775(f103(f857(f856(x41711,x41712),a844)),f775(f775(f248(x41711,x41712),x41713),x41714)),f775(f775(f248(x41711,x41712),x41713),x41715))) % 186.05/186.62 [4172]E(f775(f775(f248(x41721,x41722),x41723),f775(f775(f20(x41721,f857(x41722,a844),f857(x41722,a844)),f775(f775(f10(f857(x41722,a844),f857(f857(x41722,a844),f857(x41722,a844)),x41721),f104(f857(x41722,a844))),x41724)),x41725)),f775(f775(f104(f857(f856(x41721,x41722),a844)),f775(f775(f248(x41721,x41722),x41723),x41724)),f775(f775(f248(x41721,x41722),x41723),x41725))) % 186.05/186.62 [4176]E(f775(f775(f46(x41761,f857(x41762,a844)),x41763),f775(f775(f9(x41761,f857(x41762,a844),f857(x41762,a844)),f775(f775(f10(f857(x41762,a844),f857(f857(x41762,a844),f857(x41762,a844)),x41761),f3(f857(x41762,a844))),x41764)),x41765)),f775(f775(f3(f857(x41762,a844)),f775(f775(f46(x41761,f857(x41762,a844)),x41763),x41764)),x41765)) % 186.05/186.62 [4177]E(f775(f775(f46(x41771,f857(x41772,a844)),x41773),f775(f775(f9(x41771,f857(x41772,a844),f857(x41772,a844)),f775(f775(f10(f857(x41772,a844),f857(f857(x41772,a844),f857(x41772,a844)),x41771),f104(f857(x41772,a844))),x41774)),x41775)),f775(f775(f104(f857(x41772,a844)),f775(f775(f46(x41771,f857(x41772,a844)),x41773),x41774)),x41775)) % 186.05/186.62 [4178]E(f775(f775(f47(x41781,f857(x41782,a844)),x41783),f775(f775(f9(x41781,f857(x41782,a844),f857(x41782,a844)),f775(f775(f10(f857(x41782,a844),f857(f857(x41782,a844),f857(x41782,a844)),x41781),f103(f857(x41782,a844))),x41784)),x41785)),f775(f775(f103(f857(x41782,a844)),f775(f775(f47(x41781,f857(x41782,a844)),x41783),x41784)),x41785)) % 186.05/186.62 [4182]E(f775(f775(f46(x41821,f857(x41822,a844)),x41823),f775(f775(f20(x41821,f857(x41822,a844),f857(x41822,a844)),f775(f775(f10(f857(x41822,a844),f857(f857(x41822,a844),f857(x41822,a844)),x41821),f103(f857(x41822,a844))),x41824)),x41825)),f775(f775(f103(f857(x41822,a844)),f775(f775(f46(x41821,f857(x41822,a844)),x41823),x41824)),f775(f775(f46(x41821,f857(x41822,a844)),x41823),x41825))) % 186.05/186.62 [4183]E(f775(f775(f47(x41831,f857(x41832,a844)),x41833),f775(f775(f20(x41831,f857(x41832,a844),f857(x41832,a844)),f775(f775(f10(f857(x41832,a844),f857(f857(x41832,a844),f857(x41832,a844)),x41831),f104(f857(x41832,a844))),x41834)),x41835)),f775(f775(f104(f857(x41832,a844)),f775(f775(f47(x41831,f857(x41832,a844)),x41833),x41834)),f775(f775(f47(x41831,f857(x41832,a844)),x41833),x41835))) % 186.05/186.62 [4195]E(f775(f775(f46(x41951,f857(x41952,a844)),x41953),f775(f775(f20(x41951,f857(x41952,a844),f857(x41952,a844)),f775(f775(f10(f857(x41952,a844),f857(f857(x41952,a844),f857(x41952,a844)),x41951),f103(f857(x41952,a844))),x41954)),x41955)),f775(f775(f103(f857(x41952,a844)),f44(f857(x41952,a844),f775(f303(x41951,f857(x41952,a844),x41954),x41953))),f44(f857(x41952,a844),f775(f303(x41951,f857(x41952,a844),x41955),x41953)))) % 186.05/186.62 [4196]E(f775(f775(f47(x41961,f857(x41962,a844)),x41963),f775(f775(f20(x41961,f857(x41962,a844),f857(x41962,a844)),f775(f775(f10(f857(x41962,a844),f857(f857(x41962,a844),f857(x41962,a844)),x41961),f104(f857(x41962,a844))),x41964)),x41965)),f775(f775(f104(f857(x41962,a844)),f45(f857(x41962,a844),f775(f303(x41961,f857(x41962,a844),x41964),x41963))),f45(f857(x41962,a844),f775(f303(x41961,f857(x41962,a844),x41965),x41963)))) % 186.05/186.62 [4104]E(f775(f775(f125(f856(x41041,x41042)),f775(f775(f167(x41041,x41042),f775(f775(f159(x41041),f775(f181(f851(x41042)),x41043)),x41044)),x41043)),f775(f775(f167(x41041,x41042),f775(f775(f128(x41041),f775(f181(f851(x41042)),x41043)),x41044)),x41045)),f775(f775(f167(x41041,x41042),x41044),f775(f775(f125(x41042),x41043),x41045))) % 186.05/186.62 [4221]E(f87(x42211,f775(f775(f20(x42211,a844,a844),f775(f775(f10(a844,f857(a844,a844),x42211),a331),f775(f775(f9(x42211,f857(x42211,a844),a844),f334(x42211)),x42212))),f775(f775(f9(x42211,x42213,a844),f775(f775(f10(x42213,f857(x42213,a844),x42211),a330),x42214)),x42215))),f775(f79(x42211,x42213,x42212,x42214),x42215)) % 186.05/186.62 [4271]E(f775(f775(f88(a1,x42711),f775(f106(a1),f775(f775(f82(a1),x42712),a99))),f775(f775(f20(a1,x42711,x42711),f775(f775(f9(a1,x42711,f857(x42711,x42711)),f775(f775(f10(a844,f857(x42711,f857(x42711,x42711)),a1),f98(x42711)),a186)),f175(x42711,x42713,x42714,x42715))),f775(f775(f10(a850,x42711,a1),x42714),f775(f775(f9(a1,a850,a850),f775(f775(f10(a850,f857(a850,a850),a1),f82(a850)),a107)),x42715)))),f175(x42711,x42713,x42714,f775(f775(f82(a850),f775(f106(a850),x42712)),x42715))) % 186.05/186.62 [4305]E(f166(x43051,x43052,f775(f775(f143(f856(x43051,x43053),f856(x43051,x43052)),f775(f251(x43051,x43053,f856(x43051,x43052)),f775(f775(f9(x43051,f857(x43053,x43052),f857(x43053,f856(x43051,x43052))),f775(f775(f10(f857(x43052,f856(x43051,x43052)),f857(f857(x43053,x43052),f857(x43053,f856(x43051,x43052))),x43051),f10(x43052,f856(x43051,x43052),x43053)),f241(x43051,x43052))),x43054))),x43055)),f775(f75(f854(x43053),f854(x43052),x43051,f775(f196(x43053,x43052),x43054)),f166(x43051,x43053,x43055))) % 186.05/186.62 [4264]E(f169(x42641,x42642,f775(f775(f20(x42641,f854(x42642),f854(x42642)),f775(f775(f20(x42641,f854(x42642),f857(f854(x42642),f854(x42642))),f775(f775(f10(a844,f857(f854(x42642),f857(f854(x42642),f854(x42642))),x42641),f98(f854(x42642))),x42643)),x42644)),x42645)),f775(f775(f103(f857(x42641,a844)),f775(f775(f104(f857(x42641,a844)),f169(x42641,x42642,x42644)),f775(f256(x42641),x42643))),f775(f775(f104(f857(x42641,a844)),f169(x42641,x42642,x42645)),f775(f256(x42641),f775(f775(f10(a844,a844,x42641),a328),x42643))))) % 186.05/186.62 [4303]E(f775(f775(f88(a1,x43031),f775(f106(a1),f775(f775(f82(a1),x43032),a99))),f775(f775(f20(a1,x43031,x43031),f775(f775(f9(a1,x43031,f857(x43031,x43031)),f775(f775(f10(a844,f857(x43031,f857(x43031,x43031)),a1),f98(x43031)),a186)),f775(f174(x43031,x43033,x43034),x43035))),f775(f775(f20(a1,x43031,x43031),f775(f775(f10(a850,f857(x43031,x43031),a1),x43034),f775(f775(f9(a1,a850,a850),f775(f775(f10(a850,f857(a850,a850),a1),f82(a850)),a107)),x43035))),f775(f775(f10(a850,x43031,a1),f174(x43031,x43033,x43034)),f775(f775(f9(a1,a850,a850),f775(f775(f10(a850,f857(a850,a850),a1),f82(a850)),a107)),x43035))))),f775(f174(x43031,x43033,x43034),f775(f775(f82(a850),f775(f106(a850),x43032)),x43035))) % 186.05/186.62 [4352]E(f775(f256(f856(x43521,x43522)),f775(f251(x43521,x43522,a844),f775(f775(f10(f857(x43522,f857(x43523,a844)),f857(x43522,a844),x43521),f775(f10(f857(x43523,a844),a844,x43522),f89(x43523))),f775(f775(f9(x43521,f857(x43522,f857(x43523,a844)),f857(x43522,f857(x43523,a844))),f775(f775(f10(f857(f857(x43523,a844),f857(x43523,a844)),f857(f857(x43522,f857(x43523,a844)),f857(x43522,f857(x43523,a844))),x43521),f10(f857(x43523,a844),f857(x43523,a844),x43522)),f775(f775(f10(f857(x43523,f857(a844,a844)),f857(f857(x43523,a844),f857(x43523,a844)),x43521),f20(x43523,a844,a844)),f775(f775(f10(f857(x43523,a844),f857(x43523,f857(a844,a844)),x43521),f775(f10(a844,f857(a844,a844),x43523),a331)),f775(f775(f9(x43521,f857(f856(x43521,x43523),a844),f857(x43523,a844)),f775(f775(f10(f857(x43523,f857(f857(f856(x43521,x43523),a844),a844)),f857(f857(f856(x43521,x43523),a844),f857(x43523,a844)),x43521),f9(x43523,f857(f856(x43521,x43523),a844),a844)),f775(f775(f10(f857(x43523,f856(x43521,x43523)),f857(x43523,f857(f857(f856(x43521,x43523),a844),a844)),x43521),f775(f10(f856(x43521,x43523),f857(f857(f856(x43521,x43523),a844),a844),x43523),f334(f856(x43521,x43523)))),f241(x43521,x43523)))),x43524))))),f775(f775(f9(x43522,f857(f856(x43523,x43522),a844),f857(x43523,a844)),f775(f775(f10(f857(x43523,f857(f857(f856(x43523,x43522),a844),a844)),f857(f857(f856(x43523,x43522),a844),f857(x43523,a844)),x43522),f9(x43523,f857(f856(x43523,x43522),a844),a844)),f775(f775(f10(f857(x43523,f856(x43523,x43522)),f857(x43523,f857(f857(f856(x43523,x43522),a844),a844)),x43522),f775(f10(f856(x43523,x43522),f857(f857(f856(x43523,x43522),a844),a844),x43523),f334(f856(x43523,x43522)))),f775(f9(x43523,x43522,f856(x43523,x43522)),f241(x43523,x43522))))),x43525))))),f775(f775(f281(x43521,x43523,x43522),x43524),x43525)) % 186.05/186.62 [4453]~E(f32(x44531,x44532,x44533),f33(x44534,x44535,x44536)) % 186.05/186.62 [4456]~E(f31(x44561,x44562,x44563),f33(x44564,x44565,x44566)) % 186.05/186.62 [4457]~E(f31(x44571,x44572,x44573),f32(x44574,x44575,x44576)) % 186.05/186.62 [3947]E(f218(x39471,x39472,x39473,x39474,f215(x39471,x39472,x39475,x39476)),f775(f775(x39474,x39475),x39476)) % 186.05/186.62 [3948]E(f219(x39481,x39482,x39483,x39484,f215(x39481,x39482,x39485,x39486)),f775(f775(x39484,x39485),x39486)) % 186.05/186.62 [4211]E(f775(f75(f856(x42111,x42112),x42112,f856(x42113,x42114),f250(x42111,x42112)),f252(x42113,x42111,x42114,x42112,x42115,x42116)),f775(f75(x42114,x42112,f856(x42113,x42114),x42116),f250(x42113,x42114))) % 186.05/186.62 [4212]E(f775(f75(f856(x42121,x42122),x42121,f856(x42123,x42124),f240(x42121,x42122)),f252(x42123,x42121,x42124,x42122,x42125,x42126)),f775(f75(x42123,x42121,f856(x42123,x42124),x42125),f240(x42123,x42124))) % 186.05/186.62 [3813]E(f775(f775(f75(x38131,x38132,x38133,x38134),x38135),x38136),f775(x38134,f775(x38135,x38136))) % 186.05/186.62 [4010]E(f220(x40101,x40102,x40103,x40104,f215(x40101,x40102,x40105,x40106)),f775(f775(f82(a850),f775(f775(f82(a850),f775(x40103,x40105)),f775(x40104,x40106))),f775(a114,f2(a850)))) % 186.05/186.62 [4032]E(f775(f319(x40321,x40322,x40323,x40324,x40325),f775(f304(x40321,x40323),x40326)),f775(x40324,x40326)) % 186.05/186.62 [4033]E(f775(f319(x40331,x40332,x40333,x40334,x40335),f775(f313(x40333,x40331),x40336)),f775(x40335,x40336)) % 186.05/186.62 [4128]E(f320(x41281,x41282,x41283,x41284,x41285,f775(f304(x41281,x41283),x41286)),f775(x41284,x41286)) % 186.05/186.62 [4129]E(f320(x41291,x41292,x41293,x41294,x41295,f775(f313(x41293,x41291),x41296)),f775(x41295,x41296)) % 186.05/186.62 [3610]E(f775(f775(f251(x36101,x36102,x36103),x36104),f775(f775(f241(x36101,x36102),x36105),x36106)),f775(f775(x36104,x36105),x36106)) % 186.05/186.62 [3673]E(f775(f775(f775(f10(x36731,x36732,x36733),x36734),x36735),x36736),f775(x36734,f775(x36735,x36736))) % 186.05/186.62 [3674]E(f775(f775(f775(f9(x36741,x36742,x36743),x36744),x36745),x36746),f775(f775(x36744,x36746),x36745)) % 186.05/186.62 [3690]E(f775(f775(f775(f20(x36901,x36902,x36903),x36904),x36905),x36906),f775(f775(x36904,x36906),f775(x36905,x36906))) % 186.05/186.62 [3714]E(f775(f145(x37141,x37142,x37143,x37144),f775(f775(f140(x37142),x37145),x37146)),f775(f775(x37144,x37145),x37146)) % 186.05/186.62 [3816]E(f775(f775(f140(f856(x38161,x38162)),f775(f775(f241(x38161,x38162),x38163),x38164)),f775(f775(f167(x38161,x38162),x38165),x38166)),f775(f775(f167(x38161,x38162),f775(f775(f140(x38161),x38163),x38165)),f775(f775(f140(x38162),x38164),x38166))) % 186.05/186.62 [3818]E(f775(f775(f143(x38181,x38182),x38183),f775(f775(f148(x38181,x38184),x38185),x38186)),f775(f775(f148(x38182,f775(f775(f143(x38181,x38182),x38183),x38184)),x38185),f775(x38183,x38186))) % 186.05/186.62 [3841]E(f775(f775(f249(x38411,x38412,x38413,x38414),x38415),x38416),f775(x38414,f775(f775(f241(x38411,x38412),x38415),x38416))) % 186.05/186.62 [3858]E(f775(f132(x38581,x38582,x38583,x38584),f775(f775(f140(x38582),x38585),x38586)),f775(f132(x38581,x38582,x38583,f775(f775(x38583,x38584),x38585)),x38586)) % 186.05/186.62 [3887]E(f254(x38871,x38872,x38873,x38874,f775(f775(f241(x38871,x38872),x38875),x38876)),f775(f775(x38874,x38875),x38876)) % 186.05/186.62 [3973]E(f775(f775(f46(x39731,f857(x39732,a844)),x39733),f775(f75(x39734,f857(x39732,a844),x39731,x39735),x39736)),f775(f775(f46(x39734,f857(x39732,a844)),f775(f303(x39731,x39734,x39736),x39733)),x39735)) % 186.05/186.62 [4024]E(f775(f775(f143(x40241,x40242),x40243),f775(f775(f143(x40244,x40241),x40245),x40246)),f775(f775(f143(x40244,x40242),f775(f75(x40241,x40242,x40244,x40243),x40245)),x40246)) % 186.05/186.62 [4026]E(f775(f775(f196(x40261,x40262),x40263),f775(f775(f196(x40264,x40261),x40265),x40266)),f775(f775(f196(x40264,x40262),f775(f75(x40261,x40262,x40264,x40263),x40265)),x40266)) % 186.05/186.62 [4030]E(f775(f303(x40301,x40302,f775(f75(x40303,x40302,x40301,x40304),x40305)),x40306),f775(f303(x40303,x40302,x40304),f775(f303(x40301,x40303,x40305),x40306))) % 186.05/186.62 [4031]E(f775(f305(x40311,x40312,f775(f75(x40313,x40312,x40311,x40314),x40315)),x40316),f775(f305(x40311,x40313,x40315),f775(f305(x40313,x40312,x40314),x40316))) % 186.05/186.62 [4062]E(f170(x40621,x40622,x40623,f775(f775(f775(f74(x40621,f854(x40622)),x40624),x40625),f775(f227(x40622),x40626))),f775(f775(f775(f74(x40621,f854(x40622)),f170(x40621,x40622,x40623,x40624)),x40625),f775(f227(x40622),x40626))) % 186.05/186.62 [4064]E(f775(f132(x40641,x40642,x40643,f775(f132(x40641,x40642,x40643,x40644),x40645)),x40646),f775(f132(x40641,x40642,x40643,x40644),f775(f775(f125(x40642),x40645),x40646))) % 186.05/186.62 [4201]E(f775(f252(x42011,x42011,x42012,x42013,f39(x42011),x42014),f775(f775(f241(x42011,x42012),x42015),x42016)),f775(f775(f241(x42011,x42013),x42015),f775(x42014,x42016))) % 186.05/186.62 [4202]E(f775(f252(x42021,x42022,x42023,x42023,x42024,f39(x42023)),f775(f775(f241(x42021,x42023),x42025),x42026)),f775(f775(f241(x42022,x42023),f775(x42024,x42025)),x42026)) % 186.05/186.62 [4287]E(f775(f775(f143(f856(x42871,x42872),f856(x42871,x42873)),f775(f251(x42871,x42872,f856(x42871,x42873)),f775(f775(f9(x42871,f857(x42872,x42873),f857(x42872,f856(x42871,x42873))),f775(f775(f10(f857(x42873,f856(x42871,x42873)),f857(f857(x42872,x42873),f857(x42872,f856(x42871,x42873))),x42871),f10(x42873,f856(x42871,x42873),x42872)),f241(x42871,x42873))),x42874))),f775(f775(f167(x42871,x42872),x42875),x42876)),f775(f775(f167(x42871,x42873),x42875),f775(f775(f143(x42872,x42873),x42874),x42876))) % 186.05/186.62 [3678]E(f96(x36781,x36782,x36783,f775(f775(f775(f93(x36781),x36784),x36785),x36786)),f775(f775(f775(x36783,x36784),x36785),x36786)) % 186.05/186.62 [3679]E(f97(x36791,x36792,x36793,f775(f775(f775(f93(x36791),x36794),x36795),x36796)),f775(f775(f775(x36793,x36794),x36795),x36796)) % 186.05/186.62 [3869]E(f775(f775(f75(x38691,x38692,x38693,f775(f18(x38692,x38691),x38694)),x38695),x38696),x38694) % 186.05/186.62 [3905]E(f775(f303(x39051,x39052,x39053),f775(f303(x39054,x39051,x39055),x39056)),f775(f303(x39054,x39052,f775(f775(f10(x39051,x39052,x39054),x39053),x39055)),x39056)) % 186.05/186.62 [3911]E(f775(f775(f46(x39111,f857(x39112,a844)),f775(f303(x39113,x39111,x39114),x39115)),x39116),f775(f775(f46(x39113,f857(x39112,a844)),x39115),f775(f775(f10(x39111,f857(x39112,a844),x39113),x39116),x39114))) % 186.05/186.62 [3912]E(f775(f775(f47(x39121,f857(x39122,a844)),f775(f303(x39123,x39121,x39124),x39125)),x39126),f775(f775(f47(x39123,f857(x39122,a844)),x39125),f775(f775(f10(x39121,f857(x39122,a844),x39123),x39126),x39124))) % 186.05/186.62 [3913]E(f775(f775(f46(x39131,f857(x39132,a844)),x39133),f775(f775(f10(x39134,f857(x39132,a844),x39131),x39135),x39136)),f775(f775(f46(x39134,f857(x39132,a844)),f775(f303(x39131,x39134,x39136),x39133)),x39135)) % 186.05/186.62 [3914]E(f775(f775(f47(x39141,f857(x39142,a844)),x39143),f775(f775(f10(x39144,f857(x39142,a844),x39141),x39145),x39146)),f775(f775(f47(x39144,f857(x39142,a844)),f775(f303(x39141,x39144,x39146),x39143)),x39145)) % 186.05/186.62 [3975]E(f775(f775(f46(x39751,f857(x39752,a844)),x39753),f775(f775(f10(f857(x39754,a844),f857(x39752,a844),x39751),f303(x39754,x39752,x39755)),x39756)),f775(f303(x39754,x39752,x39755),f775(f775(f46(x39751,f857(x39754,a844)),x39753),x39756))) % 186.05/186.62 [3976]E(f775(f775(f46(x39761,f857(x39762,a844)),x39763),f775(f775(f10(f857(x39764,a844),f857(x39762,a844),x39761),f277(x39764,x39762,x39765)),x39766)),f775(f277(x39764,x39762,x39765),f775(f775(f46(x39761,f857(x39764,a844)),x39763),x39766))) % 186.05/186.62 [3977]E(f775(f775(f46(x39771,f857(x39772,a844)),x39773),f775(f775(f10(f857(x39774,a844),f857(x39772,a844),x39771),f305(x39772,x39774,x39775)),x39776)),f775(f305(x39772,x39774,x39775),f775(f775(f46(x39771,f857(x39774,a844)),x39773),x39776))) % 186.05/186.62 [3978]E(f775(f775(f47(x39781,f857(x39782,a844)),x39783),f775(f775(f10(f857(x39784,a844),f857(x39782,a844),x39781),f305(x39782,x39784,x39785)),x39786)),f775(f305(x39782,x39784,x39785),f775(f775(f47(x39781,f857(x39784,a844)),x39783),x39786))) % 186.05/186.62 [4069]E(f775(f132(x40691,x40692,f775(f9(x40692,x40691,x40691),x40693),x40694),f775(f142(x40692),f775(f775(f140(x40692),x40695),x40696))),f775(f775(x40693,x40695),f775(f132(x40691,x40692,f775(f9(x40692,x40691,x40691),x40693),x40694),f775(f142(x40692),x40696)))) % 186.05/186.62 [4130]E(f775(f775(f20(f856(x41301,x41302),x41302,x41303),f775(f775(f10(x41304,f857(x41302,x41303),f856(x41301,x41302)),x41305),f775(f775(f10(x41301,x41304,f856(x41301,x41302)),x41306),f240(x41301,x41302)))),f250(x41301,x41302)),f775(f251(x41301,x41302,x41303),f775(f775(f10(x41304,f857(x41302,x41303),x41301),x41305),x41306))) % 186.05/186.62 [4137]E(f775(f132(x41371,x41372,f775(f9(x41372,x41371,x41371),x41373),f775(f132(x41371,x41372,f775(f9(x41372,x41371,x41371),x41373),x41374),f775(f142(x41372),x41375))),f775(f142(x41372),x41376)),f775(f132(x41371,x41372,f775(f9(x41372,x41371,x41371),x41373),x41374),f775(f142(x41372),f775(f775(f125(x41372),x41376),x41375)))) % 186.05/186.62 [4139]E(f775(f775(f143(f856(x41391,x41392),f856(x41393,x41392)),f775(f251(x41391,x41392,f856(x41393,x41392)),f775(f775(f10(x41393,f857(x41392,f856(x41393,x41392)),x41391),f241(x41393,x41392)),x41394))),f775(f775(f167(x41391,x41392),x41395),x41396)),f775(f775(f167(x41393,x41392),f775(f775(f143(x41391,x41393),x41394),x41395)),x41396)) % 186.05/186.62 [4185]P1(f775(f775(f232(f857(x41851,a844)),f775(f277(x41852,x41851,x41853),f775(f775(f47(x41854,f857(x41852,a844)),x41855),x41856))),f775(f775(f47(x41854,f857(x41851,a844)),x41855),f775(f775(f10(f857(x41852,a844),f857(x41851,a844),x41854),f277(x41852,x41851,x41853)),x41856)))) % 186.05/186.62 [3988]E(f775(f775(f167(x39881,x39882),f775(f775(f148(x39881,x39883),x39884),f775(f240(x39881,x39882),x39885))),f775(f775(f148(x39882,x39886),x39884),f775(f250(x39881,x39882),x39885))),f775(f775(f148(f856(x39881,x39882),f775(f775(f167(x39881,x39882),x39883),x39886)),x39884),x39885)) % 186.05/186.62 [4051]E(f775(f775(f103(f857(f856(x40511,x40512),a844)),f775(f775(f281(x40511,x40513,x40512),x40514),x40515)),f775(f775(f281(x40511,x40513,x40512),x40514),x40516)),f775(f775(f281(x40511,x40513,x40512),x40514),f775(f775(f103(f857(f856(x40513,x40512),a844)),x40515),x40516))) % 186.05/186.62 [4151]E(f775(f775(f302(f856(x41511,x41512)),f775(f775(f241(x41511,x41512),x41513),x41514)),f775(f775(f103(f857(f856(x41511,x41512),a844)),f775(f775(f248(x41511,x41512),x41515),f775(f18(f857(x41512,a844),x41511),f775(f775(f302(x41512),x41514),x41516)))),f775(f775(f248(x41511,x41512),f775(f775(f302(x41511),x41513),x41515)),f775(f18(f857(x41512,a844),x41511),x41516)))),f775(f775(f248(x41511,x41512),f775(f775(f302(x41511),x41513),x41515)),f775(f18(f857(x41512,a844),x41511),f775(f775(f302(x41512),x41514),x41516)))) % 186.05/186.62 [4224]E(f775(f775(f104(f857(x42241,a844)),f775(f305(x42241,x42242,f775(f75(f856(x42242,x42243),x42242,x42241,f240(x42242,x42243)),x42244)),x42245)),f775(f305(x42241,x42243,f775(f75(f856(x42242,x42243),x42243,x42241,f250(x42242,x42243)),x42244)),x42246)),f775(f305(x42241,f856(x42242,x42243),x42244),f775(f775(f248(x42242,x42243),x42245),f775(f18(f857(x42243,a844),x42242),x42246)))) % 186.05/186.62 [3972]E(f775(f775(f775(f74(x39721,x39722),f775(f775(f775(f74(x39721,x39722),x39723),x39724),x39725)),x39724),x39726),f775(f775(f775(f74(x39721,x39722),x39723),x39724),x39726)) % 186.05/186.62 [4075]E(f775(f775(f103(f857(f856(x40751,x40752),a844)),f775(f775(f281(x40751,x40753,x40752),x40754),x40755)),f775(f775(f281(x40751,x40753,x40752),x40756),x40755)),f775(f775(f281(x40751,x40753,x40752),f775(f775(f103(f857(f856(x40751,x40753),a844)),x40754),x40756)),x40755)) % 186.05/186.62 [4209]E(f775(f775(f46(x42091,f857(x42092,a844)),x42093),f775(f775(f9(x42091,f857(x42094,f857(x42092,a844)),f857(x42092,a844)),f775(f775(f10(f857(x42094,a844),f857(f857(x42094,f857(x42092,a844)),f857(x42092,a844)),x42091),f46(x42094,f857(x42092,a844))),x42095)),x42096)),f775(f775(f46(x42094,f857(x42092,a844)),f775(f775(f46(x42091,f857(x42094,a844)),x42093),x42095)),x42096)) % 186.05/186.62 [4210]E(f775(f775(f47(x42101,f857(x42102,a844)),x42103),f775(f775(f9(x42101,f857(x42104,f857(x42102,a844)),f857(x42102,a844)),f775(f775(f10(f857(x42104,a844),f857(f857(x42104,f857(x42102,a844)),f857(x42102,a844)),x42101),f47(x42104,f857(x42102,a844))),x42105)),x42106)),f775(f775(f47(x42104,f857(x42102,a844)),f775(f775(f46(x42101,f857(x42104,a844)),x42103),x42105)),x42106)) % 186.05/186.62 [4259]E(f775(f251(x42591,x42592,f856(x42593,x42594)),f775(f775(f9(x42591,f857(x42592,x42594),f857(x42592,f856(x42593,x42594))),f775(f775(f10(f857(x42594,f856(x42593,x42594)),f857(f857(x42592,x42594),f857(x42592,f856(x42593,x42594))),x42591),f10(x42594,f856(x42593,x42594),x42592)),f775(f775(f10(x42593,f857(x42594,f856(x42593,x42594)),x42591),f241(x42593,x42594)),x42595))),x42596)),f252(x42591,x42593,x42592,x42594,x42595,x42596)) % 186.05/186.62 [4184]E(f775(f775(f775(f74(x41841,f854(x41842)),f172(x41841,x41842,x41843,f775(f775(f3(f857(x41841,a844)),x41844),f775(f775(f302(x41841),x41845),f180(f857(x41841,a844)))))),x41845),x41846),f775(f775(f775(f74(x41841,f854(x41842)),f172(x41841,x41842,x41843,x41844)),x41845),x41846)) % 186.05/186.62 [4282]E(f775(f303(x42821,x42822,f775(f775(f20(x42821,x42822,x42822),f775(f775(f20(x42821,x42822,f857(x42822,x42822)),f775(f775(f10(a844,f857(x42822,f857(x42822,x42822)),x42821),f98(x42822)),x42823)),x42824)),x42825)),x42826),f775(f775(f103(f857(x42822,a844)),f775(f303(x42821,x42822,x42824),f775(f775(f104(f857(x42821,a844)),x42826),f775(f256(x42821),x42823)))),f775(f303(x42821,x42822,x42825),f775(f775(f104(f857(x42821,a844)),x42826),f775(f256(x42821),f775(f775(f10(a844,a844,x42821),a328),x42823)))))) % 186.05/186.62 [4293]E(f775(f303(x42931,f856(x42932,x42933),f775(f775(f20(x42931,x42933,f856(x42932,x42933)),f775(f775(f10(x42932,f857(x42933,f856(x42932,x42933)),x42931),f241(x42932,x42933)),x42934)),x42935)),x42936),f775(f775(f248(x42932,x42933),f775(f303(x42931,x42932,x42934),x42936)),f775(f775(f10(f857(x42931,a844),f857(x42933,a844),x42932),f303(x42931,x42933,x42935)),f775(f775(f9(x42932,f857(x42931,a844),f857(x42931,a844)),f775(f775(f10(f857(x42931,a844),f857(f857(x42931,a844),f857(x42931,a844)),x42932),f104(f857(x42931,a844))),f775(f775(f10(f857(x42932,a844),f857(x42931,a844),x42932),f305(x42931,x42932,x42934)),f775(f775(f9(x42932,f857(x42932,a844),f857(x42932,a844)),f302(x42932)),f180(f857(x42932,a844)))))),x42936)))) % 186.05/186.62 [4242]E(f775(f250(x42421,x42422),f775(f252(x42423,x42421,x42424,x42422,x42425,x42426),x42427)),f775(x42426,f775(f250(x42423,x42424),x42427))) % 186.05/186.62 [4243]E(f775(f240(x42431,x42432),f775(f252(x42433,x42431,x42434,x42432,x42435,x42436),x42437)),f775(x42435,f775(f240(x42433,x42434),x42437))) % 186.05/186.62 [3949]E(f775(f775(f167(x39491,x39492),f775(f775(f148(x39491,x39493),x39494),x39495)),f775(f775(f148(x39492,x39496),x39494),x39497)),f775(f775(f148(f856(x39491,x39492),f775(f775(f167(x39491,x39492),x39493),x39496)),x39494),f775(f775(f241(x39491,x39492),x39495),x39497))) % 186.05/186.62 [4019]E(f775(f775(f775(f253(x40191,x40192,x40193,x40194),x40195),x40196),x40197),f775(f775(f251(x40192,x40193,x40194),x40196),f775(x40195,x40197))) % 186.05/186.62 [4029]E(f775(f775(f775(f253(x40291,x40292,x40293,x40294),x40295),x40296),x40297),f775(f775(x40296,f775(f240(x40292,x40293),f775(x40295,x40297))),f775(f250(x40292,x40293),f775(x40295,x40297)))) % 186.05/186.62 [4082]E(f775(f75(x40821,x40822,x40823,x40824),f775(f75(x40825,x40821,x40823,x40826),x40827)),f775(f75(x40825,x40822,x40823,f775(f75(x40821,x40822,x40825,x40824),x40826)),x40827)) % 186.05/186.62 [4146]E(f775(f75(f854(x41461),f854(x41462),x41463,f775(f196(x41461,x41462),x41464)),f775(f775(f775(f74(x41463,f854(x41461)),x41465),x41466),f775(f227(x41461),x41467))),f775(f775(f775(f74(x41463,f854(x41462)),f775(f75(f854(x41461),f854(x41462),x41463,f775(f196(x41461,x41462),x41464)),x41465)),x41466),f775(f227(x41462),f775(x41464,x41467)))) % 186.05/186.62 [4266]E(f775(f252(x42661,x42662,x42663,x42663,x42664,f39(x42663)),f775(f252(x42661,x42661,x42665,x42663,f39(x42661),x42666),x42667)),f775(f775(f241(x42662,x42663),f775(x42664,f775(f240(x42661,x42665),x42667))),f775(x42666,f775(f250(x42661,x42665),x42667)))) % 186.05/186.62 [4267]E(f775(f252(x42671,x42671,x42672,x42673,f39(x42671),x42674),f775(f252(x42675,x42671,x42672,x42672,x42676,f39(x42672)),x42677)),f775(f775(f241(x42671,x42673),f775(x42676,f775(f240(x42675,x42672),x42677))),f775(x42674,f775(f250(x42675,x42672),x42677)))) % 186.05/186.62 [4280]E(f775(f252(x42801,x42802,x42803,x42803,x42804,f39(x42803)),f775(f252(x42805,x42801,x42803,x42803,x42806,f39(x42803)),x42807)),f775(f252(x42805,x42802,x42803,x42803,f775(f75(x42801,x42802,x42805,x42804),x42806),f39(x42803)),x42807)) % 186.05/186.62 [4281]E(f775(f252(x42811,x42811,x42812,x42813,f39(x42811),x42814),f775(f252(x42811,x42811,x42815,x42812,f39(x42811),x42816),x42817)),f775(f252(x42811,x42811,x42815,x42813,f39(x42811),f775(f75(x42812,x42813,x42815,x42814),x42816)),x42817)) % 186.05/186.62 [4290]E(f775(f252(x42901,x42902,x42903,x42903,x42904,f39(x42903)),f775(f252(x42901,x42901,x42905,x42903,f39(x42901),x42906),x42907)),f775(f252(x42902,x42902,x42905,x42903,f39(x42902),x42906),f775(f252(x42901,x42902,x42905,x42905,x42904,f39(x42905)),x42907))) % 186.05/186.62 [3985]E(f775(f775(f281(x39851,x39852,x39853),f775(f775(f281(x39851,x39854,x39852),x39855),x39856)),x39857),f775(f775(f281(x39851,x39854,x39853),x39855),f775(f775(f281(x39854,x39852,x39853),x39856),x39857))) % 186.05/186.62 [4057]E(f775(f775(f251(x40571,x40572,x40573),f775(f75(x40574,f857(x40572,x40573),x40571,x40575),x40576)),x40577),f775(f775(x40575,f775(x40576,f775(f240(x40571,x40572),x40577))),f775(f250(x40571,x40572),x40577))) % 186.05/186.62 [4107]E(f775(f75(x41071,x41072,x41073,x41074),f775(f775(f775(f74(x41073,x41071),x41075),x41076),x41077)),f775(f775(f775(f74(x41073,x41072),f775(f75(x41071,x41072,x41073,x41074),x41075)),x41076),f775(x41074,x41077))) % 186.05/186.62 [4142]E(f775(f132(x41421,x41422,f775(f9(x41422,x41421,x41421),x41423),x41424),f775(f142(x41422),f775(f775(f143(x41425,x41422),x41426),x41427))),f775(f132(x41421,x41425,f775(f9(x41425,x41421,x41421),f775(f75(x41422,f857(x41421,x41421),x41425,x41423),x41426)),x41424),f775(f142(x41425),x41427))) % 186.05/186.62 [4147]E(f319(x41471,f854(x41472),x41473,f775(f75(f854(x41474),f854(x41472),x41471,f775(f196(x41474,x41472),x41475)),x41476),f775(f75(f854(x41474),f854(x41472),x41473,f775(f196(x41474,x41472),x41475)),x41477)),f775(f75(f854(x41474),f854(x41472),f858(x41471,x41473),f775(f196(x41474,x41472),x41475)),f319(x41471,f854(x41474),x41473,x41476,x41477))) % 186.05/186.62 [4083]E(f775(f775(f46(x40831,f857(f856(x40832,x40833),a844)),x40834),f775(f775(f10(f857(f856(x40835,x40833),a844),f857(f856(x40832,x40833),a844),x40831),f775(f281(x40832,x40835,x40833),x40836)),x40837)),f775(f775(f281(x40832,x40835,x40833),x40836),f775(f775(f46(x40831,f857(f856(x40835,x40833),a844)),x40834),x40837))) % 186.05/186.62 [4118]E(f170(x41181,x41182,f775(f775(f775(f74(x41181,f854(x41182)),x41183),x41184),f775(f227(x41182),x41185)),f166(x41181,x41182,f775(f142(f856(x41181,x41182)),f775(f775(f167(x41181,x41182),x41186),x41187)))),f170(x41181,x41182,x41183,f166(x41181,x41182,f775(f142(f856(x41181,x41182)),f775(f775(f167(x41181,x41182),f775(f775(f140(x41181),x41184),x41186)),f775(f775(f140(x41182),x41185),x41187)))))) % 186.05/186.62 [4229]E(f775(f775(f46(x42291,f857(f856(x42292,x42293),a844)),x42294),f775(f775(f9(x42291,f857(f856(x42295,x42293),a844),f857(f856(x42292,x42293),a844)),f775(f775(f10(f857(f856(x42292,x42295),a844),f857(f857(f856(x42295,x42293),a844),f857(f856(x42292,x42293),a844)),x42291),f281(x42292,x42295,x42293)),x42296)),x42297)),f775(f775(f281(x42292,x42295,x42293),f775(f775(f46(x42291,f857(f856(x42292,x42295),a844)),x42294),x42296)),x42297)) % 186.05/186.62 [4230]E(f775(f132(x42301,x42302,f775(f775(f9(x42301,f857(x42302,x42303),f857(x42302,x42301)),f775(f775(f10(f857(x42303,x42301),f857(f857(x42302,x42303),f857(x42302,x42301)),x42301),f10(x42303,x42301,x42302)),x42304)),x42305),x42306),x42307),f775(f132(x42301,x42303,x42304,x42306),f775(f775(f143(x42302,x42303),x42305),x42307))) % 186.05/186.62 [4291]E(f775(f775(f47(x42911,f857(x42912,a844)),x42913),f775(f775(f10(f857(x42914,f857(x42912,a844)),f857(x42912,a844),x42911),f775(f47(x42914,f857(x42912,a844)),x42915)),f775(f775(f9(x42911,f857(x42914,f857(x42912,a844)),f857(x42914,f857(x42912,a844))),f775(f775(f10(f857(f857(x42912,a844),f857(x42912,a844)),f857(f857(x42914,f857(x42912,a844)),f857(x42914,f857(x42912,a844))),x42911),f10(f857(x42912,a844),f857(x42912,a844),x42914)),f775(f775(f10(f857(x42912,a844),f857(f857(x42912,a844),f857(x42912,a844)),x42911),f103(f857(x42912,a844))),x42916))),x42917))),f775(f775(f103(f857(x42912,a844)),f775(f775(f47(x42911,f857(x42912,a844)),x42913),x42916)),f775(f775(f47(x42914,f857(x42912,a844)),x42915),x42917))) % 186.05/186.62 [4292]E(f775(f775(f46(x42921,f857(x42922,a844)),x42923),f775(f775(f10(f857(x42924,f857(x42922,a844)),f857(x42922,a844),x42921),f775(f46(x42924,f857(x42922,a844)),x42925)),f775(f775(f9(x42921,f857(x42924,f857(x42922,a844)),f857(x42924,f857(x42922,a844))),f775(f775(f10(f857(f857(x42922,a844),f857(x42922,a844)),f857(f857(x42924,f857(x42922,a844)),f857(x42924,f857(x42922,a844))),x42921),f10(f857(x42922,a844),f857(x42922,a844),x42924)),f775(f775(f10(f857(x42922,a844),f857(f857(x42922,a844),f857(x42922,a844)),x42921),f104(f857(x42922,a844))),x42926))),x42927))),f775(f775(f104(f857(x42922,a844)),f775(f775(f46(x42921,f857(x42922,a844)),x42923),x42926)),f775(f775(f46(x42924,f857(x42922,a844)),x42925),x42927))) % 186.05/186.62 [4285]E(f192(x42851,x42852,f775(f775(f775(x42853,x42854),x42855),x42856),f775(f775(f9(x42851,f856(a101,a101),f857(a101,f852(x42852))),f775(f775(f9(x42851,a101,f857(f856(a101,a101),f857(a101,f852(x42852)))),f775(f775(f9(x42851,a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(x42852))))),x42857),x42854)),x42855)),x42856)),f775(f775(f775(f204(x42851,x42852,x42853,x42857),x42854),x42855),x42856)) % 186.05/186.62 [4298]E(f193(x42981,x42982,f775(f775(f775(x42983,x42984),x42985),x42986),f775(f775(f9(x42981,f856(a101,a101),f857(a101,f852(x42982))),f775(f775(f9(x42981,a101,f857(f856(a101,a101),f857(a101,f852(x42982)))),f775(f775(f9(x42981,a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(x42982))))),x42987),x42984)),x42985)),x42986)),f206(x42981,x42982,x42983,x42987,x42984,x42985,x42986)) % 186.05/186.62 [4289]E(f190(x42891,x42892,f775(f775(f775(x42893,x42894),x42895),x42896),f775(f775(f9(x42891,f856(a101,a101),f857(a101,f852(f854(x42892)))),f775(f775(f9(x42891,a101,f857(f856(a101,a101),f857(a101,f852(f854(x42892))))),f775(f775(f9(x42891,a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(f854(x42892)))))),x42897),x42894)),x42895)),x42896)),f775(f775(f775(f200(x42891,x42892,x42893,x42897),x42894),x42895),x42896)) % 186.05/186.62 [4300]E(f191(x43001,x43002,f775(f775(f775(x43003,x43004),x43005),x43006),f775(f775(f9(x43001,f856(a101,a101),f857(a101,f852(f854(x43002)))),f775(f775(f9(x43001,a101,f857(f856(a101,a101),f857(a101,f852(f854(x43002))))),f775(f775(f9(x43001,a101,f857(a101,f857(f856(a101,a101),f857(a101,f852(f854(x43002)))))),x43007),x43004)),x43005)),x43006)),f202(x43001,x43002,x43003,x43007,x43004,x43005,x43006)) % 186.05/186.62 [4203]E(f775(f252(x42031,x42032,x42033,x42034,x42035,x42036),f775(f775(f241(x42031,x42033),x42037),x42038)),f775(f775(f241(x42032,x42034),f775(x42035,x42037)),f775(x42036,x42038))) % 186.05/186.62 [4302]E(f775(f775(f143(f856(x43021,x43022),f856(x43023,x43024)),f775(f251(x43021,x43022,f856(x43023,x43024)),f775(f775(f9(x43021,f857(x43022,x43024),f857(x43022,f856(x43023,x43024))),f775(f775(f10(f857(x43024,f856(x43023,x43024)),f857(f857(x43022,x43024),f857(x43022,f856(x43023,x43024))),x43021),f10(x43024,f856(x43023,x43024),x43022)),f775(f775(f10(x43023,f857(x43024,f856(x43023,x43024)),x43021),f241(x43023,x43024)),x43025))),x43026))),f775(f775(f167(x43021,x43022),x43027),x43028)),f775(f775(f167(x43023,x43024),f775(f775(f143(x43021,x43023),x43025),x43027)),f775(f775(f143(x43022,x43024),x43026),x43028))) % 186.05/186.62 [4306]E(f775(f775(f143(f856(x43061,x43062),x43063),f775(f251(x43061,x43062,x43063),f775(f775(f10(f857(x43062,f856(x43061,x43064)),f857(x43062,x43063),x43061),f775(f10(f856(x43061,x43064),x43063,x43062),x43065)),f775(f775(f9(x43061,f857(x43062,x43064),f857(x43062,f856(x43061,x43064))),f775(f775(f10(f857(x43064,f856(x43061,x43064)),f857(f857(x43062,x43064),f857(x43062,f856(x43061,x43064))),x43061),f10(x43064,f856(x43061,x43064),x43062)),f241(x43061,x43064))),x43066)))),f775(f775(f167(x43061,x43062),x43067),x43068)),f775(f775(f143(f856(x43061,x43064),x43063),x43065),f775(f775(f167(x43061,x43064),x43067),f775(f775(f143(x43062,x43064),x43066),x43068)))) % 186.05/186.62 [4234]E(f775(f775(f143(f856(x42341,x42342),x42343),f775(f251(x42341,x42342,x42343),f775(f775(f10(f857(x42342,f856(x42344,x42342)),f857(x42342,x42343),x42341),f775(f10(f856(x42344,x42342),x42343,x42342),x42345)),f775(f775(f10(x42344,f857(x42342,f856(x42344,x42342)),x42341),f241(x42344,x42342)),x42346)))),f775(f775(f167(x42341,x42342),x42347),x42348)),f775(f775(f143(f856(x42344,x42342),x42343),x42345),f775(f775(f167(x42344,x42342),f775(f775(f143(x42341,x42344),x42346),x42347)),x42348))) % 186.05/186.62 [4194]E(f775(f775(f251(x41941,x41942,x41943),f775(f775(f10(f857(x41942,f856(x41944,x41945)),f857(x41942,x41943),x41941),f775(f10(f856(x41944,x41945),x41943,x41942),f775(f251(x41944,x41945,x41943),x41946))),x41947)),x41948),f775(f775(f251(x41944,x41945,x41943),x41946),f775(f775(f251(x41941,x41942,f856(x41944,x41945)),x41947),x41948))) % 186.05/186.62 [4307]E(f775(f775(f46(f856(x43071,x43072),f857(f856(x43073,x43074),a844)),f775(f775(f248(x43071,x43072),x43075),f775(f18(f857(x43072,a844),x43071),x43076))),f775(f251(x43071,x43072,f857(f856(x43073,x43074),a844)),f775(f775(f9(x43071,f857(x43072,f857(x43073,f857(x43074,a844))),f857(x43072,f857(f856(x43073,x43074),a844))),f775(f775(f10(f857(f857(x43073,f857(x43074,a844)),f857(f856(x43073,x43074),a844)),f857(f857(x43072,f857(x43073,f857(x43074,a844))),f857(x43072,f857(f856(x43073,x43074),a844))),x43071),f10(f857(x43073,f857(x43074,a844)),f857(f856(x43073,x43074),a844),x43072)),f775(f775(f10(f857(x43073,a844),f857(f857(x43073,f857(x43074,a844)),f857(f856(x43073,x43074),a844)),x43071),f248(x43073,x43074)),x43077))),f775(f775(f10(f857(x43074,a844),f857(x43073,f857(x43074,a844)),x43072),f18(f857(x43074,a844),x43073)),x43078)))),f775(f775(f248(x43073,x43074),f775(f775(f46(x43071,f857(x43073,a844)),x43075),x43077)),f775(f18(f857(x43074,a844),x43073),f775(f775(f46(x43072,f857(x43074,a844)),x43076),x43078)))) % 186.05/186.62 [4337]E(f37(x43371,x43372,x43373,x43374,x43375,x43376,x43377,x43378,x43379,a25),x43372) % 186.05/186.62 [4338]E(f38(x43381,x43382,x43383,x43384,x43385,x43386,x43387,x43388,x43389,a25),x43382) % 186.05/186.62 [4248]E(f775(f775(f253(x42481,x42482,x42483,x42484),f775(f775(f253(x42481,x42485,x42486,f856(x42482,x42483)),x42487),x42488)),x42489),f775(f775(f253(x42481,x42485,x42486,x42484),x42487),f775(f775(f9(x42485,f857(x42482,f857(x42483,x42484)),f857(x42486,x42484)),f775(f775(f10(f857(x42486,f856(x42482,x42483)),f857(f857(x42482,f857(x42483,x42484)),f857(x42486,x42484)),x42485),f253(x42486,x42482,x42483,x42484)),x42488)),x42489))) % 186.05/186.62 [4339]E(f37(x43391,x43392,x43393,x43394,x43395,x43396,x43397,x43398,x43399,f775(a27,x433910)),f775(x43398,x433910)) % 186.05/186.62 [4340]E(f38(x43401,x43402,x43403,x43404,x43405,x43406,x43407,x43408,x43409,f775(a27,x434010)),f775(x43408,x434010)) % 186.05/186.62 [4278]E(f775(f75(f856(x42781,x42782),f856(x42783,x42784),f856(x42785,x42786),f252(x42781,x42783,x42782,x42784,x42787,x42788)),f252(x42785,x42781,x42786,x42782,x42789,x427810)),f252(x42785,x42783,x42786,x42784,f775(f75(x42781,x42783,x42785,x42787),x42789),f775(f75(x42782,x42784,x42786,x42788),x427810))) % 186.05/186.62 [4341]E(f37(x43411,x43412,x43413,x43414,x43415,x43416,x43417,x43418,x43419,f35(x434110,x434111)),f775(f775(x43417,x434110),x434111)) % 186.05/186.62 [4342]E(f37(x43421,x43422,x43423,x43424,x43425,x43426,x43427,x43428,x43429,f36(x434210,x434211)),f775(f775(x43425,x434210),x434211)) % 186.05/186.62 [4343]E(f37(x43431,x43432,x43433,x43434,x43435,x43436,x43437,x43438,x43439,f28(x434310,x434311)),f775(f775(x43433,x434310),x434311)) % 186.05/186.62 [4344]E(f38(x43441,x43442,x43443,x43444,x43445,x43446,x43447,x43448,x43449,f28(x434410,x434411)),f775(f775(x43443,x434410),x434411)) % 186.05/186.62 [4350]E(f775(f775(f775(x43501,x43502),x43503),f38(x43504,x43505,x43506,x43507,x43508,x43509,x43501,x435010,x435011,x43503)),f38(x43504,x43505,x43506,x43507,x43508,x43509,x43501,x435010,x435011,f35(x43502,x43503))) % 186.05/186.62 [4354]E(f775(f775(f775(f775(x43541,x43542),x43543),f38(x43544,x43545,x43546,x43547,x43541,x43548,x43549,x435410,x435411,x43542)),f38(x43544,x43545,x43546,x43547,x43541,x43548,x43549,x435410,x435411,x43543)),f38(x43544,x43545,x43546,x43547,x43541,x43548,x43549,x435410,x435411,f36(x43542,x43543))) % 186.05/186.62 [4283]E(f775(f252(x42831,x42832,x42833,x42834,x42835,x42836),f775(f252(x42837,x42831,x42838,x42833,x42839,x428310),x428311)),f775(f252(x42837,x42832,x42838,x42834,f775(f75(x42831,x42832,x42837,x42835),x42839),f775(f75(x42833,x42834,x42838,x42836),x428310)),x428311)) % 186.05/186.62 [4351]E(f775(f775(f775(f775(x43511,x43512),x43513),x43514),f38(x43515,x43516,x43517,x43511,x43518,x43519,x435110,x435111,x435112,x43514)),f38(x43515,x43516,x43517,x43511,x43518,x43519,x435110,x435111,x435112,f32(x43512,x43513,x43514))) % 186.05/186.62 [4355]E(f775(f775(f775(f775(f775(x43551,x43552),x43553),x43554),f38(x43555,x43556,x43557,x43558,x43559,x43551,x435510,x435511,x435512,x43553)),f38(x43555,x43556,x43557,x43558,x43559,x43551,x435510,x435511,x435512,x43554)),f38(x43555,x43556,x43557,x43558,x43559,x43551,x435510,x435511,x435512,f33(x43552,x43553,x43554))) % 186.05/186.62 [4345]E(f37(x43451,x43452,x43453,x43454,x43455,x43456,x43457,x43458,x43459,f33(x434510,x434511,x434512)),f775(f775(f775(x43456,x434510),x434511),x434512)) % 186.05/186.62 [4346]E(f37(x43461,x43462,x43463,x43464,x43465,x43466,x43467,x43468,x43469,f32(x434610,x434611,x434612)),f775(f775(f775(x43464,x434610),x434611),x434612)) % 186.05/186.62 [4347]E(f37(x43471,x43472,x43473,x43474,x43475,x43476,x43477,x43478,x43479,f31(x434710,x434711,x434712)),f775(f775(f775(x43479,x434710),x434711),x434712)) % 186.05/186.62 [4348]E(f38(x43481,x43482,x43483,x43484,x43485,x43486,x43487,x43488,x43489,f31(x434810,x434811,x434812)),f775(f775(f775(x43489,x434810),x434811),x434812)) % 186.05/186.62 [4563]~P142(a329,a776)+P1(f775(a859,a776)) % 186.05/186.62 [6356]P13(a5000)+P1(f775(f775(f334(f856(a846,a845)),a696),f775(f158(f856(a846,a845)),a29))) % 186.05/186.62 [8399]P13(a5000)+~P1(f775(f775(f251(a846,a845,a844),f775(f18(f857(a845,a844),a846),a26)),a696)) % 186.05/186.62 [4484]~P59(x44841)+P59(f854(x44841)) % 186.05/186.62 [4487]~P138(x44871)+~E(f80(x44871),f2(x44871)) % 186.05/186.62 [4489]~E(x44891,f2(a101))+E(f775(a23,x44891),f2(a1)) % 186.05/186.62 [4490]~E(x44901,f2(a1))+E(f84(a1,x44901),f2(a1)) % 186.05/186.62 [4496]~P2(x44961)+P33(x44961,f2(x44961)) % 186.05/186.62 [4498]~P100(x44981)+P18(x44981,f115(x44981)) % 186.05/186.62 [4507]P1(x45071)+P1(f775(a328,x45071)) % 186.05/186.62 [4548]~P2(x45481)+~P33(x45481,f80(x45481)) % 186.05/186.62 [4593]~P1(x45931)+~P1(f775(a328,x45931)) % 186.05/186.62 [4617]E(f775(a107,x46171),f2(a850))+~P1(f775(a186,x46171)) % 186.05/186.62 [4677]~P91(x46771)+P19(x46771,x46771,f83(x46771)) % 186.05/186.62 [4678]~P100(x46781)+P19(x46781,x46781,f236(x46781)) % 186.05/186.62 [4679]~P100(x46791)+P19(x46791,x46791,f179(x46791)) % 186.05/186.62 [4680]~P92(x46801)+P19(x46801,x46801,f103(x46801)) % 186.05/186.62 [4681]~P98(x46811)+P19(x46811,x46811,f104(x46811)) % 186.05/186.62 [4682]~P64(x46821)+P20(x46821,x46821,f83(x46821)) % 186.05/186.62 [4494]E(x44941,f2(a850))+E(f775(a114,f554(x44941)),x44941) % 186.05/186.62 [4495]~E(x44951,f2(a850))+E(f775(f102(a1),x44951),f2(a1)) % 186.05/186.62 [4501]~P88(x45011)+E(f775(f106(x45011),a85),f2(x45011)) % 186.05/186.62 [4503]~E(f601(x45031),f2(a850))+E(f775(f155(a850),x45031),f2(a850)) % 186.05/186.62 [4504]~P102(x45041)+E(f234(x45041,f232(x45041)),f236(x45041)) % 186.05/186.62 [4505]~P102(x45051)+E(f235(x45051,f232(x45051)),f179(x45051)) % 186.05/186.62 [4506]~P82(x45061)+E(f84(x45061,f2(x45061)),f2(x45061)) % 186.05/186.62 [4513]~P2(x45131)+E(f775(f102(x45131),f2(a850)),f2(x45131)) % 186.05/186.62 [4514]~P2(x45141)+E(f775(f102(x45141),f80(a850)),f80(x45141)) % 186.05/186.62 [4515]~P133(x45151)+E(f775(f105(x45151),f2(a1)),f2(x45151)) % 186.05/186.62 [4516]~P133(x45161)+E(f775(f105(x45161),f80(a1)),f80(x45161)) % 186.05/186.62 [4517]E(x45171,f2(a850))+~E(f775(f102(a1),x45171),f2(a1)) % 186.05/186.62 [4542]~P69(x45421)+E(f775(f81(x45421),f2(x45421)),f2(x45421)) % 186.05/186.62 [4543]~P90(x45431)+E(f775(f81(x45431),f239(x45431)),f180(x45431)) % 186.05/186.62 [4544]~P90(x45441)+E(f775(f81(x45441),f180(x45441)),f239(x45441)) % 186.05/186.62 [4545]~P79(x45451)+E(f775(f77(x45451),f2(x45451)),f2(x45451)) % 186.05/186.62 [4546]~P110(x45461)+E(f775(f77(x45461),f80(x45461)),f80(x45461)) % 186.05/186.62 [4547]~P67(x45471)+E(f775(f155(x45471),f115(x45471)),f2(x45471)) % 186.05/186.62 [4569]~P35(x45691)+P38(f775(f158(a1),x45691)) % 186.05/186.62 [4598]~P88(x45981)+E(f775(f81(x45981),f80(x45981)),f775(f106(x45981),a99)) % 186.05/186.62 [4616]~P88(x46161)+P33(x46161,f775(f106(x46161),a85)) % 186.05/186.62 [4641]P35(x46411)+~P38(f775(f158(a1),x46411)) % 186.05/186.62 [4683]E(f775(f102(a1),f775(a107,x46831)),x46831)+P1(f775(a186,x46831)) % 186.05/186.62 [4749]~P105(x47491)+E(f243(x47491,f80(x47491),f83(x47491)),f242(x47491)) % 186.05/186.62 [4777]~P88(x47771)+~P33(x47771,f775(f106(x47771),a99)) % 186.05/186.62 [4787]E(f775(a30,x47871),f183(a845))+P1(f775(a26,f775(a27,x47871))) % 186.05/186.62 [4917]E(f775(f77(a1),x49171),x49171)+P1(f775(f775(f233(a1),x49171),f2(a1))) % 186.05/186.62 [4937]~E(f775(a107,x49371),f2(a850))+P1(f775(f775(f232(a1),x49371),f2(a1))) % 186.05/186.62 [4972]~E(f775(f77(a1),x49721),f80(a1))+P1(f775(f775(f279(a1),x49721),f80(a1))) % 186.05/186.62 [5002]~P1(f775(a186,x50021))+P1(f775(f775(f233(a1),x50021),f2(a1))) % 186.05/186.62 [5042]~P2(x50421)+P1(f775(f775(f334(x50421),f2(x50421)),f176(x50421))) % 186.05/186.62 [5043]~P133(x50431)+P1(f775(f775(f334(x50431),f2(x50431)),f112(x50431))) % 186.05/186.62 [5044]~P2(x50441)+P1(f775(f775(f334(x50441),f80(x50441)),f176(x50441))) % 186.05/186.62 [5045]~P133(x50451)+P1(f775(f775(f334(x50451),f80(x50451)),f112(x50451))) % 186.05/186.62 [5046]~P117(x50461)+P1(f775(f775(f233(x50461),f2(x50461)),f80(x50461))) % 186.05/186.62 [5047]~P117(x50471)+P1(f775(f775(f232(x50471),f2(x50471)),f80(x50471))) % 186.05/186.62 [5050]E(f775(f227(a845),f449(x50501)),f775(a30,x50501))+~P1(f775(a26,f775(a27,x50501))) % 186.05/186.62 [5051]E(f775(f227(a845),f471(x50511)),f775(a30,x50511))+~P1(f775(a26,f775(a27,x50511))) % 186.05/186.62 [5101]E(x51011,f2(a850))+~P1(f775(f775(f232(a850),x51011),f2(a850))) % 186.05/186.62 [5102]E(x51021,f80(a850))+~P1(f775(f775(f279(a850),x51021),f80(a850))) % 186.05/186.62 [5144]E(f775(a107,x51441),f2(a850))+~P1(f775(f775(f232(a1),x51441),f2(a1))) % 186.05/186.62 [5172]E(f775(f77(a1),x51721),f80(a1))+~P1(f775(f775(f279(a1),x51721),f80(a1))) % 186.05/186.62 [5199]P1(f775(a186,x51991))+~P1(f775(f775(f233(a1),x51991),f2(a1))) % 186.05/186.62 [5204]~P100(x52041)+P20(x52041,f851(x52041),f138(x52041,x52041,f7(x52041))) % 186.05/186.62 [5222]P38(x52221)+~P1(f775(f775(f232(a1),f2(a1)),f338(x52221))) % 186.05/186.62 [5228]E(f775(f77(a1),x52281),f775(f81(a1),x52281))+~P1(f775(f775(f233(a1),x52281),f2(a1))) % 186.05/186.62 [5397]~P117(x53971)+~P1(f775(f775(f233(x53971),f80(x53971)),f2(x53971))) % 186.05/186.62 [5398]~P117(x53981)+~P1(f775(f775(f232(x53981),f80(x53981)),f2(x53981))) % 186.05/186.62 [5410]~E(x54101,f2(a1))+P1(f775(f775(f233(a1),f775(f77(a1),x54101)),f80(a1))) % 186.05/186.62 [5411]~E(x54111,f2(a850))+P1(f775(f775(f232(a1),f775(f102(a1),x54111)),f2(a1))) % 186.05/186.62 [5525]~P67(x55251)+E(f132(x55251,x55251,f82(x55251),f2(x55251)),f155(x55251)) % 186.05/186.62 [5700]~P86(x57001)+P29(a850,x57001,f102(x57001),f239(f857(a850,a844))) % 186.05/186.62 [5897]E(x58971,f2(a850))+~P1(f775(f775(f232(a1),f775(f102(a1),x58971)),f2(a1))) % 186.05/186.62 [5898]E(x58981,f2(a1))+~P1(f775(f775(f233(a1),f775(f77(a1),x58981)),f80(a1))) % 186.05/186.62 [6729]~P1(f775(f775(f233(a1),x67291),f2(a1)))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x67291),x67291)),f2(a1))) % 186.05/186.62 [7304]P1(f775(f775(f233(a1),x73041),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x73041),x73041)),f2(a1))) % 186.05/186.62 [7869]E(x78691,f775(a5,f2(a850)))+P1(f775(f775(f233(a850),f775(f775(f3(a850),f775(a22,x78691)),f775(a114,f2(a850)))),f775(a22,x78691))) % 186.05/186.62 [8611]~P1(f775(f775(f233(a1),x86111),f2(a1)))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x86111),x86111)),a99)),f2(a1))) % 186.05/186.62 [8695]~P1(f775(f775(f233(a1),x86951),f2(a1)))+P1(f775(f775(f233(a1),f775(f775(f82(a1),f775(f775(f82(a1),f80(a1)),x86951)),x86951)),f2(a1))) % 186.05/186.62 [8979]P1(f775(f775(f233(a1),x89791),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89791),x89791)),a99)),f2(a1))) % 186.05/186.62 [9043]P1(f775(f775(f233(a1),x90431),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),f775(f775(f82(a1),f80(a1)),x90431)),x90431)),f2(a1))) % 186.05/186.62 [4586]~E(a85,x45861)+E(f775(f775(f82(a1),x45861),x45861),a85) % 186.05/186.62 [4587]~E(x45871,a85)+E(f775(f775(f82(a1),x45871),x45871),a85) % 186.05/186.62 [4602]E(x46021,f2(a1))+E(f775(f775(f43(a1),x46021),x46021),f80(a1)) % 186.05/186.62 [4727]E(x47271,a85)+~E(f775(f775(f82(a1),x47271),x47271),a85) % 186.05/186.62 [4728]E(a85,x47281)+~E(f775(f775(f82(a1),x47281),x47281),a85) % 186.05/186.62 [4739]~P9(x47391)+E(f45(x47391,f239(f857(x47391,a844))),f180(x47391)) % 186.05/186.62 [4740]~P9(x47401)+E(f45(x47401,f180(f857(x47401,a844))),f239(x47401)) % 186.05/186.62 [4741]~P9(x47411)+E(f44(x47411,f239(f857(x47411,a844))),f239(x47411)) % 186.05/186.62 [4742]~P9(x47421)+E(f44(x47421,f180(f857(x47421,a844))),f180(x47421)) % 186.05/186.62 [4743]~P100(x47431)+E(f130(x47431,f180(f857(x47431,a844))),f115(x47431)) % 186.05/186.62 [4877]E(x48771,f2(a850))+P1(f775(f775(f233(a850),f2(a850)),x48771)) % 186.05/186.62 [4897]~P10(x48971)+P1(f775(f775(f232(a1),f2(a1)),x48971)) % 186.05/186.62 [4928]~E(f775(f106(a850),x49281),f2(a850))+P1(f775(f775(f232(a1),x49281),a85)) % 186.05/186.62 [4933]P38(x49331)+P1(f775(f775(f334(a1),f338(x49331)),x49331)) % 186.05/186.62 [4934]E(x49341,f775(a5,f2(a850)))+P1(f775(f775(f232(a101),f80(a101)),x49341)) % 186.05/186.62 [4977]P1(f775(a186,x49771))+P1(f775(f775(f232(a1),f2(a1)),x49771)) % 186.05/186.62 [5024]E(f775(f102(a1),f775(a107,x50241)),f2(a1))+P1(f775(f775(f232(a1),f2(a1)),x50241)) % 186.05/186.62 [5089]E(f775(f102(a1),f775(f106(a850),x50891)),f775(f106(a1),x50891))+P1(f775(a186,f775(f106(a1),x50891))) % 186.05/186.62 [5109]E(f775(f106(a850),x51091),f2(a850))+~P1(f775(a186,f775(f106(a1),x51091))) % 186.05/186.62 [5110]E(f775(f106(a850),x51101),f2(a850))+~P1(f775(f775(f232(a1),x51101),a85)) % 186.05/186.62 [5141]P10(x51411)+~P1(f775(f775(f232(a1),f2(a1)),x51411)) % 186.05/186.62 [5207]E(f775(a114,f579(x52071)),x52071)+~P1(f775(f775(f233(a850),f2(a850)),x52071)) % 186.05/186.62 [5208]E(f775(a114,f618(x52081)),x52081)+~P1(f775(f775(f233(a850),f2(a850)),x52081)) % 186.05/186.62 [5216]E(f775(a114,f775(f106(a850),x52161)),f80(a850))+~P1(f775(a186,f775(f106(a1),x52161))) % 186.05/186.62 [5224]E(f775(f102(a1),f626(x52241)),x52241)+~P1(f775(f775(f233(a1),f2(a1)),x52241)) % 186.05/186.62 [5231]~E(x52311,f775(a5,f2(a850)))+~P1(f775(f775(f232(a101),f80(a101)),x52311)) % 186.05/186.62 [5238]E(f775(f102(a1),f775(f106(a850),x52381)),f2(a1))+~P1(f775(a186,f775(f106(a1),x52381))) % 186.05/186.62 [5262]E(f775(f155(a850),x52621),f2(a850))+P1(f775(f775(f334(a850),f601(x52621)),f775(f158(a850),x52621))) % 186.05/186.62 [5282]E(f775(f102(a1),f775(a107,x52821)),x52821)+~P1(f775(f775(f232(a1),f2(a1)),x52821)) % 186.05/186.62 [5291]~P1(f775(a186,x52911))+~P1(f775(f775(f232(a1),f2(a1)),x52911)) % 186.05/186.62 [5390]E(f775(f775(f82(a850),f80(a850)),f775(f106(a850),x53901)),f80(a850))+~P1(f775(f775(f233(a1),x53901),a85)) % 186.05/186.62 [5447]E(x54471,f2(a850))+~P1(f775(f775(f233(a850),x54471),f775(a114,f2(a850)))) % 186.05/186.62 [5468]E(x54681,f775(a114,f2(a850)))+~P1(f775(f775(f279(a850),x54681),f775(a114,f2(a850)))) % 186.05/186.62 [5486]E(f775(f775(f82(a850),f775(f106(a850),x54861)),f80(a850)),f80(a850))+~P1(f775(f775(f233(a1),x54861),a85)) % 186.05/186.62 [5487]E(f775(f775(f3(a850),f775(f106(a850),x54871)),f80(a850)),f2(a850))+~P1(f775(f775(f232(a1),x54871),a85)) % 186.05/186.62 [5497]~P38(x54971)+E(f775(f42(a850),f775(f303(a1,a850,a107),x54971)),f775(f42(a1),x54971)) % 186.05/186.62 [5526]~P100(x55261)+E(f234(x55261,f775(f9(x55261,x55261,a844),f232(x55261))),f179(x55261)) % 186.05/186.62 [5527]~P100(x55271)+E(f235(x55271,f775(f9(x55271,x55271,a844),f232(x55271))),f236(x55271)) % 186.05/186.62 [5536]E(f52(a850,f775(a114,f2(a850)),f775(f106(a850),x55361)),f775(a114,f2(a850)))+~P1(f775(a186,f775(f106(a1),x55361))) % 186.05/186.62 [5544]P1(f775(f775(f233(a1),f2(a1)),x55441))+~P1(f775(f775(f232(a1),f80(a1)),x55441)) % 186.05/186.62 [5545]~P1(f775(f775(f233(a1),f2(a1)),x55451))+P1(f775(f775(f232(a1),f80(a1)),x55451)) % 186.05/186.62 [5555]E(f775(a114,f775(f775(f3(a850),x55551),f80(a850))),x55551)+~P1(f775(f775(f233(a850),f2(a850)),x55551)) % 186.05/186.62 [5613]P1(f775(f775(f233(a850),f2(a850)),f626(x56131)))+~P1(f775(f775(f233(a1),f2(a1)),x56131)) % 186.05/186.62 [5670]E(f52(a1,f775(f106(a1),a99),x56701),f775(f775(f3(a1),x56701),f80(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x56701)) % 186.05/186.62 [5715]~P1(f775(f775(f233(a1),a85),x57151))+P1(f775(f775(f233(a850),f2(a850)),f775(f106(a850),x57151))) % 186.05/186.62 [5769]P1(f775(f775(f233(a850),f2(a850)),f775(a107,x57691)))+~P1(f775(f775(f233(a1),f2(a1)),x57691)) % 186.05/186.62 [5816]~P1(f775(f775(f233(a850),f2(a850)),x58161))+P1(f775(f775(f233(a1),f2(a1)),f775(f102(a1),x58161))) % 186.05/186.62 [5851]~P1(f775(f775(f233(a850),f2(a850)),f775(a107,x58511)))+P1(f775(f775(f233(a1),f2(a1)),x58511)) % 186.05/186.62 [5866]~P38(x58661)+E(f775(f303(a850,a1,f102(a1)),f775(f303(a1,a850,a107),x58661)),x58661) % 186.05/186.62 [5877]P1(f775(f775(f233(a1),a85),x58771))+~P1(f775(f775(f233(a850),f2(a850)),f775(f106(a850),x58771))) % 186.05/186.62 [5939]P1(f775(f775(f233(a850),f2(a850)),x59391))+~P1(f775(f775(f233(a1),f2(a1)),f775(f102(a1),x59391))) % 186.05/186.62 [6055]E(f775(f303(a850,a1,f102(a1)),f775(f257(a850),f775(a107,x60551))),f775(f294(a1,f2(a1)),x60551))+~P1(f775(f775(f232(a1),f2(a1)),x60551)) % 186.05/186.62 [6071]~P117(x60711)+P1(f775(f775(f233(x60711),f2(x60711)),f775(f775(f82(x60711),f80(x60711)),f80(x60711)))) % 186.05/186.62 [6122]P1(f775(f775(f233(a850),f775(a114,f2(a850))),f775(a107,x61221)))+~P1(f775(f775(f233(a1),f80(a1)),x61221)) % 186.05/186.62 [6219]E(x62191,f2(a1))+P1(f775(f56(f2(a1),x62191),f775(f775(f241(a1,a1),f2(a1)),f2(a1)))) % 186.05/186.62 [6399]~P1(f775(f775(f233(a850),f775(a114,f2(a850))),f775(a107,x63991)))+P1(f775(f775(f233(a1),f80(a1)),x63991)) % 186.05/186.62 [6851]~P107(x68511)+P36(x68511,f775(f256(f856(x68511,x68511)),f775(f251(x68511,x68511,a844),f233(x68511)))) % 186.05/186.62 [5107]~P35(x51071)+E(f129(f775(f775(f143(a1,a850),a107),x51071)),x51071) % 186.05/186.62 [5437]E(f775(f106(a850),f775(f775(f3(a1),x54371),a99)),f775(a114,f775(f106(a850),x54371)))+P1(f775(a186,f775(f106(a1),x54371))) % 186.05/186.62 [5462]P31(a843,a600,x54621)+~P1(f775(f775(f334(f849(a843)),x54621),a860)) % 186.05/186.62 [5561]E(f775(f81(a1),f775(f102(a1),f775(a114,f684(x55611)))),x55611)+~P1(f775(f775(f233(a1),x55611),f2(a1))) % 186.05/186.62 [5571]E(f775(f775(f82(a850),f80(a850)),f775(f106(a850),x55711)),f775(f106(a850),f775(f775(f3(a1),x55711),a99)))+P1(f775(f775(f233(a1),x55711),a85)) % 186.05/186.62 [5615]E(f775(f775(f43(a1),f775(f106(a1),a99)),x56151),f775(f106(a1),a99))+~P1(f775(f775(f233(a1),f2(a1)),x56151)) % 186.05/186.62 [5711]E(f775(f775(f82(a850),f775(f106(a850),x57111)),f80(a850)),f775(f106(a850),f775(f775(f3(a1),x57111),a99)))+P1(f775(f775(f233(a1),x57111),a85)) % 186.05/186.62 [5712]E(f775(f775(f3(a850),f775(f106(a850),x57121)),f80(a850)),f775(f106(a850),f775(f775(f82(a1),x57121),a99)))+P1(f775(f775(f232(a1),x57121),a85)) % 186.05/186.62 [5755]E(f775(a107,f775(f775(f82(a1),f80(a1)),x57551)),f775(a114,f775(a107,x57551)))+~P1(f775(f775(f232(a1),f2(a1)),x57551)) % 186.05/186.62 [5793]E(f775(a114,f775(f775(f3(a850),x57931),f775(a114,f2(a850)))),x57931)+~P1(f775(f775(f233(a850),f2(a850)),x57931)) % 186.05/186.62 [6000]E(f52(a850,f775(a114,f2(a850)),f775(f106(a850),x60001)),f775(a107,f52(a1,f80(a1),f775(f106(a1),x60001))))+P1(f775(a186,f775(f106(a1),x60001))) % 186.05/186.62 [6046]~P1(f775(f775(f233(a1),a99),x60461))+P1(f775(f775(f233(a1),a99),f775(f775(f82(a1),x60461),x60461))) % 186.05/186.62 [6047]~P1(f775(f775(f233(a1),a85),x60471))+P1(f775(f775(f233(a1),a85),f775(f775(f82(a1),x60471),x60471))) % 186.05/186.62 [6048]~P1(f775(f775(f233(a1),a99),x60481))+P1(f775(f775(f232(a1),a99),f775(f775(f82(a1),x60481),x60481))) % 186.05/186.62 [6049]~P1(f775(f775(f232(a1),a85),x60491))+P1(f775(f775(f232(a1),a85),f775(f775(f82(a1),x60491),x60491))) % 186.05/186.62 [6233]~P1(f775(f63(x62331),f239(f857(x62331,a844))))+P1(f775(f63(f854(x62331)),f239(f857(f854(x62331),a844)))) % 186.05/186.62 [6324]~P1(f775(f775(f232(a1),f2(a1)),x63241))+P1(f775(f775(f233(a1),f2(a1)),f775(f775(f82(a1),f80(a1)),x63241))) % 186.05/186.62 [6330]E(f775(f240(a1,a1),f54(f80(a1),f775(f106(a1),x63301))),f775(f775(f43(a1),f80(a1)),f775(f106(a1),x63301)))+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x63301))) % 186.05/186.62 [6355]E(f775(f250(a1,a1),f54(f80(a1),f775(f106(a1),x63551))),f52(a1,f80(a1),f775(f106(a1),x63551)))+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x63551))) % 186.05/186.62 [6368]P1(f775(f63(x63681),f239(f857(x63681,a844))))+~P1(f775(f63(f854(x63681)),f239(f857(f854(x63681),a844)))) % 186.05/186.62 [6400]P1(f775(f775(f233(a1),a99),x64001))+~P1(f775(f775(f233(a1),a99),f775(f775(f82(a1),x64001),x64001))) % 186.05/186.62 [6401]P1(f775(f775(f233(a1),a99),x64011))+~P1(f775(f775(f232(a1),a99),f775(f775(f82(a1),x64011),x64011))) % 186.05/186.62 [6402]P1(f775(f775(f233(a1),a85),x64021))+~P1(f775(f775(f233(a1),a85),f775(f775(f82(a1),x64021),x64021))) % 186.05/186.62 [6403]P1(f775(f775(f232(a1),a85),x64031))+~P1(f775(f775(f232(a1),a85),f775(f775(f82(a1),x64031),x64031))) % 186.05/186.62 [6735]~P1(f775(f63(x67351),f239(f857(x67351,a844))))+P1(f775(f775(f233(a850),f2(a850)),f775(f42(x67351),f239(f857(x67351,a844))))) % 186.05/186.62 [7349]P1(f775(f63(a850),x73491))+~P1(f775(f63(a1),f775(f303(a850,a1,f102(a1)),x73491))) % 186.05/186.62 [5365]~E(a99,x53651)+E(f775(f775(f3(a1),f775(f775(f82(a1),x53651),x53651)),a99),a99) % 186.05/186.62 [5366]~E(x53661,a99)+E(f775(f775(f3(a1),f775(f775(f82(a1),x53661),x53661)),a99),a99) % 186.05/186.62 [5871]E(x58711,a99)+~E(f775(f775(f3(a1),f775(f775(f82(a1),x58711),x58711)),a99),a99) % 186.05/186.62 [5872]E(a99,x58721)+~E(f775(f775(f3(a1),f775(f775(f82(a1),x58721),x58721)),a99),a99) % 186.05/186.62 [6293]~E(f775(f106(a850),x62931),f2(a850))+P1(f775(a186,f775(f106(a1),f775(f775(f82(a1),x62931),a99)))) % 186.05/186.62 [6659]~P1(f775(a186,f775(f106(a1),x66591)))+P1(f775(a186,f775(f106(a1),f775(f775(f82(a1),x66591),x66591)))) % 186.05/186.62 [6660]~P1(f775(f775(f232(a1),x66601),a99))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x66601),x66601)),a99)) % 186.05/186.62 [6661]~P1(f775(f775(f233(a1),x66611),a85))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x66611),x66611)),a85)) % 186.05/186.62 [6662]~P1(f775(f775(f232(a1),x66621),a99))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x66621),x66621)),a99)) % 186.05/186.62 [6663]~P1(f775(f775(f232(a1),x66631),a85))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x66631),x66631)),a85)) % 186.05/186.62 [6993]E(f775(f106(a850),x69931),f2(a850))+~P1(f775(a186,f775(f106(a1),f775(f775(f82(a1),x69931),a99)))) % 186.05/186.62 [7252]~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x72521)))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),f775(f775(f82(a1),x72521),x72521)))) % 186.05/186.62 [7253]P1(f775(a186,f775(f106(a1),x72531)))+~P1(f775(a186,f775(f106(a1),f775(f775(f82(a1),x72531),x72531)))) % 186.05/186.62 [7254]P1(f775(f775(f233(a1),x72541),a85))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x72541),x72541)),a85)) % 186.05/186.62 [7255]P1(f775(f775(f232(a1),x72551),a99))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x72551),x72551)),a99)) % 186.05/186.62 [7256]P1(f775(f775(f232(a1),x72561),a99))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x72561),x72561)),a99)) % 186.05/186.62 [7257]P1(f775(f775(f232(a1),x72571),a85))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x72571),x72571)),a85)) % 186.05/186.62 [7636]E(f775(a109,f571(x76361)),x76361)+~P1(f775(f775(f334(f857(f856(a850,a850),a844)),x76361),a100)) % 186.05/186.62 [6206]~P88(x62061)+E(f775(f106(x62061),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f80(x62061)) % 186.05/186.62 [6713]~P1(f775(a186,f775(f106(a1),x67131)))+E(f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x67131),x67131)),a99)),f2(a850)) % 186.05/186.62 [7815]~P1(f775(f775(f233(a1),f775(f106(a1),x78151)),f2(a1)))+E(f775(f240(a1,a1),f775(a58,f57(f775(f81(a1),f80(a1)),f775(f81(a1),f775(f106(a1),x78151))))),f775(f775(f43(a1),f80(a1)),f775(f106(a1),x78151))) % 186.05/186.62 [7828]~P1(f775(f775(f233(a1),f775(f106(a1),x78281)),f2(a1)))+E(f775(f250(a1,a1),f775(a58,f57(f775(f81(a1),f80(a1)),f775(f81(a1),f775(f106(a1),x78281))))),f52(a1,f80(a1),f775(f106(a1),x78281))) % 186.05/186.62 [7875]~P1(f775(f775(f233(a1),a99),x78751))+P1(f775(f775(f233(a1),a99),f775(f775(f3(a1),f775(f775(f82(a1),x78751),x78751)),a99))) % 186.05/186.62 [7876]~P1(f775(f775(f232(a1),a85),x78761))+P1(f775(f775(f233(a1),a85),f775(f775(f3(a1),f775(f775(f82(a1),x78761),x78761)),a99))) % 186.05/186.62 [7877]~P1(f775(f775(f232(a1),a99),x78771))+P1(f775(f775(f232(a1),a99),f775(f775(f3(a1),f775(f775(f82(a1),x78771),x78771)),a99))) % 186.05/186.62 [7878]~P1(f775(f775(f232(a1),a85),x78781))+P1(f775(f775(f232(a1),a85),f775(f775(f3(a1),f775(f775(f82(a1),x78781),x78781)),a99))) % 186.05/186.62 [8175]~P88(x81751)+~P33(x81751,f775(f106(x81751),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))) % 186.05/186.62 [8355]P1(f775(f775(f233(a1),a99),x83551))+~P1(f775(f775(f233(a1),a99),f775(f775(f3(a1),f775(f775(f82(a1),x83551),x83551)),a99))) % 186.05/186.62 [8356]P1(f775(f775(f232(a1),a99),x83561))+~P1(f775(f775(f232(a1),a99),f775(f775(f3(a1),f775(f775(f82(a1),x83561),x83561)),a99))) % 186.05/186.62 [8357]P1(f775(f775(f232(a1),a85),x83571))+~P1(f775(f775(f233(a1),a85),f775(f775(f3(a1),f775(f775(f82(a1),x83571),x83571)),a99))) % 186.05/186.62 [8358]P1(f775(f775(f232(a1),a85),x83581))+~P1(f775(f775(f232(a1),a85),f775(f775(f3(a1),f775(f775(f82(a1),x83581),x83581)),a99))) % 186.05/186.62 [8654]E(f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x86541),x86541)),a99)),f775(f775(f88(a850,a850),f775(f106(a850),x86541)),f775(f775(f10(a850,a850,a850),a114),f775(f775(f20(a850,a850,a850),f82(a850)),f7(a850)))))+P1(f775(a186,f775(f106(a1),x86541))) % 186.05/186.62 [9427]E(x94271,f180(f857(f856(a850,a850),a844)))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x94271),f180(f857(f856(a850,a850),a844)))),a70)) % 186.05/186.62 [8588]~P1(f775(a186,f775(f106(a1),x85881)))+P1(f775(a186,f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x85881),x85881)),a99)))) % 186.05/186.62 [8589]~P1(f775(f775(f233(a1),x85891),a99))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x85891),x85891)),a99)),a99)) % 186.05/186.62 [8590]~P1(f775(f775(f233(a1),x85901),a85))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x85901),x85901)),a99)),a85)) % 186.05/186.62 [8591]~P1(f775(f775(f232(a1),x85911),a99))+P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x85911),x85911)),a99)),a99)) % 186.05/186.62 [8592]~P1(f775(f775(f233(a1),x85921),a85))+P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x85921),x85921)),a99)),a85)) % 186.05/186.62 [8688]~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x86881)))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x86881),x86881)),a99)))) % 186.05/186.62 [8818]~P88(x88181)+E(f775(f775(f82(x88181),f80(x88181)),f80(x88181)),f775(f106(x88181),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))) % 186.05/186.62 [8965]P1(f775(a186,f775(f106(a1),x89651)))+~P1(f775(a186,f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89651),x89651)),a99)))) % 186.05/186.62 [8966]P1(f775(f775(f233(a1),x89661),a99))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89661),x89661)),a99)),a99)) % 186.05/186.62 [8967]P1(f775(f775(f233(a1),x89671),a85))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89671),x89671)),a99)),a85)) % 186.05/186.62 [8968]P1(f775(f775(f233(a1),x89681),a85))+~P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89681),x89681)),a99)),a85)) % 186.05/186.62 [8969]P1(f775(f775(f232(a1),x89691),a99))+~P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89691),x89691)),a99)),a99)) % 186.05/186.62 [9475]~P1(f775(f63(f856(a850,a850)),x94751))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f180(f857(f856(a850,a850),a844))),x94751)),a71)) % 186.05/186.62 [9261]~P2(x92611)+E(f775(f775(f242(x92611),f2(x92611)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f2(x92611)) % 186.05/186.62 [9262]~P2(x92621)+E(f775(f775(f242(x92621),f80(x92621)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(x92621)) % 186.05/186.62 [9672]~P1(f775(f775(f233(a850),f80(a850)),x96721))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f43(a850),x96721),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.62 [9678]~P1(f775(f775(f233(a850),f2(a850)),x96781))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f43(a850),f775(f775(f82(a850),x96781),f80(a850))),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.62 [9717]~E(f52(a850,x97171,f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(a850))+P1(f775(f775(f233(a850),f2(a850)),f52(a850,x97171,f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.62 [9752]E(f52(a850,x97521,f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(a850))+~P1(f775(f775(f233(a850),f2(a850)),f52(a850,x97521,f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.62 [4521]~P36(x45211,x45212)+P56(x45211,x45212) % 186.05/186.62 [4522]~P42(x45221,x45222)+P56(x45221,x45222) % 186.05/186.62 [4485]~E(x44851,x44852)+E(f266(x44851,x44852),f80(a101)) % 186.05/186.62 [4488]E(f211(x44881,x44882),x44881)+~E(x44882,f2(a850)) % 186.05/186.62 [4493]P37(x44931,x44932)+~E(x44932,f183(x44931)) % 186.05/186.62 [4499]~P37(x44992,x44991)+E(x44991,f183(x44992)) % 186.05/186.62 [4526]~P99(x45262)+P99(f857(x45261,x45262)) % 186.05/186.62 [4527]~P103(x45272)+P103(f857(x45271,x45272)) % 186.05/186.62 [4528]~P102(x45282)+P102(f857(x45281,x45282)) % 186.05/186.62 [4529]~P90(x45292)+P90(f857(x45291,x45292)) % 186.05/186.62 [4530]~P84(x45302)+P84(f857(x45301,x45302)) % 186.05/186.62 [4531]~P71(x45312)+P71(f857(x45311,x45312)) % 186.05/186.62 [4532]~P93(x45322)+P92(f857(x45321,x45322)) % 186.05/186.62 [4533]~P93(x45332)+P93(f857(x45331,x45332)) % 186.05/186.62 [4534]~P9(x45342)+P9(f857(x45341,x45342)) % 186.05/186.62 [4535]~P106(x45352)+P106(f857(x45351,x45352)) % 186.05/186.62 [4536]~P96(x45362)+P94(f857(x45361,x45362)) % 186.05/186.62 [4537]~P101(x45372)+P101(f857(x45371,x45372)) % 186.05/186.62 [4538]~P96(x45382)+P95(f857(x45381,x45382)) % 186.05/186.62 [4539]~P97(x45392)+P97(f857(x45391,x45392)) % 186.05/186.62 [4540]~P93(x45402)+P98(f857(x45401,x45402)) % 186.05/186.62 [4541]~P96(x45412)+P96(f857(x45411,x45412)) % 186.05/186.62 [4554]E(x45541,x45542)+~E(f775(a114,x45541),f775(a114,x45542)) % 186.05/186.62 [4555]E(x45551,x45552)+~E(f775(a27,x45551),f775(a27,x45552)) % 186.05/186.62 [4556]E(x45561,x45562)+~E(f775(a5,x45561),f775(a5,x45562)) % 186.05/186.62 [4558]E(x45581,x45582)+~E(f775(a22,x45581),f775(a22,x45582)) % 186.05/186.62 [4559]E(x45591,x45592)+~E(f775(a109,x45591),f775(a109,x45592)) % 186.05/186.62 [4657]~P7(x46571)+E(f52(x46571,x46572,x46572),f2(x46571)) % 186.05/186.62 [4690]~P36(x46901,x46902)+P36(f851(x46901),f136(x46901,x46902)) % 186.05/186.62 [4691]~P36(x46911,x46912)+P36(f851(x46911),f135(x46911,x46912)) % 186.05/186.62 [4782]~P36(x47821,x47822)+P36(f857(x47821,a844),f326(x47821,x47822)) % 186.05/186.62 [4783]~P36(x47831,x47832)+P36(f857(x47831,a844),f324(x47831,x47832)) % 186.05/186.62 [4902]~P10(x49021)+P38(f295(a1,x49021,x49022)) % 186.05/186.62 [5005]~P36(x50051,x50052)+P58(x50051,f69(x50051,x50051,x50052)) % 186.05/186.62 [5491]~P77(x54911)+P29(x54911,x54911,f81(x54911),x54912) % 186.05/186.62 [4509]~E(x45092,f115(x45091))+E(f775(f141(x45091),x45092),f115(x45091)) % 186.05/186.62 [4510]~E(x45102,f115(x45101))+E(f775(f142(x45101),x45102),f115(x45101)) % 186.05/186.62 [4564]E(x45641,f775(a107,x45642))+~E(f775(f102(a1),x45641),x45642) % 186.05/186.62 [4567]E(x45671,f115(x45672))+~E(f775(f141(x45672),x45671),f115(x45672)) % 186.05/186.62 [4568]E(x45681,f115(x45682))+~E(f775(f142(x45682),x45681),f115(x45682)) % 186.05/186.62 [4583]~P88(x45831)+E(f775(f106(x45831),x45832),f775(f105(x45831),x45832)) % 186.05/186.62 [4590]~E(x45902,f183(x45901))+E(f226(x45901,x45902),f180(f857(x45901,a844))) % 186.05/186.62 [4592]~P59(x45921)+P1(f775(f63(x45921),x45922)) % 186.05/186.62 [4599]E(x45991,f183(x45992))+E(f775(f227(x45992),f491(x45992,x45991)),x45991) % 186.05/186.62 [4600]E(x46001,f183(x46002))+E(f775(f227(x46002),f492(x46002,x46001)),x46001) % 186.05/186.62 [4601]E(x46011,f183(x46012))+E(f775(f227(x46012),f503(x46012,x46011)),x46011) % 186.05/186.62 [4603]~E(f722(x46032,x46031),f115(x46031))+E(f164(x46031,x46032),f115(f851(x46031))) % 186.05/186.62 [4612]~E(x46122,f115(x46121))+E(f775(f158(x46121),x46122),f180(f857(x46121,a844))) % 186.05/186.62 [4613]~E(x46132,f115(x46131))+E(f180(f857(x46131,a844)),f775(f158(x46131),x46132)) % 186.05/186.62 [4615]E(x46151,x46152)+~E(f775(f102(a1),x46151),f775(f102(a1),x46152)) % 186.05/186.62 [4618]E(f209(x46181,x46182),f2(a850))+P1(f775(f63(x46181),x46182)) % 186.05/186.62 [4636]~P110(x46361)+E(f84(x46361,f84(x46361,x46362)),f84(x46361,x46362)) % 186.05/186.62 [4648]~P85(x46481)+E(f775(f775(f242(x46481),x46482),f80(a850)),x46482) % 186.05/186.62 [4649]~P75(x46491)+E(f775(f775(f242(x46491),x46492),f80(a850)),x46492) % 186.05/186.62 [4651]E(x46511,x46512)+E(f266(x46511,x46512),f775(f775(f82(a101),x46512),f80(a101))) % 186.05/186.62 [4654]E(f775(f42(x46541),x46542),f2(a850))+P1(f775(f63(x46541),x46542)) % 186.05/186.62 [4660]~P66(x46601)+E(f775(f775(f82(x46601),x46602),f2(x46601)),x46602) % 186.05/186.62 [4661]~P67(x46611)+E(f775(f775(f82(x46611),x46612),f2(x46611)),x46612) % 186.05/186.62 [4662]~P85(x46621)+E(f775(f775(f82(x46621),x46622),f2(x46621)),x46622) % 186.05/186.62 [4663]~P85(x46631)+E(f775(f775(f83(x46631),x46632),f80(x46631)),x46632) % 186.05/186.62 [4664]~P70(x46641)+E(f775(f775(f83(x46641),x46642),f80(x46641)),x46642) % 186.05/186.62 [4665]~P75(x46651)+E(f775(f775(f83(x46651),x46652),f80(x46651)),x46652) % 186.05/186.62 [4666]~P7(x46661)+E(f775(f775(f43(x46661),x46662),f80(x46661)),x46662) % 186.05/186.62 [4667]~P69(x46671)+E(f775(f775(f3(x46671),x46672),f2(x46671)),x46672) % 186.05/186.62 [4668]~P113(x46681)+E(f775(f775(f283(x46681),x46682),f80(x46681)),x46682) % 186.05/186.62 [4669]~P95(x46691)+E(f775(f775(f103(x46691),x46692),f180(x46691)),x46692) % 186.05/186.62 [4670]~P94(x46701)+E(f775(f775(f104(x46701),x46702),f239(x46701)),x46702) % 186.05/186.62 [4671]~P85(x46711)+E(f775(f775(f242(x46711),x46712),f2(a850)),f80(x46711)) % 186.05/186.62 [4672]~P105(x46721)+E(f775(f775(f242(x46721),x46722),f2(a850)),f80(x46721)) % 186.05/186.62 [4673]~E(x46732,f180(f857(x46731,a844)))+E(f775(f42(x46731),x46732),f2(a850)) % 186.05/186.62 [4684]~P7(x46841)+E(f52(x46841,x46842,f2(x46841)),x46842) % 186.05/186.62 [4692]~P85(x46921)+E(f775(f775(f83(x46921),x46922),f2(x46921)),f2(x46921)) % 186.05/186.62 [4693]~P122(x46931)+E(f775(f775(f83(x46931),x46932),f2(x46931)),f2(x46931)) % 186.05/186.62 [4694]~P7(x46941)+E(f775(f775(f43(x46941),x46942),f2(x46941)),f2(x46941)) % 186.05/186.62 [4695]~P114(x46951)+E(f775(f775(f283(x46951),x46952),f2(x46951)),f2(x46951)) % 186.05/186.62 [4696]~P94(x46961)+E(f775(f775(f103(x46961),x46962),f239(x46961)),f239(x46961)) % 186.05/186.62 [4697]~P95(x46971)+E(f775(f775(f104(x46971),x46972),f180(x46971)),f180(x46971)) % 186.05/186.62 [4698]E(x46981,f183(x46982))+~E(f226(x46982,x46981),f180(f857(x46982,a844))) % 186.05/186.62 [4699]~P7(x46991)+E(f52(x46991,x46992,f80(x46991)),f2(x46991)) % 186.05/186.62 [4700]~P7(x47001)+E(f52(x47001,f2(x47001),x47002),f2(x47001)) % 186.05/186.62 [4751]P36(x47511,x47512)+~E(f602(x47512,x47511),f180(f857(x47511,a844))) % 186.05/186.62 [4752]E(x47521,f115(x47522))+~E(f775(f158(x47522),x47521),f180(f857(x47522,a844))) % 186.05/186.62 [4753]E(x47531,f115(x47532))+~E(f180(f857(x47532,a844)),f775(f158(x47532),x47531)) % 186.05/186.62 [4756]~E(x47561,x47562)+P1(f775(f775(a330,x47561),x47562)) % 186.05/186.62 [4766]P1(x47661)+P1(f775(f775(a335,x47661),x47662)) % 186.05/186.62 [4767]E(x47671,f115(x47672))+E(f775(f775(f153(x47672),x47671),f2(a850)),f775(f131(x47672),x47671)) % 186.05/186.62 [4773]~P1(x47732)+P1(f775(f775(a335,x47731),x47732)) % 186.05/186.62 [4774]~P1(x47742)+P1(f775(f775(a332,x47741),x47742)) % 186.05/186.62 [4775]~P1(x47751)+P1(f775(f775(a332,x47751),x47752)) % 186.05/186.62 [4785]~E(f723(x47852,x47851),f727(x47852,x47851))+P1(f775(f127(x47851),x47852)) % 186.05/186.62 [4793]E(f775(f256(x47931),x47932),f180(f857(x47931,a844)))+P1(f775(x47932,f557(x47932))) % 186.05/186.62 [4794]E(f180(f857(x47941,a844)),f775(f256(x47941),x47942))+P1(f775(x47942,f558(x47942))) % 186.05/186.62 [4858]~P110(x48581)+E(f775(f775(f83(x48581),x48582),f84(x48581,x48582)),f775(f77(x48581),x48582)) % 186.05/186.62 [4870]~E(x48701,f2(a1))+E(f53(x48701,x48702),f775(f775(f241(a1,a1),f2(a1)),f2(a1))) % 186.05/186.62 [4901]~P56(x49011,x49012)+P56(x49011,f775(f278(x49011,x49011),x49012)) % 186.05/186.62 [4918]~E(f775(a30,x49181),f775(f227(a845),x49182))+P1(f775(a26,f775(a27,x49181))) % 186.05/186.62 [4922]E(x49221,x49222)+~P1(f775(f775(a330,x49221),x49222)) % 186.05/186.62 [4926]~P1(f775(a26,x49262))+P1(f775(a26,f35(x49261,x49262))) % 186.05/186.62 [4935]P1(x49351)+~P1(f775(f775(a331,x49352),x49351)) % 186.05/186.62 [4936]P1(x49361)+~P1(f775(f775(a331,x49361),x49362)) % 186.05/186.62 [4940]~P106(x49401)+P1(f775(f775(f232(x49401),x49402),f239(x49401))) % 186.05/186.62 [4941]~P85(x49411)+P1(f775(f775(f279(x49411),x49412),f2(x49411))) % 186.05/186.62 [4945]E(x49451,x49452)+~E(f775(x49451,f373(x49452,x49451)),f775(x49452,f373(x49452,x49451))) % 186.05/186.62 [4979]E(x49791,f2(a850))+E(f211(x49791,f52(a850,x49792,x49791)),f211(x49792,x49791)) % 186.05/186.62 [4984]~P100(x49841)+P18(x49841,f775(f775(f140(x49841),x49842),f115(x49841))) % 186.05/186.62 [4986]E(x49861,f2(a1))+P1(f775(f56(x49862,x49861),f53(x49862,x49861))) % 186.05/186.62 [5003]~E(x50031,x50032)+P1(f775(f775(f233(a850),x50031),f775(a114,x50032))) % 186.05/186.62 [5013]~E(x50131,f2(a850))+P1(f775(f775(f233(a850),x50131),f775(a114,x50132))) % 186.05/186.62 [5023]P1(f775(x50231,x50232))+P1(f775(f775(f232(a1),f2(a1)),f777(x50231))) % 186.05/186.62 [5060]P1(f775(a26,x50601))+~P1(f775(a26,f35(x50602,x50601))) % 186.05/186.62 [5062]P1(f775(a26,x50621))+~P1(f775(a26,f36(x50622,x50621))) % 186.05/186.62 [5064]P1(f775(a26,x50641))+~P1(f775(a26,f36(x50641,x50642))) % 186.05/186.62 [5092]P56(x50921,x50922)+~P56(x50921,f775(f278(x50921,x50921),x50922)) % 186.05/186.62 [5094]~E(f52(a850,x50942,x50941),f2(a850))+E(f775(f775(f83(a850),x50941),f789(x50941,x50942)),x50942) % 186.05/186.62 [5095]~E(f52(a1,x50952,x50951),f2(a1))+E(f775(f775(f83(a1),x50951),f790(x50951,x50952)),x50952) % 186.05/186.62 [5122]~P1(f775(x51221,x51222))+P1(f775(f775(f232(a1),f2(a1)),f760(x51221))) % 186.05/186.62 [5133]E(f775(f775(f3(a850),f775(a107,x51331)),f775(a107,x51332)),f775(a107,x51331))+~P1(f775(a186,x51332)) % 186.05/186.62 [5161]E(f267(x51611,x51612),f80(a101))+~P1(f775(f775(f232(a101),x51611),f80(a101))) % 186.05/186.62 [5250]E(f775(f775(f153(x52501),x52502),f723(x52502,x52501)),f775(f775(f153(x52501),x52502),f727(x52502,x52501)))+P1(f775(f127(x52501),x52502)) % 186.05/186.62 [5292]~P1(f775(x52921,f92(x52922,x52921)))+P1(f775(x52921,f603(x52922,x52921))) % 186.05/186.62 [5355]P58(x53551,x53552)+~P1(f775(f321(x53551,x53552),f580(x53552,x53551))) % 186.05/186.62 [5498]~E(f775(a114,f52(a850,x54981,x54982)),x54982)+E(f52(a850,f775(a114,x54981),x54982),f2(a850)) % 186.05/186.62 [5551]P36(x55511,x55512)+P1(f775(f775(f334(x55511),f682(x55512,x55511)),f683(x55512,x55511))) % 186.05/186.62 [5557]~P2(x55571)+P1(f775(f775(f334(x55571),f775(f102(x55571),x55572)),f176(x55571))) % 186.05/186.62 [5558]~P133(x55581)+P1(f775(f775(f334(x55581),f775(f102(x55581),x55582)),f112(x55581))) % 186.05/186.62 [5559]~P133(x55591)+P1(f775(f775(f334(x55591),f775(f105(x55591),x55592)),f112(x55591))) % 186.05/186.62 [5560]~P88(x55601)+P1(f775(f775(f334(x55601),f775(f106(x55601),x55602)),f112(x55601))) % 186.05/186.62 [5714]E(f775(a114,f52(a850,x57141,x57142)),x57142)+E(f52(a850,f775(a114,x57141),x57142),f775(a114,f52(a850,x57141,x57142))) % 186.05/186.62 [6135]P36(x61351,x61352)+~P1(f775(f775(f334(x61351),f582(x61352,x61351)),f322(x61351,x61352))) % 186.05/186.62 [6169]~P117(x61691)+~P1(f775(f775(f233(x61691),f775(f102(x61691),x61692)),f2(x61691))) % 186.05/186.62 [6170]~P79(x61701)+~P1(f775(f775(f233(x61701),f775(f77(x61701),x61702)),f2(x61701))) % 186.05/186.62 [6262]P1(f775(f775(f233(a1),x62621),f52(a1,x62622,x62621)))+~P1(f775(f775(f233(a1),x62621),f2(a1))) % 186.05/186.62 [6370]E(f775(f775(f302(a850),f775(a114,x63701)),f295(a850,x63702,x63701)),f295(a850,x63702,f775(a114,x63701)))+~P1(f775(f775(f232(a850),x63702),f775(a114,x63701))) % 186.05/186.62 [6597]E(f775(f141(x65971),x65972),x65972)+~P1(f775(f775(f232(a850),f775(f181(f851(x65971)),x65972)),f80(a850))) % 186.05/186.62 [6620]~P79(x66201)+P1(f775(f775(f232(x66201),f775(f81(x66201),f775(f77(x66201),x66202))),f2(x66201))) % 186.05/186.62 [6656]~P36(x66561,x66562)+P36(x66561,f775(f775(f281(x66561,x66561,x66561),x66562),f300(x66561,x66562))) % 186.05/186.62 [6888]~P1(f775(f775(f233(a1),x68882),f2(a1)))+P1(f775(f775(f232(a1),f52(a1,x68881,x68882)),f2(a1))) % 186.05/186.62 [7299]~P2(x72991)+E(f182(x72991,f775(f775(f9(x72991,x72991,x72991),f82(x72991)),f80(x72991)),x72992,f2(x72991)),f775(f102(x72991),x72992)) % 186.05/186.62 [7332]~P118(x73321)+~P1(f775(f775(f233(x73321),f775(f775(f83(x73321),x73322),x73322)),f2(x73321))) % 186.05/186.62 [9847]~P110(x98471)+~P1(f775(f775(f233(x98471),f775(f775(f242(x98471),x98472),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f2(x98471))) % 186.05/186.62 [4565]~E(x45652,f115(x45651))+E(f775(f181(f851(x45651)),x45652),f2(a850)) % 186.05/186.62 [4604]~E(x46041,f2(a850))+E(f775(f775(f82(a850),x46041),x46042),x46042) % 186.05/186.62 [4605]~E(x46052,f2(a850))+E(f775(f775(f83(a850),x46051),x46052),f2(a850)) % 186.05/186.62 [4607]~E(x46071,f2(a850))+E(f775(f775(f83(a850),x46071),x46072),f2(a850)) % 186.05/186.62 [4608]~E(x46082,f2(a1))+E(f775(f775(f43(a1),x46081),x46082),f2(a1)) % 186.05/186.62 [4609]~E(x46092,f2(a850))+E(f775(f775(f242(a850),x46091),x46092),f80(a850)) % 186.05/186.62 [4619]E(x46191,f115(x46192))+~E(f775(f181(f851(x46192)),x46191),f2(a850)) % 186.05/186.62 [4621]~P91(x46211)+E(f775(f775(f83(x46211),x46212),x46212),x46212) % 186.05/186.62 [4623]~P100(x46231)+E(f775(f775(f236(x46231),x46232),x46232),x46232) % 186.05/186.62 [4625]~P100(x46251)+E(f775(f775(f179(x46251),x46252),x46252),x46252) % 186.05/186.62 [4627]~P92(x46271)+E(f775(f775(f103(x46271),x46272),x46272),x46272) % 186.05/186.62 [4628]~P93(x46281)+E(f775(f775(f103(x46281),x46282),x46282),x46282) % 186.05/186.62 [4629]~P93(x46291)+E(f775(f775(f104(x46291),x46292),x46292),x46292) % 186.05/186.62 [4631]~P98(x46311)+E(f775(f775(f104(x46311),x46312),x46312),x46312) % 186.05/186.62 [4647]~P69(x46471)+E(f775(f775(f3(x46471),x46472),x46472),f2(x46471)) % 186.05/186.62 [4658]~P69(x46581)+E(f775(f81(x46581),f775(f81(x46581),x46582)),x46582) % 186.05/186.62 [4659]~P90(x46591)+E(f775(f81(x46591),f775(f81(x46591),x46592)),x46592) % 186.05/186.62 [4676]~E(x46762,f2(a850))+E(f775(f775(f242(a850),x46761),x46762),f775(a114,f2(a850))) % 186.05/186.62 [4708]~P66(x47081)+E(f775(f775(f82(x47081),f2(x47081)),x47082),x47082) % 186.05/186.62 [4709]~P67(x47091)+E(f775(f775(f82(x47091),f2(x47091)),x47092),x47092) % 186.05/186.62 [4710]~P85(x47101)+E(f775(f775(f82(x47101),f2(x47101)),x47102),x47102) % 186.05/186.62 [4711]~P85(x47111)+E(f775(f775(f83(x47111),f80(x47111)),x47112),x47112) % 186.05/186.62 [4712]~P70(x47121)+E(f775(f775(f83(x47121),f80(x47121)),x47122),x47122) % 186.05/186.62 [4713]~P75(x47131)+E(f775(f775(f83(x47131),f80(x47131)),x47132),x47132) % 186.05/186.62 [4714]~P95(x47141)+E(f775(f775(f103(x47141),f180(x47141)),x47142),x47142) % 186.05/186.62 [4715]~P94(x47151)+E(f775(f775(f104(x47151),f239(x47151)),x47152),x47152) % 186.05/186.62 [4732]~P85(x47321)+E(f775(f775(f83(x47321),f2(x47321)),x47322),f2(x47321)) % 186.05/186.62 [4733]~P122(x47331)+E(f775(f775(f83(x47331),f2(x47331)),x47332),f2(x47331)) % 186.05/186.62 [4734]~P7(x47341)+E(f775(f775(f43(x47341),f2(x47341)),x47342),f2(x47341)) % 186.05/186.62 [4735]~P75(x47351)+E(f775(f775(f242(x47351),f80(x47351)),x47352),f80(x47351)) % 186.05/186.62 [4736]~P113(x47361)+E(f775(f775(f283(x47361),f2(x47361)),x47362),f2(x47361)) % 186.05/186.62 [4737]~P94(x47371)+E(f775(f775(f103(x47371),f239(x47371)),x47372),f239(x47371)) % 186.05/186.62 [4738]~P95(x47381)+E(f775(f775(f104(x47381),f180(x47381)),x47382),f180(x47381)) % 186.05/186.62 [4746]E(x47461,f115(x47462))+E(f134(x47462,f775(f142(x47462),x47461)),f775(f131(x47462),x47461)) % 186.05/186.62 [4747]E(x47471,f115(x47472))+E(f775(f131(x47472),f775(f142(x47472),x47471)),f134(x47472,x47471)) % 186.05/186.62 [4748]E(x47481,f2(a850))+~E(f775(f775(f82(a850),x47482),x47481),x47482) % 186.05/186.62 [4754]~P133(x47541)+E(f775(f105(x47541),f775(f102(a1),x47542)),f775(f102(x47541),x47542)) % 186.05/186.62 [4755]~P88(x47551)+E(f775(f105(x47551),f775(f106(a1),x47552)),f775(f106(x47551),x47552)) % 186.05/186.62 [4762]E(x47621,f2(a850))+~E(f775(f775(f82(a850),x47622),x47621),f2(a850)) % 186.05/186.62 [4763]E(x47631,f2(a850))+~E(f775(f775(f82(a850),x47631),x47632),f2(a850)) % 186.05/186.62 [4764]E(x47641,f80(a850))+~E(f775(f775(f83(a850),x47642),x47641),f80(a850)) % 186.05/186.62 [4765]E(x47651,f80(a850))+~E(f775(f775(f83(a850),x47651),x47652),f80(a850)) % 186.05/186.62 [4778]~P110(x47781)+E(f775(f77(x47781),f775(f102(x47781),x47782)),f775(f102(x47781),x47782)) % 186.05/186.62 [4779]~P79(x47791)+E(f775(f77(x47791),f775(f81(x47791),x47792)),f775(f77(x47791),x47792)) % 186.05/186.62 [4780]~P79(x47801)+E(f775(f77(x47801),f775(f77(x47801),x47802)),f775(f77(x47801),x47802)) % 186.05/186.62 [4781]~P66(x47811)+E(f775(f155(x47811),f775(f142(x47811),x47812)),f775(f155(x47811),x47812)) % 186.05/186.62 [4786]~E(x47861,f775(a114,f2(a850)))+E(f775(f775(f242(a850),x47861),x47862),f775(a114,f2(a850))) % 186.05/186.62 [4796]~P69(x47961)+E(f775(f775(f3(x47961),f2(x47961)),x47962),f775(f81(x47961),x47962)) % 186.05/186.62 [4797]~E(x47972,f2(a850))+E(f130(a850,f775(f294(a850,x47971),x47972)),f115(a850)) % 186.05/186.62 [4806]~P88(x48061)+E(f775(f775(f82(x48061),x48062),f775(f106(x48061),a85)),x48062) % 186.05/186.62 [4807]E(x48071,f2(a1))+E(f54(f775(f77(a1),x48072),f775(f77(a1),x48071)),f60(x48072,x48071)) % 186.05/186.62 [4819]~E(x48191,x48192)+P1(f775(f775(f232(a850),x48191),x48192)) % 186.05/186.62 [4823]~E(x48231,x48232)+P1(f775(f775(f279(a850),x48231),x48232)) % 186.05/186.62 [4830]~E(x48301,f2(a101))+E(f775(f775(f82(a850),f775(a22,x48301)),x48302),x48302) % 186.05/186.62 [4831]~E(f775(f106(a1),x48312),f775(f102(a1),x48311))+E(x48311,f775(a107,f775(f106(a1),x48312))) % 186.05/186.62 [4840]~P10(x48401)+P10(f775(f775(f242(a1),x48401),x48402)) % 186.05/186.62 [4841]~P69(x48411)+E(f775(f775(f82(x48411),x48412),f775(f81(x48411),x48412)),f2(x48411)) % 186.05/186.62 [4842]~P90(x48421)+E(f775(f775(f103(x48421),x48422),f775(f81(x48421),x48422)),f239(x48421)) % 186.05/186.62 [4843]~P90(x48431)+E(f775(f775(f104(x48431),x48432),f775(f81(x48431),x48432)),f180(x48431)) % 186.05/186.62 [4867]E(x48671,f2(a850))+~E(f775(f81(a1),f775(f102(a1),x48672)),f775(f102(a1),x48671)) % 186.05/186.62 [4868]E(x48681,f2(a850))+~E(f775(f81(a1),f775(f102(a1),x48681)),f775(f102(a1),x48682)) % 186.05/186.62 [4878]E(f188(x48781,x48782),f2(a1))+P1(f775(f775(f232(a1),x48782),x48781)) % 186.05/186.62 [4879]E(f238(x48791,x48792),f2(a101))+P1(f775(f775(f233(a101),x48791),x48792)) % 186.05/186.62 [4880]E(f163(x48801,x48802),f115(a1))+P1(f775(f775(f232(a1),x48801),x48802)) % 186.05/186.62 [4893]E(x48931,f775(a114,f2(a850)))+~E(f775(f775(f83(a850),x48932),x48931),f775(a114,f2(a850))) % 186.05/186.62 [4894]E(x48941,f775(a114,f2(a850)))+~E(f775(f775(f83(a850),x48941),x48942),f775(a114,f2(a850))) % 186.05/186.62 [4895]~P103(x48951)+P1(f775(f775(f232(x48951),x48952),x48952)) % 186.05/186.62 [4896]~P85(x48961)+P1(f775(f775(f279(x48961),x48962),x48962)) % 186.05/186.62 [4899]~P88(x48991)+E(f775(f775(f83(x48991),x48992),f775(f106(x48991),a99)),f775(f81(x48991),x48992)) % 186.05/186.62 [4915]~P133(x49151)+E(f775(f81(x49151),f775(f105(x49151),x49152)),f775(f105(x49151),f775(f81(a1),x49152))) % 186.05/186.62 [4916]~P88(x49161)+E(f775(f81(x49161),f775(f106(x49161),x49162)),f775(f106(x49161),f775(f81(a1),x49162))) % 186.05/186.62 [4950]~E(x49501,f775(a114,x49502))+P1(f775(f775(f233(a850),f2(a850)),x49501)) % 186.05/186.62 [4967]~P100(x49671)+E(f775(f81(f857(x49671,a844)),f775(f257(x49671),x49672)),f775(f258(x49671),x49672)) % 186.05/186.62 [4968]~P100(x49681)+E(f775(f81(f857(x49681,a844)),f775(f296(x49681),x49682)),f775(f293(x49681),x49682)) % 186.05/186.62 [4969]~P100(x49691)+E(f775(f81(f857(x49691,a844)),f775(f293(x49691),x49692)),f775(f296(x49691),x49692)) % 186.05/186.62 [4970]~P100(x49701)+E(f775(f81(f857(x49701,a844)),f775(f258(x49701),x49702)),f775(f257(x49701),x49702)) % 186.05/186.62 [4978]~E(f775(f102(a1),x49782),x49781)+P1(f775(f775(f232(a1),f2(a1)),x49781)) % 186.05/186.62 [4985]~E(x49852,f2(a1))+E(f60(x49851,x49852),f775(f775(f241(a1,a1),f2(a1)),f775(f77(a1),x49851))) % 186.05/186.62 [4987]~P101(x49871)+P1(f775(f775(f232(x49871),f180(x49871)),x49872)) % 186.05/186.62 [4988]~P85(x49881)+P1(f775(f775(f279(x49881),f80(x49881)),x49882)) % 186.05/186.62 [5018]E(x50181,x50182)+~E(f775(f775(f82(a1),x50181),x50181),f775(f775(f82(a1),x50182),x50182)) % 186.05/186.62 [5022]~P1(f775(x50221,x50222))+P1(f775(x50221,f775(a107,f760(x50221)))) % 186.05/186.62 [5048]~P110(x50481)+E(f775(f775(f83(x50481),f84(x50481,x50482)),f775(f77(x50481),x50482)),x50482) % 186.05/186.62 [5049]E(x50491,x50492)+~P1(f775(f775(f187(a25),x50491),x50492)) % 186.05/186.62 [5058]~E(x50582,f2(a850))+E(f87(f856(a850,a850),f55(x50581,x50582)),f775(f775(f241(a850,a850),f2(a850)),x50581)) % 186.05/186.62 [5069]~E(x50691,x50692)+~P1(f775(f775(f233(a850),x50691),x50692)) % 186.05/186.62 [5070]~E(x50701,x50702)+~P1(f775(f775(f233(a1),x50701),x50702)) % 186.05/186.62 [5073]~P2(x50731)+E(f775(f775(f82(x50731),f80(x50731)),f775(f102(x50731),x50732)),f775(f102(x50731),f775(a114,x50732))) % 186.05/186.62 [5077]~E(x50771,f2(a850))+~P1(f775(f775(f233(a850),x50772),x50771)) % 186.05/186.62 [5090]E(f775(f42(x50901),f775(f158(x50901),x50902)),f775(f181(f851(x50901)),x50902))+~P1(f775(f127(x50901),x50902)) % 186.05/186.62 [5099]~P1(f775(x50991,f728(x50991)))+P1(f775(x50991,f775(f102(a1),x50992))) % 186.05/186.62 [5111]E(f238(x51111,x51112),x51112)+~P1(f775(f775(f233(a101),x51111),x51112)) % 186.05/186.62 [5113]E(f267(x51131,x51132),f80(a101))+~P1(f775(f775(f233(a101),x51132),x51131)) % 186.05/186.62 [5114]E(f163(x51141,x51142),f115(a1))+~P1(f775(f775(f233(a1),x51142),x51141)) % 186.05/186.62 [5117]~P99(x51171)+E(f295(x51171,x51172,x51172),f775(f775(f302(x51171),x51172),f180(f857(x51171,a844)))) % 186.05/186.62 [5136]~E(f775(f775(f3(a850),x51361),x51362),f2(a850))+P1(f775(f775(f232(a850),x51361),x51362)) % 186.05/186.62 [5162]~P103(x51621)+~P1(f775(f775(f233(x51621),x51622),x51622)) % 186.05/186.62 [5165]~E(f52(a1,x51651,x51652),f2(a1))+E(f52(a1,x51651,f775(f81(a1),x51652)),f2(a1)) % 186.05/186.62 [5167]~E(f52(a1,x51671,x51672),f2(a1))+E(f52(a1,f775(f81(a1),x51671),x51672),f2(a1)) % 186.05/186.62 [5174]E(f775(f294(a850,x51741),f775(a114,x51742)),f180(f857(a850,a844)))+P1(f775(f775(f232(a850),x51741),x51742)) % 186.05/186.62 [5191]E(f130(a850,f775(f294(a850,x51911),x51912)),f115(a850))+P1(f775(f775(f233(a850),x51911),x51912)) % 186.05/186.62 [5196]~E(f775(f42(x51961),f775(f158(x51961),x51962)),f775(f181(f851(x51961)),x51962))+P1(f775(f127(x51961),x51962)) % 186.05/186.62 [5200]~P1(f775(f127(x52001),x52002))+P1(f775(f127(x52001),f775(f141(x52001),x52002))) % 186.05/186.62 [5201]~P1(f775(f127(x52011),x52012))+P1(f775(f127(x52011),f775(f157(x52011),x52012))) % 186.05/186.62 [5202]~P1(f775(f127(x52021),x52022))+P1(f775(f127(x52021),f775(f142(x52021),x52022))) % 186.05/186.62 [5210]P1(f775(x52101,x52102))+~P1(f775(x52101,f775(a107,f777(x52101)))) % 186.05/186.62 [5211]P1(f775(f775(f232(a850),x52112),x52111))+P1(f775(f775(f232(a850),x52111),x52112)) % 186.05/186.62 [5212]P1(f775(f775(f232(a1),x52122),x52121))+P1(f775(f775(f232(a1),x52121),x52122)) % 186.05/186.62 [5214]~P79(x52141)+P1(f775(f775(f232(x52141),x52142),f775(f77(x52141),x52142))) % 186.05/186.62 [5217]P1(f775(x52171,f729(x52171)))+~P1(f775(x52171,f775(f102(a1),x52172))) % 186.05/186.62 [5241]E(f775(f775(f43(a850),x52411),x52412),f2(a850))+~P1(f775(f775(f233(a850),x52411),x52412)) % 186.05/186.62 [5243]E(f775(f775(f3(a850),x52431),x52432),f2(a850))+~P1(f775(f775(f232(a850),x52431),x52432)) % 186.05/186.62 [5260]E(f52(a850,x52601,x52602),x52601)+~P1(f775(f775(f233(a850),x52601),x52602)) % 186.05/186.62 [5267]E(f52(a1,x52671,f775(f81(a1),x52672)),f284(x52671,x52672))+P1(f775(f775(f232(a1),f2(a1)),x52672)) % 186.05/186.62 [5280]E(f775(f775(f3(a1),x52801),x52802),f188(x52801,x52802))+~P1(f775(f775(f232(a1),x52802),x52801)) % 186.05/186.62 [5298]P1(f775(f775(f232(a1),f2(a1)),f728(x52981)))+P1(f775(x52981,f775(f102(a1),x52982))) % 186.05/186.62 [5311]~P117(x53111)+P1(f775(f775(f232(x53111),f2(x53111)),f775(f102(x53111),x53112))) % 186.05/186.62 [5312]~P79(x53121)+P1(f775(f775(f232(x53121),f2(x53121)),f775(f77(x53121),x53122))) % 186.05/186.62 [5340]E(f775(f775(f82(a850),x53401),f681(x53402,x53401)),x53402)+~P1(f775(f775(f232(a850),x53401),x53402)) % 186.05/186.62 [5341]E(f775(f775(f82(a850),x53411),f604(x53412,x53411)),x53412)+~P1(f775(f775(f233(a850),x53411),x53412)) % 186.05/186.62 [5353]~E(f775(f106(a1),x53531),f775(f102(a1),x53532))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x53531))) % 186.05/186.62 [5356]E(f295(a1,x53561,x53562),f180(f857(a1,a844)))+~P1(f775(f775(f233(a1),x53562),x53561)) % 186.05/186.62 [5359]~P110(x53591)+E(f775(f775(f83(x53591),f775(f77(x53591),x53592)),f775(f77(x53591),x53592)),f775(f775(f83(x53591),x53592),x53592)) % 186.05/186.62 [5364]E(f130(a850,f775(f294(a850,x53641),f775(a114,x53642))),f115(a850))+P1(f775(f775(f232(a850),x53641),x53642)) % 186.05/186.62 [5368]E(f775(f775(f43(a1),x53681),x53682),f285(x53681,x53682))+~P1(f775(f775(f232(a1),f2(a1)),x53682)) % 186.05/186.62 [5388]P1(f775(f127(x53881),x53882))+~P1(f775(f127(x53881),f775(f141(x53881),x53882))) % 186.05/186.62 [5389]P1(f775(f127(x53891),x53892))+~P1(f775(f127(x53891),f775(f142(x53891),x53892))) % 186.05/186.62 [5412]P1(f775(f63(a850),x54121))+P1(f775(f775(f334(a850),f375(x54121,x54122)),x54121)) % 186.05/186.62 [5413]P1(f775(f63(a850),x54131))+P1(f775(f775(f334(a850),f400(x54131,x54132)),x54131)) % 186.05/186.62 [5414]P1(f775(f775(f233(a850),x54142),f775(a114,x54141)))+P1(f775(f775(f233(a850),x54141),x54142)) % 186.05/186.62 [5415]E(f52(a1,x54151,x54152),f284(x54151,x54152))+~P1(f775(f775(f232(a1),f2(a1)),x54152)) % 186.05/186.62 [5418]E(f130(a850,f775(f294(a850,x54181),x54182)),f115(a850))+~P1(f775(f775(f232(a850),x54182),x54181)) % 186.05/186.62 [5419]~P77(x54191)+E(f775(f303(x54191,x54191,f81(x54191)),f775(f257(x54191),x54192)),f775(f296(x54191),f775(f81(x54191),x54192))) % 186.05/186.62 [5420]~P77(x54201)+E(f775(f303(x54201,x54201,f81(x54201)),f775(f296(x54201),x54202)),f775(f257(x54201),f775(f81(x54201),x54202))) % 186.05/186.62 [5421]~P77(x54211)+E(f775(f303(x54211,x54211,f81(x54211)),f775(f293(x54211),x54212)),f775(f258(x54211),f775(f81(x54211),x54212))) % 186.05/186.62 [5422]~P77(x54221)+E(f775(f303(x54221,x54221,f81(x54221)),f775(f258(x54221),x54222)),f775(f293(x54221),f775(f81(x54221),x54222))) % 186.05/186.62 [5433]E(x54331,f180(f857(x54332,a844)))+P1(f775(f775(f334(x54332),f402(x54331,x54332)),x54331)) % 186.05/186.62 [5434]E(x54341,f180(f857(x54342,a844)))+P1(f775(f775(f334(x54342),f403(x54341,x54342)),x54341)) % 186.05/186.62 [5445]~P1(f775(f775(f233(a850),x54451),x54452))+P1(f775(f775(f232(a850),x54451),x54452)) % 186.05/186.62 [5446]~P1(f775(f775(f233(a1),x54461),x54462))+P1(f775(f775(f232(a1),x54461),x54462)) % 186.05/186.62 [5458]E(f54(x54581,x54582),f775(f775(f241(a1,a1),f2(a1)),x54581))+~P1(f775(f775(f233(a1),x54581),x54582)) % 186.05/186.62 [5459]E(f210(f775(f81(a1),x54591),f775(f81(a1),x54592)),f210(x54591,x54592))+~P1(f775(f775(f233(a1),x54592),f2(a1))) % 186.05/186.62 [5472]E(x54721,x54722)+~E(f775(a5,f775(a114,f775(a22,x54721))),f775(a5,f775(a114,f775(a22,x54722)))) % 186.05/186.62 [5477]E(f54(x54771,x54772),f775(f775(f241(a1,a1),f2(a1)),x54771))+~P1(f775(f775(f232(a1),x54772),f2(a1))) % 186.05/186.62 [5504]E(f52(a850,f775(f106(a850),x55041),f775(f106(a850),x55042)),f2(a850))+~P1(f775(a186,f775(f106(a1),x55041))) % 186.05/186.62 [5518]P1(f775(f775(f232(a1),f2(a1)),f729(x55181)))+~P1(f775(x55181,f775(f102(a1),x55182))) % 186.05/186.62 [5549]P38(f295(a1,x55491,x55492))+~P1(f775(f775(f232(a1),f2(a1)),x55491)) % 186.05/186.62 [5553]~P1(f775(f63(x55531),x55532))+P1(f775(f63(f857(x55531,a844)),f775(f301(x55531),x55532))) % 186.05/186.62 [5566]E(f775(f775(f82(a1),x55661),f775(f102(a1),f791(x55662,x55661))),x55662)+~P1(f775(f775(f232(a1),x55661),x55662)) % 186.05/186.62 [5574]P1(f775(f775(f232(a850),x55741),x55742))+P1(f775(f775(f232(a850),f775(a114,x55742)),x55741)) % 186.05/186.62 [5619]E(f775(f775(f43(a850),f775(f106(a850),x56191)),f775(f106(a850),x56192)),f2(a850))+~P1(f775(a186,f775(f106(a1),x56191))) % 186.05/186.62 [5620]E(f775(f775(f83(a850),f775(f106(a850),x56201)),f775(f106(a850),x56202)),f2(a850))+~P1(f775(f775(f233(a1),x56201),a85)) % 186.05/186.62 [5622]P1(f775(f775(f233(a850),x56221),f775(a114,x56222)))+~P1(f775(f775(f233(a850),x56221),x56222)) % 186.05/186.62 [5624]P1(f775(f775(f233(a850),x56241),f775(a114,x56242)))+~P1(f775(f775(f232(a850),x56241),x56242)) % 186.05/186.62 [5626]P1(f775(f775(f232(a850),x56261),f775(a114,x56262)))+~P1(f775(f775(f232(a850),x56261),x56262)) % 186.05/186.62 [5627]~E(x56271,x56272)+P1(f775(f775(f233(a1),x56271),f775(f775(f82(a1),x56272),f80(a1)))) % 186.05/186.62 [5630]E(f52(a1,x56301,x56302),f2(a1))+E(f775(f775(f3(a1),x56302),f52(a1,x56301,x56302)),f52(a1,f775(f81(a1),x56301),x56302)) % 186.05/186.62 [5638]E(x56381,f115(x56382))+P1(f775(f775(f334(x56382),f134(x56382,x56381)),f775(f158(x56382),x56381))) % 186.05/186.62 [5650]E(f87(f856(a850,a850),f55(x56501,x56502)),f775(f775(f241(a850,a850),f2(a850)),x56501))+~P1(f775(f775(f233(a850),x56501),x56502)) % 186.05/186.62 [5690]E(f775(f775(f82(a850),f775(f106(a850),x56901)),f775(f106(a850),x56902)),f775(f106(a850),x56902))+~P1(f775(f775(f233(a1),x56901),a85)) % 186.05/186.62 [5691]E(f775(f775(f3(a850),f775(f106(a850),x56911)),f775(f106(a850),x56912)),f775(f106(a850),x56911))+~P1(f775(f775(f233(a1),x56912),a85)) % 186.05/186.62 [5696]E(f775(a114,f775(f775(f82(a850),x56961),f581(x56962,x56961))),x56962)+~P1(f775(f775(f233(a850),x56961),x56962)) % 186.05/186.62 [5697]E(f775(a114,f775(f775(f82(a850),x56971),f605(x56972,x56971))),x56972)+~P1(f775(f775(f233(a850),x56971),x56972)) % 186.05/186.62 [5704]~P1(f775(f775(f279(a1),x57041),x57042))+P1(f775(f775(f279(a1),x57041),f775(f81(a1),x57042))) % 186.05/186.62 [5705]P1(f775(f775(f233(a850),f2(a850)),f604(x57051,x57052)))+~P1(f775(f775(f233(a850),x57052),x57051)) % 186.05/186.62 [5724]P1(f775(x57241,x57242))+~P1(f775(x57241,f775(a91,f606(x57242,x57241)))) % 186.05/186.62 [5732]~P1(f775(f775(f233(a850),x57321),f775(a114,x57322)))+P1(f775(f775(f232(a850),x57321),x57322)) % 186.05/186.62 [5781]E(f775(f775(f302(a850),x57811),f775(f294(a850,x57812),x57811)),f775(f294(a850,x57812),f775(a114,x57811)))+~P1(f775(f775(f232(a850),x57812),x57811)) % 186.05/186.62 [5786]E(x57861,f115(x57862))+E(f775(f775(f125(x57862),f116(x57862,x57861)),f775(f775(f140(x57862),f134(x57862,x57861)),f115(x57862))),x57861) % 186.05/186.62 [5797]P1(f775(f63(x57971),x57972))+~P1(f775(f775(f233(a850),f2(a850)),f775(f42(x57971),x57972))) % 186.05/186.62 [5801]~E(x58011,f180(f857(x58012,a844)))+~P1(f775(f775(f233(a850),f2(a850)),f775(f42(x58012),x58011))) % 186.05/186.62 [5811]~P1(f775(f775(f233(a850),x58111),x58112))+P1(f775(f775(f232(a850),f775(a114,x58111)),x58112)) % 186.05/186.62 [5819]E(x58191,f115(x58192))+P1(f775(f775(f334(x58192),f775(f131(x58192),x58191)),f775(f158(x58192),x58191))) % 186.05/186.62 [5825]~P117(x58251)+P1(f775(f775(f233(x58251),x58252),f775(f775(f82(x58251),x58252),f80(x58251)))) % 186.05/186.62 [5827]~P79(x58271)+P1(f775(f775(f232(x58271),f775(f81(x58271),x58272)),f775(f77(x58271),x58272))) % 186.05/186.62 [5839]P1(f775(f775(f279(a1),x58391),x58392))+~P1(f775(f775(f279(a1),x58391),f775(f81(a1),x58392))) % 186.05/186.62 [5840]~E(x58401,x58402)+E(f282(a850,f279(a850),x58401,x58402),f775(f775(f302(a850),x58401),f180(f857(a850,a844)))) % 186.05/186.62 [5858]P1(f775(f63(a850),x58581))+~P1(f775(f775(f233(a850),f400(x58581,x58582)),x58582)) % 186.05/186.62 [5859]P1(f775(f63(a850),x58591))+~P1(f775(f775(f232(a850),f375(x58591,x58592)),x58592)) % 186.05/186.62 [5863]~P1(f775(f63(f856(x58631,x58631)),x58632))+P1(f775(f63(x58631),f775(f276(x58631),x58632))) % 186.05/186.62 [5914]E(f282(a850,f279(a850),x59141,x59142),f180(f857(a850,a844)))+P1(f775(f775(f279(a850),x59141),x59142)) % 186.05/186.62 [5920]~P1(f775(f775(f233(a850),x59202),f775(a114,x59201)))+~P1(f775(f775(f233(a850),x59201),x59202)) % 186.05/186.62 [5921]~P99(x59211)+E(f775(f775(f104(f857(x59211,a844)),f775(f293(x59211),x59212)),f775(f258(x59211),x59212)),f775(f775(f302(x59211),x59212),f180(f857(x59211,a844)))) % 186.05/186.62 [5934]P1(f775(f63(x59341),x59342))+~P1(f775(f63(f857(x59341,a844)),f775(f301(x59341),x59342))) % 186.05/186.62 [5958]P1(f775(f775(f233(a850),f775(a114,x59581)),f775(a114,x59582)))+~P1(f775(f775(f233(a850),x59581),x59582)) % 186.05/186.62 [5959]P1(f775(f775(f233(a850),f775(a22,x59591)),f775(a22,x59592)))+~P1(f775(f775(f233(a101),x59591),x59592)) % 186.05/186.62 [5960]P1(f775(f775(f233(a101),f775(a5,x59601)),f775(a5,x59602)))+~P1(f775(f775(f233(a850),x59601),x59602)) % 186.05/186.62 [5961]P1(f775(f775(f232(a850),f775(a114,x59611)),f775(a114,x59612)))+~P1(f775(f775(f232(a850),x59611),x59612)) % 186.05/186.62 [5962]P1(f775(f775(f232(a850),f775(a22,x59621)),f775(a22,x59622)))+~P1(f775(f775(f232(a101),x59621),x59622)) % 186.05/186.62 [5963]P1(f775(f775(f232(a101),f775(a5,x59631)),f775(a5,x59632)))+~P1(f775(f775(f232(a850),x59631),x59632)) % 186.05/186.62 [5966]E(x59661,x59662)+~E(f775(f303(a850,a1,f102(a1)),x59661),f775(f303(a850,a1,f102(a1)),x59662)) % 186.05/186.62 [5982]P1(f775(f775(f233(a850),x59821),x59822))+~P1(f775(f775(f233(a850),f775(a114,x59821)),x59822)) % 186.05/186.62 [5985]P1(f775(f775(f233(a850),x59851),x59852))+~P1(f775(f775(f232(a850),f775(a114,x59851)),x59852)) % 186.05/186.62 [5986]P1(f775(f775(f232(a850),x59861),x59862))+~P1(f775(f775(f232(a850),f775(a114,x59861)),x59862)) % 186.05/186.62 [6003]E(f52(a1,x60031,x60032),f2(a1))+E(f775(f775(f3(a1),f52(a1,x60031,x60032)),x60032),f52(a1,x60031,f775(f81(a1),x60032))) % 186.05/186.62 [6074]E(f775(f42(f857(x60741,a844)),f775(f301(x60741),x60742)),f775(f775(f242(a850),f775(a114,f775(a114,f2(a850)))),f775(f42(x60741),x60742)))+~P1(f775(f63(x60741),x60742)) % 186.05/186.62 [6077]E(x60771,f115(x60772))+E(f775(f775(f153(x60772),x60771),f775(f775(f3(a850),f775(f181(f851(x60772)),x60771)),f80(a850))),f134(x60772,x60771)) % 186.05/186.62 [6101]E(x61011,f115(x61012))+E(f775(f775(f125(x61012),f775(f157(x61012),x61011)),f775(f775(f140(x61012),f775(f131(x61012),x61011)),f115(x61012))),f775(f141(x61012),x61011)) % 186.05/186.62 [6132]~P1(f775(f63(x61321),f44(f857(x61321,a844),x61322)))+P1(f775(f63(f857(x61321,a844)),x61322)) % 186.05/186.62 [6153]P1(f775(f775(f232(a850),f775(f106(a850),x61531)),f775(f106(a850),x61532)))+~P1(f775(f775(f232(a1),x61531),a85)) % 186.05/186.62 [6173]~P1(f775(f775(f233(a1),x61731),x61732))+P1(f775(f775(f233(a1),x61731),f775(f775(f82(a1),x61732),f80(a1)))) % 186.05/186.62 [6174]~P1(f775(f775(f232(a1),x61741),x61742))+P1(f775(f775(f233(a1),x61741),f775(f775(f82(a1),x61742),f80(a1)))) % 186.05/186.62 [6175]~P1(f775(f775(f233(a1),x61751),x61752))+P1(f775(f775(f232(a1),x61751),f775(f775(f3(a1),x61752),f80(a1)))) % 186.05/186.62 [6178]~P1(f775(f775(f233(a850),x61781),x61782))+P1(f775(f775(f233(a1),f775(f102(a1),x61781)),f775(f102(a1),x61782))) % 186.05/186.62 [6179]~P1(f775(f775(f233(a1),x61791),x61792))+P1(f775(f775(f233(a1),f775(f106(a1),x61791)),f775(f106(a1),x61792))) % 186.05/186.62 [6180]~P1(f775(f775(f232(a1),x61801),x61802))+P1(f775(f775(f232(a850),f775(f106(a850),x61801)),f775(f106(a850),x61802))) % 186.05/186.62 [6182]~P1(f775(f775(f232(a850),x61821),x61822))+P1(f775(f775(f232(a1),f775(f102(a1),x61821)),f775(f102(a1),x61822))) % 186.05/186.62 [6183]~P1(f775(f775(f232(a1),x61831),x61832))+P1(f775(f775(f232(a1),f775(f106(a1),x61831)),f775(f106(a1),x61832))) % 186.05/186.62 [6185]~P1(f775(f775(f279(a850),x61851),x61852))+P1(f775(f775(f279(a1),f775(f102(a1),x61851)),f775(f102(a1),x61852))) % 186.05/186.62 [6201]~P1(f775(f775(f232(a850),x62011),x62012))+~P1(f775(f775(f232(a850),f775(a114,x62012)),x62011)) % 186.05/186.62 [6249]~P1(f775(f775(f233(a850),f775(a114,x62491)),f775(a114,x62492)))+P1(f775(f775(f233(a850),x62491),x62492)) % 186.05/186.62 [6250]~P1(f775(f775(f233(a101),f775(a5,x62501)),f775(a5,x62502)))+P1(f775(f775(f233(a850),x62501),x62502)) % 186.05/186.62 [6251]~P1(f775(f775(f233(a850),f775(a107,x62511)),f775(a107,x62512)))+P1(f775(f775(f233(a1),x62511),x62512)) % 186.05/186.62 [6252]~P1(f775(f775(f233(a850),f775(a22,x62521)),f775(a22,x62522)))+P1(f775(f775(f233(a101),x62521),x62522)) % 186.05/186.62 [6253]~P1(f775(f775(f232(a850),f775(a114,x62531)),f775(a114,x62532)))+P1(f775(f775(f232(a850),x62531),x62532)) % 186.05/186.62 [6254]~P1(f775(f775(f232(a101),f775(a5,x62541)),f775(a5,x62542)))+P1(f775(f775(f232(a850),x62541),x62542)) % 186.05/186.62 [6255]~P1(f775(f775(f232(a850),f775(a22,x62551)),f775(a22,x62552)))+P1(f775(f775(f232(a101),x62551),x62552)) % 186.05/186.62 [6299]~P1(f775(f775(f233(a850),f775(a107,x62992)),f775(a107,x62991)))+P1(f775(f775(f233(a1),f2(a1)),x62991)) % 186.05/186.62 [6310]~E(f52(a1,f775(f106(a1),x63102),f775(f106(a1),x63101)),f2(a1))+P1(f775(f775(f279(a1),f775(f106(a1),x63101)),f775(f106(a1),x63102))) % 186.05/186.62 [6329]P1(f775(f775(f232(a1),f2(a1)),f52(a1,x63291,x63292)))+~P1(f775(f775(f233(a1),f2(a1)),x63292)) % 186.05/186.62 [6498]P36(x64981,x64982)+~E(f775(f775(f281(x64981,x64981,x64981),x64982),x64982),f180(f857(f856(x64981,x64981),a844))) % 186.05/186.62 [6514]~P36(x65141,x65142)+P36(x65141,f775(f775(f281(x65141,x65141,x65141),x65142),x65142)) % 186.05/186.62 [6526]P1(f775(f775(f233(a1),x65261),x65262))+~P1(f775(f775(f232(a1),x65261),f775(f775(f3(a1),x65262),f80(a1)))) % 186.05/186.62 [6527]P1(f775(f775(f232(a1),x65271),x65272))+~P1(f775(f775(f233(a1),x65271),f775(f775(f82(a1),x65272),f80(a1)))) % 186.05/186.62 [6530]P1(f775(f775(f233(a850),x65301),x65302))+~P1(f775(f775(f233(a1),f775(f102(a1),x65301)),f775(f102(a1),x65302))) % 186.05/186.62 [6531]P1(f775(f775(f233(a1),x65311),x65312))+~P1(f775(f775(f233(a850),f775(f106(a850),x65311)),f775(f106(a850),x65312))) % 186.05/186.62 [6532]P1(f775(f775(f233(a1),x65321),x65322))+~P1(f775(f775(f233(a1),f775(f106(a1),x65321)),f775(f106(a1),x65322))) % 186.05/186.62 [6534]P1(f775(f775(f232(a850),x65341),x65342))+~P1(f775(f775(f232(a1),f775(f102(a1),x65341)),f775(f102(a1),x65342))) % 186.05/186.62 [6535]P1(f775(f775(f232(a1),x65351),x65352))+~P1(f775(f775(f232(a1),f775(f106(a1),x65351)),f775(f106(a1),x65352))) % 186.05/186.62 [6537]P1(f775(f775(f279(a850),x65371),x65372))+~P1(f775(f775(f279(a1),f775(f102(a1),x65371)),f775(f102(a1),x65372))) % 186.05/186.62 [6593]E(f52(a1,f775(f106(a1),x65931),f775(f106(a1),x65932)),f2(a1))+~P1(f775(f775(f279(a1),f775(f106(a1),x65932)),f775(f106(a1),x65931))) % 186.05/186.62 [6608]~E(f282(a850,f279(a850),x66081,x66082),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x66081),x66082)) % 186.05/186.62 [6636]~E(f769(x66362,x66361),f115(x66361))+E(f775(f132(f851(x66361),f851(x66361),f125(x66361),f115(x66361)),x66362),f115(x66361)) % 186.05/186.62 [6637]~E(f770(x66372,x66371),f115(x66371))+E(f775(f132(f851(x66371),f851(x66371),f125(x66371),f115(x66371)),x66372),f115(x66371)) % 186.05/186.62 [6644]~P9(x66441)+E(f775(f132(x66441,x66441,f104(x66441),f239(x66441)),x66442),f45(x66441,f775(f158(x66441),x66442))) % 186.05/186.62 [6645]~P9(x66451)+E(f775(f132(x66451,x66451,f103(x66451),f180(x66451)),x66452),f44(x66451,f775(f158(x66451),x66452))) % 186.05/186.62 [6657]E(x66571,f2(a101))+E(f775(f775(f82(a850),f775(a22,f775(f775(f3(a101),x66571),f80(a101)))),f775(a114,x66572)),f775(f775(f82(a850),f775(a22,x66571)),x66572)) % 186.05/186.62 [6709]P1(f775(f775(f233(a1),f775(f775(f3(a1),x67091),x67092)),f2(a1)))+~P1(f775(f775(f233(a1),x67091),x67092)) % 186.05/186.62 [6737]~P100(x67371)+E(f775(f775(f103(f857(x67371,a844)),f775(f775(f302(x67371),x67372),f180(f857(x67371,a844)))),f775(f296(x67371),x67372)),f775(f258(x67371),x67372)) % 186.05/186.62 [6819]~P58(x68191,x68192)+P36(x68191,f775(f256(f856(x68191,x68191)),f775(f251(x68191,x68191,a844),x68192))) % 186.05/186.62 [6820]~P58(x68201,x68202)+P56(x68201,f775(f256(f856(x68201,x68201)),f775(f251(x68201,x68201,a844),x68202))) % 186.05/186.62 [6821]E(x68211,f180(f857(x68212,a844)))+~P1(f775(f775(f232(f857(x68212,a844)),x68211),f180(f857(x68212,a844)))) % 186.05/186.62 [6906]~P1(f775(f775(f233(a850),f2(a850)),x69062))+P1(f775(f775(f233(a850),f52(a850,x69061,x69062)),x69062)) % 186.05/186.62 [6908]~P1(f775(f775(f233(a1),f2(a1)),x69082))+P1(f775(f775(f233(a1),f52(a1,x69081,x69082)),x69082)) % 186.05/186.62 [6909]~P1(f775(f775(f233(a850),f2(a850)),x69092))+P1(f775(f775(f232(a850),f52(a850,x69091,x69092)),x69092)) % 186.05/186.62 [6910]~P1(f775(f775(f232(a1),f2(a1)),x69101))+P1(f775(f775(f232(a1),f52(a1,x69101,x69102)),x69101)) % 186.05/186.62 [6982]~P99(x69821)+E(f775(f775(f3(f857(x69821,a844)),f775(f775(f302(x69821),x69822),f180(f857(x69821,a844)))),f775(f257(x69821),x69822)),f775(f775(f302(x69821),x69822),f180(f857(x69821,a844)))) % 186.05/186.62 [7060]~P49(x70601,x70602)+P47(x70601,f239(f857(x70601,a844)),f775(f256(f856(x70601,x70601)),f775(f251(x70601,x70601,a844),x70602))) % 186.05/186.62 [7061]P1(f775(x70611,x70612))+P1(f775(f775(f334(f857(f856(a850,a850),a844)),f606(x70612,x70611)),a100)) % 186.05/186.62 [7104]E(f775(f775(f125(a850),f130(a850,f775(f294(a850,x71041),x71042))),f775(f775(f140(a850),x71042),f115(a850))),f130(a850,f775(f294(a850,x71041),f775(a114,x71042))))+~P1(f775(f775(f232(a850),x71041),x71042)) % 186.05/186.62 [7261]E(x72611,f2(a850))+~E(f775(f132(a850,a850,f82(a850),x72611),x72612),f2(a850)) % 186.05/186.62 [7290]~P1(f775(f775(f233(a1),f775(f775(f3(a1),x72901),x72902)),f2(a1)))+P1(f775(f775(f233(a1),x72901),x72902)) % 186.05/186.62 [7320]P36(x73201,x73202)+~P36(x73201,f775(f775(f281(x73201,x73201,x73201),x73202),x73202)) % 186.05/186.62 [7352]~P1(f775(f775(f232(a850),f775(a114,x73521)),x73522))+P1(f175(a844,a178,f775(f232(a850),x73521),x73522)) % 186.05/186.62 [7512]P29(a850,a850,f775(f775(f9(a850,a850,a850),f3(a850)),x75121),x75122)+P1(f775(f775(f334(a850),f608(x75121,x75122)),x75122)) % 186.05/186.62 [7571]E(f775(f775(f775(f67(a850,x75711,f82(a850)),f775(f18(a850,x75711),f80(a850))),f2(a850)),x75712),f775(f42(x75711),x75712))+~P1(f775(f63(x75711),x75712)) % 186.05/186.62 [7614]P29(a850,a850,f775(f775(f9(a850,a850,a850),f3(a850)),x76141),x76142)+~P1(f775(f775(f232(a850),x76141),f608(x76141,x76142))) % 186.05/186.62 [7671]P36(x76711,x76712)+P1(f775(f775(f232(f857(x76711,a844)),f602(x76712,x76711)),f775(f277(x76711,x76711,x76712),f602(x76712,x76711)))) % 186.05/186.62 [7675]P58(x76751,x76752)+~P36(x76751,f775(f256(f856(x76751,x76751)),f775(f251(x76751,x76751,a844),x76752))) % 186.05/186.62 [7747]P1(f775(f775(f232(a850),f775(a114,x77471)),x77472))+~P1(f175(a844,a178,f775(f232(a850),x77471),x77472)) % 186.05/186.62 [7803]P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x78031),x78032)),f300(a850,a323)))+~P1(f775(f775(f232(a850),x78031),x78032)) % 186.05/186.62 [7897]P49(x78971,x78972)+~P47(x78971,f239(f857(x78971,a844)),f775(f256(f856(x78971,x78971)),f775(f251(x78971,x78971,a844),x78972))) % 186.05/186.62 [8153]~P36(x81531,f775(f278(x81531,x81531),x81532))+P36(x81531,f775(f278(x81531,x81531),f775(f775(f281(x81531,x81531,x81531),x81532),f300(x81531,x81532)))) % 186.05/186.62 [8270]P1(f775(f63(f856(x82701,x82701)),f775(f775(f281(x82701,x82701,x82701),x82702),f300(x82701,x82702))))+~P1(f775(f63(f856(x82701,x82701)),x82702)) % 186.05/186.62 [8300]E(x83001,f2(a1))+P1(f775(f56(x83002,x83001),f775(f775(f241(a1,a1),f775(f775(f43(a1),x83002),x83001)),f52(a1,x83002,x83001)))) % 186.05/186.62 [8314]~P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x83141),x83142)),f300(a850,a323)))+P1(f775(f775(f232(a850),x83141),x83142)) % 186.05/186.62 [8335]~P67(x83351)+E(f775(f132(x83351,x83351,f775(f9(x83351,x83351,x83351),f82(x83351)),f2(x83351)),f775(f142(x83351),x83352)),f775(f132(x83351,x83351,f82(x83351),f2(x83351)),x83352)) % 186.05/186.62 [8610]P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x86101),x86102)),f775(f775(f281(a850,a850,a850),a323),f300(a850,a323))))+~P1(f775(f775(f233(a850),x86101),x86102)) % 186.05/186.62 [8652]~P1(f775(f63(f856(x86521,x86521)),f775(f775(f281(x86521,x86521,x86521),x86522),f300(x86521,x86522))))+P1(f775(f63(f856(x86521,x86521)),x86522)) % 186.05/186.62 [8872]P56(x88721,x88722)+P1(f775(f775(f334(f856(x88721,x88721)),f775(f775(f241(x88721,x88721),f635(x88722,x88721)),f635(x88722,x88721))),f775(f775(f281(x88721,x88721,x88721),x88722),f300(x88721,x88722)))) % 186.05/186.62 [8873]P56(x88731,x88732)+P1(f775(f775(f334(f856(x88731,x88731)),f775(f775(f241(x88731,x88731),f642(x88732,x88731)),f642(x88732,x88731))),f775(f775(f281(x88731,x88731,x88731),x88732),f300(x88731,x88732)))) % 186.05/186.62 [8982]~P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x89821),x89822)),f775(f775(f281(a850,a850,a850),a323),f300(a850,a323))))+P1(f775(f775(f233(a850),x89821),x89822)) % 186.05/186.62 [4963]~P88(x49631)+E(f775(f775(f82(x49631),f775(f106(x49631),a85)),x49632),x49632) % 186.05/186.62 [4993]~P69(x49931)+E(f775(f775(f82(x49931),f775(f81(x49931),x49932)),x49932),f2(x49931)) % 186.05/186.62 [4994]~P6(x49941)+E(f775(f775(f82(x49941),f775(f81(x49941),x49942)),x49942),f2(x49941)) % 186.05/186.62 [4995]~P90(x49951)+E(f775(f775(f103(x49951),f775(f81(x49951),x49952)),x49952),f239(x49951)) % 186.05/186.62 [4996]~P90(x49961)+E(f775(f775(f104(x49961),f775(f81(x49961),x49962)),x49962),f180(x49961)) % 186.05/186.62 [5026]~P88(x50261)+E(f775(f775(f83(x50261),f775(f106(x50261),a99)),x50262),f775(f81(x50261),x50262)) % 186.05/186.62 [5185]~P104(x51851)+E(f775(f775(f83(x51851),f775(f81(x51851),f80(x51851))),x51852),f775(f81(x51851),x51852)) % 186.05/186.62 [5227]E(f775(f77(a1),x52271),f80(a1))+~E(f775(f77(a1),f775(f775(f83(a1),x52271),x52272)),f80(a1)) % 186.05/186.62 [5314]~P88(x53141)+E(f775(f775(f82(x53141),f80(x53141)),f775(f106(x53141),x53142)),f775(f106(x53141),f775(f775(f3(a1),x53142),a99))) % 186.05/186.62 [5369]~P93(x53691)+E(f15(x53691,f775(f775(f302(x53691),x53692),f180(f857(x53691,a844)))),x53692) % 186.05/186.62 [5370]~P100(x53701)+E(f16(x53701,f775(f775(f302(x53701),x53702),f180(f857(x53701,a844)))),x53702) % 186.05/186.62 [5371]~P100(x53711)+E(f17(x53711,f775(f775(f302(x53711),x53712),f180(f857(x53711,a844)))),x53712) % 186.05/186.62 [5372]~P93(x53721)+E(f12(x53721,f775(f775(f302(x53721),x53722),f180(f857(x53721,a844)))),x53722) % 186.05/186.62 [5373]~P9(x53731)+E(f45(x53731,f775(f775(f302(x53731),x53732),f180(f857(x53731,a844)))),x53732) % 186.05/186.62 [5374]~P9(x53741)+E(f44(x53741,f775(f775(f302(x53741),x53742),f180(f857(x53741,a844)))),x53742) % 186.05/186.62 [5396]E(f775(f775(f82(a850),x53961),f775(f775(f3(a850),x53962),x53961)),x53962)+P1(f775(f775(f233(a850),x53962),x53961)) % 186.05/186.62 [5428]E(x54281,f115(x54282))+P1(f775(f775(f233(a850),f2(a850)),f775(f181(f851(x54282)),x54281))) % 186.05/186.62 [5546]~P100(x55461)+E(f13(x55461,f179(x55461),f775(f775(f302(x55461),x55462),f180(f857(x55461,a844)))),x55462) % 186.05/186.62 [5547]~P100(x55471)+E(f14(x55471,f236(x55471),f775(f775(f302(x55471),x55472),f180(f857(x55471,a844)))),x55472) % 186.05/186.62 [5608]E(f775(f775(f82(a850),x56081),f775(f775(f3(a850),x56082),x56081)),x56082)+~P1(f775(f775(f232(a850),x56081),x56082)) % 186.05/186.62 [5609]E(f775(f775(f83(a1),x56091),f775(f775(f43(a1),x56092),x56091)),x56092)+~P1(f775(f775(f279(a1),x56091),x56092)) % 186.05/186.62 [5610]E(f775(f775(f3(a850),x56101),f775(f775(f3(a850),x56101),x56102)),x56102)+~P1(f775(f775(f232(a850),x56102),x56101)) % 186.05/186.62 [5629]E(f52(a850,f775(f775(f3(a850),x56291),x56292),x56292),f52(a850,x56291,x56292))+P1(f775(f775(f233(a850),x56291),x56292)) % 186.05/186.62 [5639]E(f775(f81(a1),f775(f775(f43(a1),x56391),f775(f81(a1),x56392))),f285(x56391,x56392))+P1(f775(f775(f232(a1),f2(a1)),x56392)) % 186.05/186.62 [5641]~E(x56412,f2(a850))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f242(a850),x56411),x56412))) % 186.05/186.62 [5701]~P88(x57011)+E(f775(f775(f82(x57011),f775(f81(x57011),f80(x57011))),f775(f106(x57011),x57012)),f775(f106(x57011),f775(f775(f82(a1),x57012),a99))) % 186.05/186.62 [5702]E(f775(f775(f242(a850),f775(f106(a850),x57021)),x57022),f775(f775(f242(a850),f2(a850)),x57022))+~P1(f775(a186,f775(f106(a1),x57021))) % 186.05/186.62 [5803]E(f775(f131(a850),f130(a850,f775(f294(a850,x58031),x58032))),x58031)+~P1(f775(f775(f233(a850),x58031),x58032)) % 186.05/186.62 [5820]E(f775(f775(f83(a850),f775(f106(a850),x58201)),f775(f106(a850),x58202)),f775(f106(a850),f775(f775(f83(a1),x58201),x58202)))+P1(f775(f775(f233(a1),x58201),a85)) % 186.05/186.62 [5826]~P118(x58261)+P1(f775(f775(f232(x58261),f2(x58261)),f775(f775(f83(x58261),x58262),x58262))) % 186.05/186.62 [5838]E(f775(f775(f3(a850),f775(a114,x58381)),x58382),f775(a114,f775(f775(f3(a850),x58381),x58382)))+~P1(f775(f775(f232(a850),x58382),x58381)) % 186.05/186.62 [5841]E(f52(a850,f775(f775(f3(a850),x58411),x58412),x58412),f52(a850,x58411,x58412))+~P1(f775(f775(f232(a850),x58412),x58411)) % 186.05/186.62 [5893]E(f775(f775(f242(a850),f775(a107,x58931)),x58932),f775(a107,f775(f775(f242(a1),x58931),x58932)))+~P1(f775(f775(f232(a1),f2(a1)),x58931)) % 186.05/186.62 [5909]P1(f775(f127(x59091),x59092))+P1(f775(f775(f233(a850),f723(x59092,x59091)),f775(f181(f851(x59091)),x59092))) % 186.05/186.62 [5910]P1(f775(f127(x59101),x59102))+P1(f775(f775(f233(a850),f727(x59102,x59101)),f775(f181(f851(x59101)),x59102))) % 186.05/186.62 [5925]~P1(f775(f775(f279(a1),x59251),x59252))+P1(f775(f775(f279(a1),f775(f81(a1),x59251)),x59252)) % 186.05/186.62 [5928]~E(x59281,f115(x59282))+~P1(f775(f775(f233(a850),f2(a850)),f775(f181(f851(x59282)),x59281))) % 186.05/186.62 [5941]E(f134(a850,f130(a850,f775(f294(a850,x59411),x59412))),f775(f775(f3(a850),x59412),f80(a850)))+~P1(f775(f775(f233(a850),x59411),x59412)) % 186.05/186.62 [5944]E(f775(f775(f82(a1),x59441),f775(f102(a1),f775(a114,f629(x59442,x59441)))),x59442)+~P1(f775(f775(f233(a1),x59441),x59442)) % 186.05/186.62 [5950]E(x59501,f2(a850))+E(f775(f775(f83(a850),x59502),f775(f775(f242(a850),x59502),f775(f775(f3(a850),x59501),f80(a850)))),f775(f775(f242(a850),x59502),x59501)) % 186.05/186.62 [5976]E(f775(f775(f83(a850),f775(a107,x59761)),f775(a107,x59762)),f775(a107,f775(f775(f83(a1),x59761),x59762)))+~P1(f775(f775(f232(a1),f2(a1)),x59761)) % 186.05/186.62 [5977]E(f775(f775(f43(a850),f775(a107,x59771)),f775(a107,x59772)),f775(a107,f775(f775(f43(a1),x59771),x59772)))+~P1(f775(f775(f232(a1),f2(a1)),x59771)) % 186.05/186.62 [5991]~P85(x59911)+E(f775(f775(f82(x59911),x59912),x59912),f775(f775(f83(x59911),f775(f775(f82(x59911),f80(x59911)),f80(x59911))),x59912)) % 186.05/186.62 [6010]E(f775(f775(f43(a1),f775(f77(a1),x60101)),f775(f77(a1),x60102)),f775(f77(a1),f775(f775(f43(a1),x60101),x60102)))+~P1(f775(f775(f279(a1),x60102),x60101)) % 186.05/186.62 [6011]E(f775(f775(f3(a1),f775(f102(a1),x60111)),f775(f102(a1),x60112)),f775(f102(a1),f775(f775(f3(a850),x60111),x60112)))+~P1(f775(f775(f232(a850),x60112),x60111)) % 186.05/186.62 [6013]E(f775(f775(f241(a1,a1),f775(f106(a1),a99)),f775(f775(f82(a1),x60131),x60132)),f57(x60131,x60132))+~P1(f775(f775(f232(a1),x60132),f2(a1))) % 186.05/186.62 [6052]E(f164(x60521,x60522),f115(f851(x60521)))+P1(f775(f775(f334(f851(x60521)),f722(x60522,x60521)),f775(f158(f851(x60521)),x60522))) % 186.05/186.62 [6116]~P1(f775(f775(f279(a850),x61161),x61162))+P1(f775(f775(f279(a850),x61161),f775(f775(f82(a850),x61162),x61161))) % 186.05/186.62 [6138]E(f775(f775(f140(a1),x61381),f163(f775(f775(f82(a1),x61381),f80(a1)),x61382)),f163(x61381,x61382))+~P1(f775(f775(f232(a1),x61381),x61382)) % 186.05/186.62 [6176]~P1(f775(f775(f233(a850),x61762),x61761))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f3(a850),x61761),x61762))) % 186.05/186.62 [6208]~P1(f775(f775(f233(a850),x62081),f775(a107,x62082)))+P1(f775(f775(f233(a1),f775(f102(a1),x62081)),x62082)) % 186.05/186.62 [6209]P1(f775(f775(f279(a1),x62091),x62092))+~P1(f775(f775(f279(a1),f775(f81(a1),x62091)),x62092)) % 186.05/186.62 [6239]~P100(x62391)+E(f775(f775(f103(f857(x62391,a844)),f775(f257(x62391),x62392)),f775(f775(f302(x62391),x62392),f180(f857(x62391,a844)))),f775(f293(x62391),x62392)) % 186.05/186.62 [6242]~P1(f775(f775(f233(a850),f2(a850)),x62421))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f242(a850),x62421),x62422))) % 186.05/186.62 [6243]~P1(f775(f775(f232(a1),f2(a1)),x62431))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f242(a1),x62431),x62432))) % 186.05/186.62 [6271]~E(f775(x62711,f2(a850)),f2(a850))+E(f775(f775(f8(a850,a850),x62711),f295(a850,f775(a114,f2(a850)),x62712)),f775(f775(f8(a850,a850),x62711),f295(a850,f2(a850),x62712))) % 186.05/186.62 [6337]~P88(x63371)+E(f775(f775(f83(x63371),f775(f775(f82(x63371),f80(x63371)),f80(x63371))),f775(f106(x63371),x63372)),f775(f106(x63371),f775(f775(f82(a1),x63372),x63372))) % 186.05/186.62 [6359]E(f775(f775(f302(a1),x63591),f295(a1,f775(f775(f82(a1),x63591),f80(a1)),x63592)),f295(a1,x63591,x63592))+P1(f775(f775(f233(a1),x63592),x63591)) % 186.05/186.62 [6360]P1(f775(f775(f233(a850),x63601),f775(a107,x63602)))+~P1(f775(f775(f233(a1),f775(f102(a1),x63601)),x63602)) % 186.05/186.62 [6462]P1(f775(f775(f279(a850),x64621),x64622))+~P1(f775(f775(f279(a850),x64621),f775(f775(f82(a850),x64622),x64621))) % 186.05/186.62 [6468]E(f775(a107,f775(f775(f43(a1),f775(f106(a1),x64681)),f775(f106(a1),x64682))),f775(f775(f43(a850),f775(f106(a850),x64681)),f775(f106(a850),x64682)))+P1(f775(a186,f775(f106(a1),x64681))) % 186.05/186.62 [6528]P1(f775(f775(f233(a850),x65281),x65282))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f3(a850),x65282),x65281))) % 186.05/186.62 [6571]P1(f775(f775(f233(a850),f2(a850)),x65711))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f83(a850),x65712),x65711))) % 186.05/186.62 [6572]P1(f775(f775(f233(a850),f2(a850)),x65721))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f83(a850),x65721),x65722))) % 186.05/186.62 [6589]~P1(f775(f775(f232(a1),x65891),f2(a1)))+E(f775(f775(f83(a850),f775(a107,f775(f81(a1),x65891))),f775(a107,f775(f81(a1),x65892))),f775(a107,f775(f775(f83(a1),x65891),x65892))) % 186.05/186.62 [6655]~E(x66552,f180(f857(x66551,a844)))+P1(f775(f775(f232(f857(x66551,a844)),x66552),f775(f81(f857(x66551,a844)),x66552))) % 186.05/186.62 [6718]~P88(x67181)+E(f775(f775(f82(x67181),f775(f775(f82(x67181),f2(x67181)),f775(f106(x67181),x67182))),f775(f106(x67181),x67182)),f775(f106(x67181),f775(f775(f82(a1),x67182),x67182))) % 186.05/186.62 [6727]~P1(f775(f775(f279(a1),f775(f102(a1),x67271)),x67272))+P1(f775(f775(f279(a850),x67271),f775(a107,f775(f77(a1),x67272)))) % 186.05/186.62 [6779]~P1(f775(f775(f233(a1),x67791),x67792))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x67791),f80(a1))),x67792)) % 186.05/186.62 [6818]P1(f775(f775(f279(a1),f775(f102(a1),x68181)),x68182))+~P1(f775(f775(f279(a850),x68181),f775(a107,f775(f77(a1),x68182)))) % 186.05/186.62 [6852]E(x68521,f2(a850))+~P1(f775(f775(f232(a1),f775(f102(a1),x68522)),f775(f81(a1),f775(f102(a1),x68521)))) % 186.05/186.62 [6853]E(x68531,f2(a850))+~P1(f775(f775(f232(a1),f775(f102(a1),x68531)),f775(f81(a1),f775(f102(a1),x68532)))) % 186.05/186.62 [6958]E(f775(f775(f241(a1,a1),f775(f106(a1),a99)),f775(f775(f82(a1),x69581),x69582)),f57(x69581,x69582))+~P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),x69581),x69582))) % 186.05/186.62 [6995]~P30(x69951,x69952)+P36(x69951,f775(f240(f857(f856(x69951,x69951),a844),f857(f856(x69951,x69951),a844)),x69952)) % 186.05/186.62 [7016]~P1(f775(f775(f232(a850),f775(a114,f2(a850))),x70161))+P1(f775(f775(f232(a850),f775(a114,f2(a850))),f775(f775(f242(a850),x70161),x70162))) % 186.05/186.62 [7186]~P1(f775(f775(f233(a1),x71861),x71862))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x71861),x71861)),f775(f775(f82(a1),x71862),x71862))) % 186.05/186.62 [7198]~P1(f775(f775(f232(a1),x71981),x71982))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x71981),x71981)),f775(f775(f82(a1),x71982),x71982))) % 186.05/186.62 [7265]~P1(f775(f775(f233(a850),f2(a850)),x72651))+P1(f775(f775(f233(a850),f775(f775(f3(a850),x72651),f775(a114,x72652))),x72651)) % 186.05/186.62 [7302]P1(f775(f775(f232(a850),f775(a114,f2(a850))),x73021))+~P1(f775(f775(f232(a850),f775(a114,f2(a850))),f775(f775(f83(a850),x73022),x73021))) % 186.05/186.62 [7303]P1(f775(f775(f232(a850),f775(a114,f2(a850))),x73031))+~P1(f775(f775(f232(a850),f775(a114,f2(a850))),f775(f775(f83(a850),x73031),x73032))) % 186.05/186.62 [7307]P1(f775(f775(f232(a850),f775(f775(f153(a850),x73071),x73072)),f775(f155(a850),x73071)))+~P1(f775(f775(f233(a850),x73072),f775(f181(f851(a850)),x73071))) % 186.05/186.62 [7351]P1(f775(f775(f233(a1),x73511),x73512))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x73511),f80(a1))),x73512)) % 186.05/186.62 [7397]P1(f775(f63(x73971),f239(f857(x73971,a844))))+~P1(f775(f63(f857(x73972,x73971)),f239(f857(f857(x73972,x73971),a844)))) % 186.05/186.62 [7398]P1(f775(f63(x73981),f239(f857(x73981,a844))))+~P1(f775(f63(f858(x73982,x73981)),f239(f857(f858(x73982,x73981),a844)))) % 186.05/186.62 [7399]P1(f775(f63(x73991),f239(f857(x73991,a844))))+~P1(f775(f63(f858(x73991,x73992)),f239(f857(f858(x73991,x73992),a844)))) % 186.05/186.62 [7438]E(x74381,f180(f857(x74382,a844)))+~P1(f775(f775(f232(f857(x74382,a844)),x74381),f775(f81(f857(x74382,a844)),x74381))) % 186.05/186.62 [7581]E(f775(f132(f851(x75811),f851(x75811),f125(x75811),f115(x75811)),x75812),f115(x75811))+P1(f775(f775(f334(f851(x75811)),f769(x75812,x75811)),f775(f158(f851(x75811)),x75812))) % 186.05/186.62 [7582]E(f775(f132(f851(x75821),f851(x75821),f125(x75821),f115(x75821)),x75822),f115(x75821))+P1(f775(f775(f334(f851(x75821)),f770(x75822,x75821)),f775(f158(f851(x75821)),x75822))) % 186.05/186.62 [7823]P1(f775(f775(f233(a1),x78231),x78232))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x78231),x78231)),f775(f775(f82(a1),x78232),x78232))) % 186.05/186.62 [7826]P1(f775(f775(f232(a1),x78261),x78262))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x78261),x78261)),f775(f775(f82(a1),x78262),x78262))) % 186.05/186.62 [7918]~P85(x79181)+E(f775(f775(f83(x79181),f775(f775(f82(x79181),f80(x79181)),f80(x79181))),f775(f775(f8(a850,x79181),f102(x79181)),f295(a850,f80(a850),x79182))),f775(f775(f83(x79181),f775(f102(x79181),x79182)),f775(f775(f82(x79181),f775(f102(x79181),x79182)),f80(x79181)))) % 186.05/186.62 [7974]P1(f775(f775(f334(a850),x79741),x79742))+~P1(f775(f775(f334(a1),f775(f102(a1),x79741)),f775(f303(a850,a1,f102(a1)),x79742))) % 186.05/186.62 [8124]~P1(f775(f63(x81241),x81242))+E(f775(f303(a850,x81241,f583(x81242,x81241)),f775(f256(a850),f775(f775(f9(a850,a850,a844),f233(a850)),f584(x81242,x81241)))),x81242) % 186.05/186.62 [8408]P48(x84081,x84082)+P1(f775(f775(f334(f856(x84081,x84081)),f775(f775(f241(x84081,x84081),f473(x84082,x84081)),f473(x84082,x84081))),x84082)) % 186.05/186.62 [8544]~P88(x85441)+E(f775(f775(f3(x85441),f80(x85441)),f775(f106(x85441),x85442)),f775(f106(x85441),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f81(a1),x85442)))) % 186.05/186.62 [8648]~P1(f775(f775(f233(f857(a850,a844)),x86481),x86482))+P1(f775(f775(f233(f857(a1,a844)),f775(f303(a850,a1,f102(a1)),x86481)),f775(f303(a850,a1,f102(a1)),x86482))) % 186.05/186.62 [8675]~P1(f775(f775(f233(a1),x86751),x86752))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x86751),x86751)),a99)),f775(f775(f82(a1),x86752),x86752))) % 186.05/186.62 [8677]~P1(f775(f775(f233(a1),x86771),x86772))+P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x86771),x86771)),a99)),f775(f775(f82(a1),x86772),x86772))) % 186.05/186.62 [8744]~P1(f775(f775(f334(a850),x87441),f775(f158(a850),x87442)))+P1(f775(f775(f232(a850),x87441),f775(f132(a850,a850,f82(a850),f2(a850)),x87442))) % 186.05/186.62 [8816]P44(x88161,x88162)+~P1(f775(f775(f334(f856(x88161,x88161)),f775(f775(f241(x88161,x88161),f427(x88162,x88161)),f427(x88162,x88161))),x88162)) % 186.05/186.62 [8949]~P1(f775(f775(f233(f857(a1,a844)),f775(f303(a850,a1,f102(a1)),x89491)),f775(f303(a850,a1,f102(a1)),x89492)))+P1(f775(f775(f233(f857(a850,a844)),x89491),x89492)) % 186.05/186.62 [8950]~P1(f775(f775(f232(f857(a1,a844)),f775(f303(a850,a1,f102(a1)),x89501)),f775(f303(a850,a1,f102(a1)),x89502)))+P1(f775(f775(f232(f857(a850,a844)),x89501),x89502)) % 186.05/186.62 [9032]P1(f775(f775(f233(a1),x90321),x90322))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x90321),x90321)),a99)),f775(f775(f82(a1),x90322),x90322))) % 186.05/186.62 [9034]P1(f775(f775(f233(a1),x90341),x90342))+~P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x90341),x90341)),a99)),f775(f775(f82(a1),x90342),x90342))) % 186.05/186.62 [9887]~P1(f775(f63(x98871),x98872))+E(f775(f181(f851(x98871)),f92(f851(x98871),f775(f775(f20(f851(x98871),a844,a844),f775(f775(f10(a844,f857(a844,a844),f851(x98871)),a331),f775(f775(f9(f851(x98871),f857(x98871,a844),a844),f775(f775(f10(f857(x98871,a844),f857(f857(x98871,a844),a844),f851(x98871)),a330),f158(x98871))),x98872))),f127(x98871)))),f209(x98871,x98872)) % 186.05/186.62 [5940]E(f775(f775(f82(a850),f775(f775(f3(a850),x59401),x59402)),x59402),x59401)+~P1(f775(f775(f232(a850),x59402),x59401)) % 186.05/186.62 [6006]E(f775(f775(f43(a850),f775(f775(f83(a850),x60061),x60062)),x60062),x60061)+~P1(f775(f775(f233(a850),f2(a850)),x60062)) % 186.05/186.62 [6007]E(f775(f775(f43(a850),f775(f775(f83(a850),x60071),x60072)),x60071),x60072)+~P1(f775(f775(f233(a850),f2(a850)),x60071)) % 186.05/186.62 [6012]~P66(x60121)+E(f775(f775(f8(a850,x60121),f775(f153(x60121),x60122)),f775(f294(a850,f2(a850)),f775(f181(f851(x60121)),x60122))),f775(f155(x60121),x60122)) % 186.05/186.62 [6130]E(f52(a850,f775(a114,f775(f775(f83(a850),x61301),x61302)),x61301),f80(a850))+~P1(f775(f775(f233(a850),f80(a850)),x61301)) % 186.05/186.62 [6136]E(f775(a114,f775(f775(f82(a850),f775(f106(a850),x61361)),x61362)),f775(f775(f82(a850),f80(a850)),x61362))+~P1(f775(a186,f775(f106(a1),x61361))) % 186.05/186.62 [6162]E(f775(a107,f775(f775(f242(a1),f775(f106(a1),x61621)),x61622)),f775(f775(f242(a850),f775(f106(a850),x61621)),x61622))+P1(f775(a186,f775(f106(a1),x61621))) % 186.05/186.62 [6415]E(f775(f775(f3(a850),x64151),f775(f106(a850),f775(f775(f82(a1),x64152),a99))),f775(f775(f3(a850),f775(a114,x64151)),f775(f106(a850),x64152)))+~P1(f775(f775(f233(a1),a85),x64152)) % 186.05/186.62 [6497]E(x64971,f2(a850))+E(f775(a114,f775(f775(f82(a850),f775(f775(f3(a850),x64971),f80(a850))),x64972)),f775(f775(f82(a850),x64971),x64972)) % 186.05/186.62 [6542]E(x65421,f2(a1))+P1(f775(f775(f233(a1),f2(a1)),f775(f775(f242(a1),f775(f77(a1),x65421)),x65422))) % 186.05/186.62 [6557]~E(x65572,f2(a850))+P1(f775(f775(f233(a1),f2(a1)),f775(f775(f242(a1),f775(f77(a1),x65571)),x65572))) % 186.05/186.62 [6594]E(x65941,f2(a850))+E(f775(f775(f82(a850),x65942),f775(f775(f83(a850),f775(f775(f3(a850),x65941),f80(a850))),x65942)),f775(f775(f83(a850),x65941),x65942)) % 186.05/186.62 [6649]~P1(f775(f775(f232(a1),x66491),x66492))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x66491),a99)),x66492)) % 186.05/186.62 [6783]E(f775(f775(f140(a850),x67831),f130(a850,f775(f294(a850,f775(a114,x67831)),x67832))),f130(a850,f775(f294(a850,x67831),x67832)))+~P1(f775(f775(f233(a850),x67831),x67832)) % 186.05/186.62 [6952]~P1(f775(f775(f279(a1),x69521),f775(f102(a1),x69522)))+P1(f775(f775(f279(a850),f775(a107,f775(f77(a1),x69521))),x69522)) % 186.05/186.62 [6986]E(x69861,x69862)+~E(f775(f775(f3(a1),f775(f775(f82(a1),x69861),x69861)),a99),f775(f775(f3(a1),f775(f775(f82(a1),x69862),x69862)),a99)) % 186.05/186.62 [6989]E(x69891,f115(x69892))+E(f263(x69892,f775(f775(f143(x69892,f856(a101,x69892)),f775(f241(a101,x69892),f80(a101))),x69891)),f270(x69892,x69891)) % 186.05/186.62 [7228]P1(f775(f775(f232(a1),x72281),x72282))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x72281),a99)),x72282)) % 186.05/186.62 [7370]P1(f775(f775(f279(a1),x73701),f775(f102(a1),x73702)))+~P1(f775(f775(f279(a850),f775(a107,f775(f77(a1),x73701))),x73702)) % 186.05/186.62 [7720]~P1(f775(f775(f233(a850),x77201),x77202))+P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x77201),x77202)),a237)) % 186.05/186.62 [7948]~P1(f775(f775(f233(a101),f2(a101)),x79481))+P1(f775(f775(f233(a101),f775(f240(a101,f856(a101,a101)),f775(f264(x79481),x79482))),x79481)) % 186.05/186.62 [8249]~P79(x82491)+P1(f775(f775(f232(x82491),f775(f77(x82491),f775(f155(x82491),x82492))),f775(f155(x82491),f775(f775(f143(x82491,x82491),f77(x82491)),x82492)))) % 186.05/186.62 [8272]P1(f775(f775(f233(a850),x82721),x82722))+~P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),x82721),x82722)),a237)) % 186.05/186.62 [8432]E(f775(f775(f241(x84321,x84321),f654(x84322,x84321)),f654(x84322,x84321)),x84322)+~P1(f775(f775(f334(f856(x84321,x84321)),x84322),f300(x84321,f180(f857(f856(x84321,x84321),a844))))) % 186.05/186.62 [8477]E(f775(f294(a850,x84771),f775(f775(f82(a850),x84771),f775(f42(a850),x84772))),x84772)+~P1(f775(f775(f232(f857(a850,a844)),x84772),f775(f294(a850,x84771),f775(f775(f82(a850),x84771),f775(f42(a850),x84772))))) % 186.05/186.62 [8777]E(f775(f775(f43(a1),f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x87771),x87771)),a99))),f775(f106(a1),f775(f775(f82(a1),x87772),x87772))),f775(f775(f43(a1),f775(f106(a1),x87771)),f775(f106(a1),x87772)))+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x87772))) % 186.05/186.62 [8882]E(f162(f851(x88821),f775(f775(f10(a844,a844,f851(x88821)),a328),f775(f775(f9(f851(x88821),f851(x88821),a844),a330),f115(x88821))),x88822),f164(x88821,f164(x88821,x88822)))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x88821),a850),f181(f851(x88821))),x88822))) % 186.05/186.62 [8885]E(f775(f775(f43(a1),f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x88851),x88851)),a99))),f775(f106(a1),f775(f775(f82(a1),x88852),x88852))),f775(f775(f43(a1),f775(f775(f82(a1),f775(f106(a1),x88851)),f80(a1))),f775(f106(a1),x88852)))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x88852))) % 186.05/186.62 [9657]P1(f775(a186,x96572))+E(f775(f775(f88(a1,a850),f775(f775(f3(a1),x96571),x96572)),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f2(a850))),a107)),f775(f775(f3(a850),f775(a107,x96571)),f775(a107,x96572))) % 186.05/186.62 [9661]E(f775(f775(f88(a1,a850),f775(f106(a1),f775(f775(f82(a1),x96611),f775(f81(a1),x96612)))),f775(f775(f20(a1,a850,a850),f775(f775(f9(a1,a850,f857(a850,a850)),f775(f775(f10(a844,f857(a850,f857(a850,a850)),a1),f98(a850)),a186)),f2(a850))),a107)),f775(f775(f3(a850),f775(f106(a850),x96611)),f775(f106(a850),x96612)))+P1(f775(f775(f233(a1),x96612),a85)) % 186.05/186.62 [9662]~P30(x96621,x96622)+P1(f775(f775(f232(f857(f856(x96621,x96621),a844)),f775(f775(f281(x96621,x96621,x96621),f775(f240(f857(f856(x96621,x96621),a844),f857(f856(x96621,x96621),a844)),x96622)),f775(f250(f857(f856(x96621,x96621),a844),f857(f856(x96621,x96621),a844)),x96622))),f775(f240(f857(f856(x96621,x96621),a844),f857(f856(x96621,x96621),a844)),x96622))) % 186.05/186.62 [9718]~E(f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,f857(a850,a844),a844),f334(a850)),x97181))),f775(f775(f9(a850,a850,a844),f233(a850)),f775(a114,x97182))))),f2(a850))+~P1(f775(f775(f334(a850),f2(a850)),x97181)) % 186.05/186.62 [9731]E(f291(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97311,x97312),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x97312),x97311)) % 186.05/186.62 [9739]E(f292(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97391,x97392),f180(f857(a850,a844)))+P1(f775(f775(f279(a850),x97391),x97392)) % 186.05/186.62 [9740]E(f289(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97401,x97402),f180(f857(a850,a844)))+P1(f775(f775(f279(a850),x97401),x97402)) % 186.05/186.62 [9744]E(f292(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97441,x97442),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x97442),x97441)) % 186.05/186.62 [9746]E(f289(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97461,x97462),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x97462),x97461)) % 186.05/186.62 [9789]E(f52(a1,f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x97891),x97891)),a99)),f775(f106(a1),f775(f775(f82(a1),x97892),x97892))),f775(f775(f82(a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a1,f775(f106(a1),x97891),f775(f106(a1),x97892)))),f80(a1)))+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x97892))) % 186.05/186.62 [9798]E(f52(a1,f775(f106(a1),f775(f775(f3(a1),f775(f775(f82(a1),x97981),x97981)),a99)),f775(f106(a1),f775(f775(f82(a1),x97982),x97982))),f775(f775(f3(a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a1,f775(f775(f82(a1),f775(f106(a1),x97981)),f80(a1)),f775(f106(a1),x97982)))),f80(a1)))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x97982))) % 186.05/186.62 [9856]~P9(x98561)+E(f44(x98561,f775(f256(x98561),f775(f775(f10(f857(x98561,a844),a844,x98561),f90(x98561)),f775(f775(f10(f857(x98561,a844),f857(x98561,a844),x98561),f775(f20(x98561,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98561),a335),f775(f775(f9(x98561,f857(x98561,a844),a844),f334(x98561)),x98562)))),f232(x98561))))),f45(x98561,x98562)) % 186.05/186.62 [9880]~P36(x98801,x98802)+P58(x98801,f775(f775(f9(x98801,f857(f856(x98801,x98801),a844),f857(x98801,a844)),f775(f775(f10(f857(x98801,f857(f857(f856(x98801,x98801),a844),a844)),f857(f857(f856(x98801,x98801),a844),f857(x98801,a844)),x98801),f9(x98801,f857(f856(x98801,x98801),a844),a844)),f775(f775(f10(f857(x98801,f856(x98801,x98801)),f857(x98801,f857(f857(f856(x98801,x98801),a844),a844)),x98801),f775(f10(f856(x98801,x98801),f857(f857(f856(x98801,x98801),a844),a844),x98801),f334(f856(x98801,x98801)))),f241(x98801,x98801)))),x98802)) % 186.05/186.62 [9881]~P12(x98811,f239(f857(x98811,a844)),x98812)+P11(x98811,f775(f775(f9(x98811,f857(f856(x98811,x98811),a844),f857(x98811,a844)),f775(f775(f10(f857(x98811,f857(f857(f856(x98811,x98811),a844),a844)),f857(f857(f856(x98811,x98811),a844),f857(x98811,a844)),x98811),f9(x98811,f857(f856(x98811,x98811),a844),a844)),f775(f775(f10(f857(x98811,f856(x98811,x98811)),f857(x98811,f857(f857(f856(x98811,x98811),a844),a844)),x98811),f775(f10(f856(x98811,x98811),f857(f857(f856(x98811,x98811),a844),a844),x98811),f334(f856(x98811,x98811)))),f241(x98811,x98811)))),x98812)) % 186.05/186.62 [9918]P36(x99181,x99182)+~P58(x99181,f775(f775(f9(x99181,f857(f856(x99181,x99181),a844),f857(x99181,a844)),f775(f775(f10(f857(x99181,f857(f857(f856(x99181,x99181),a844),a844)),f857(f857(f856(x99181,x99181),a844),f857(x99181,a844)),x99181),f9(x99181,f857(f856(x99181,x99181),a844),a844)),f775(f775(f10(f857(x99181,f856(x99181,x99181)),f857(x99181,f857(f857(f856(x99181,x99181),a844),a844)),x99181),f775(f10(f856(x99181,x99181),f857(f857(f856(x99181,x99181),a844),a844),x99181),f334(f856(x99181,x99181)))),f241(x99181,x99181)))),x99182)) % 186.05/186.62 [9919]P12(x99191,f239(f857(x99191,a844)),x99192)+~P11(x99191,f775(f775(f9(x99191,f857(f856(x99191,x99191),a844),f857(x99191,a844)),f775(f775(f10(f857(x99191,f857(f857(f856(x99191,x99191),a844),a844)),f857(f857(f856(x99191,x99191),a844),f857(x99191,a844)),x99191),f9(x99191,f857(f856(x99191,x99191),a844),a844)),f775(f775(f10(f857(x99191,f856(x99191,x99191)),f857(x99191,f857(f857(f856(x99191,x99191),a844),a844)),x99191),f775(f10(f856(x99191,x99191),f857(f857(f856(x99191,x99191),a844),a844),x99191),f334(f856(x99191,x99191)))),f241(x99191,x99191)))),x99192)) % 186.05/186.62 [7174]E(f775(f775(f82(a850),f775(f106(a850),f775(f775(f3(a1),x71741),a99))),x71742),f775(a114,f775(f775(f82(a850),f775(f106(a850),x71741)),x71742)))+P1(f775(a186,f775(f106(a1),x71741))) % 186.05/186.62 [7639]~P88(x76391)+E(f775(f775(f82(x76391),f775(f775(f82(x76391),f80(x76391)),f775(f106(x76391),x76392))),f775(f106(x76391),x76392)),f775(f106(x76391),f775(f775(f3(a1),f775(f775(f82(a1),x76392),x76392)),a99))) % 186.05/186.62 [8274]~P1(f775(f775(f232(a1),x82741),x82742))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x82741),x82741)),f775(f775(f3(a1),f775(f775(f82(a1),x82742),x82742)),a99))) % 186.05/186.62 [8276]~P1(f775(f775(f232(a1),x82761),x82762))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x82761),x82761)),f775(f775(f3(a1),f775(f775(f82(a1),x82762),x82762)),a99))) % 186.05/186.62 [8679]P1(f775(f775(f232(a1),x86791),x86792))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),x86791),x86791)),f775(f775(f3(a1),f775(f775(f82(a1),x86792),x86792)),a99))) % 186.05/186.62 [8681]P1(f775(f775(f232(a1),x86811),x86812))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x86811),x86811)),f775(f775(f3(a1),f775(f775(f82(a1),x86812),x86812)),a99))) % 186.05/186.62 [8940]~P1(f775(f775(f233(a1),x89401),x89402))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89401),x89401)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x89402),x89402)),a99))) % 186.05/186.62 [8942]~P1(f775(f775(f232(a1),x89421),x89422))+P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x89421),x89421)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x89422),x89422)),a99))) % 186.05/186.62 [9176]P1(f775(f775(f233(a1),x91761),x91762))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),x91761),x91761)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x91762),x91762)),a99))) % 186.05/186.62 [9178]P1(f775(f775(f232(a1),x91781),x91782))+~P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),x91781),x91781)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),x91782),x91782)),a99))) % 186.05/186.62 [9209]~P1(f775(f63(x92091),x92092))+P1(f775(f63(f857(x92091,a844)),f775(f256(f857(x92091,a844)),f775(f775(f9(f857(x92091,a844),f857(x92091,a844),a844),f232(f857(x92091,a844))),x92092)))) % 186.05/186.62 [9256]~E(f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),x92561),f180(f857(f856(a850,a850),a844)))),f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),x92562),f180(f857(f856(a850,a850),a844)))))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x92561),x92562)),a111)) % 186.05/186.62 [9342]E(f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),x93421),f180(f857(f856(a850,a850),a844)))),f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),x93422),f180(f857(f856(a850,a850),a844)))))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x93421),x93422)),a111)) % 186.05/186.62 [9376]P1(f775(f775(f232(a1),f2(a1)),f699(x93761,x93762)))+E(f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93761)),f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93762))) % 186.05/186.62 [9866]~P9(x98661)+E(f45(x98661,f775(f256(x98661),f775(f775(f10(f857(x98661,a844),a844,x98661),f90(x98661)),f775(f775(f10(f857(x98661,a844),f857(x98661,a844),x98661),f775(f20(x98661,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98661),a335),f775(f775(f9(x98661,f857(x98661,a844),a844),f334(x98661)),x98662)))),f775(f9(x98661,x98661,a844),f232(x98661)))))),f44(x98661,x98662)) % 186.05/186.62 [9886]P1(f775(f775(f334(a850),f2(a850)),x98861))+E(f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),a850),f334(a850)),a114)),x98861))),f775(f775(f9(a850,a850,a844),f233(a850)),x98862)))),f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,f857(a850,a844),a844),f334(a850)),x98861))),f775(f775(f9(a850,a850,a844),f233(a850)),f775(a114,x98862)))))) % 186.05/186.62 [9933]P1(f775(f775(f279(a850),x99331),x99332))+~P1(f775(f775(f334(a850),x99332),f287(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99331))) % 186.05/186.62 [9934]P1(f775(f775(f279(a850),x99341),x99342))+~P1(f775(f775(f334(a850),x99341),f290(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99342))) % 186.05/186.62 [9935]~P1(f775(f775(f279(a850),x99351),x99352))+~P1(f775(f775(f334(a850),x99352),f290(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99351))) % 186.05/186.62 [9936]~P1(f775(f775(f279(a850),x99361),x99362))+~P1(f775(f775(f334(a850),x99361),f287(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99362))) % 186.05/186.62 [7506]~P88(x75061)+E(f775(f775(f83(x75061),x75062),f775(f106(x75061),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),x75062) % 186.05/186.62 [7773]~P88(x77731)+E(f775(f775(f82(x77731),f775(f106(x77731),x77732)),f80(x77731)),f775(f106(x77731),f775(f775(f82(a1),x77732),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))) % 186.05/186.62 [7917]P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x79172)))+E(f775(f775(f242(a1),x79171),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x79172),x79172)),a99))),f80(a1)) % 186.05/186.62 [9233]~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x92332)))+E(f775(f775(f242(a1),x92331),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x92332),x92332)),a99))),f775(f775(f88(a1,a1),f775(f775(f242(a1),x92331),f775(f106(a850),x92332))),f775(f775(f20(a1,a1,a1),f775(f775(f10(a1,f857(a1,a1),a1),f83(a1)),f775(f83(a1),x92331))),f7(a1)))) % 186.05/186.62 [9708]~P1(f775(f775(f233(a850),f775(f106(a850),x97081)),f775(a114,x97082)))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x97081),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),f233(a850)),a107)),x97082)))) % 186.05/186.62 [9709]~P1(f775(f775(f232(a850),f775(f106(a850),x97091)),f775(a114,x97092)))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x97091),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),f232(a850)),a107)),x97092)))) % 186.05/186.62 [9773]P1(f775(f775(f233(a850),f775(f106(a850),x97731)),f775(a114,x97732)))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x97731),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),f233(a850)),a107)),x97732)))) % 186.05/186.62 [9774]P1(f775(f775(f232(a850),f775(f106(a850),x97741)),f775(a114,x97742)))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x97741),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),f232(a850)),a107)),x97742)))) % 186.05/186.62 [9804]~P1(f775(f775(f233(a850),f775(a114,x98042)),f775(f106(a850),x98041)))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98041),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f10(a850,a844,a1),f775(f233(a850),x98042)),a107))))) % 186.05/186.62 [9805]~P1(f775(f775(f232(a850),f775(a114,x98052)),f775(f106(a850),x98051)))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98051),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f10(a850,a844,a1),f775(f232(a850),x98052)),a107))))) % 186.05/186.62 [9854]P1(f775(f775(f233(a850),f775(a114,x98541)),f775(f106(a850),x98542)))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98542),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f10(a850,a844,a1),f775(f233(a850),x98541)),a107))))) % 186.05/186.62 [9855]P1(f775(f775(f232(a850),f775(a114,x98551)),f775(f106(a850),x98552)))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98552),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f10(a850,a844,a1),f775(f232(a850),x98551)),a107))))) % 186.05/186.62 [9926]~P1(f775(f775(f334(a850),f2(a850)),x99261))+E(f775(a114,f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,f857(a850,a844),a844),f775(f775(f10(a850,f857(f857(a850,a844),a844),a850),f334(a850)),a114)),x99261))),f775(f775(f9(a850,a850,a844),f233(a850)),x99262))))),f775(f42(a850),f775(f256(a850),f775(f775(f20(a850,a844,a844),f775(f775(f10(a844,f857(a844,a844),a850),a331),f775(f775(f9(a850,f857(a850,a844),a844),f334(a850)),x99261))),f775(f775(f9(a850,a850,a844),f233(a850)),f775(a114,x99262)))))) % 186.05/186.62 [8458]~P88(x84581)+E(f775(f775(f83(x84581),f775(f106(x84581),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),x84582),x84582) % 186.05/186.62 [8518]~P88(x85181)+E(f775(f775(f82(x85181),f80(x85181)),f775(f106(x85181),x85182)),f775(f106(x85181),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),x85182))) % 186.05/186.62 [8564]~P88(x85641)+E(f775(f775(f3(x85641),f775(f106(x85641),x85642)),f80(x85641)),f775(f106(x85641),f775(f775(f82(a1),x85642),f775(f81(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [8697]~P1(f775(f775(f233(a850),f775(f106(a850),a85)),x86972))+E(f775(f775(f3(a850),x86971),f775(f775(f3(a850),x86972),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f3(a850),f775(a114,x86971)),x86972)) % 186.05/186.62 [9272]~P85(x92721)+E(f775(f775(f83(x92721),x92722),x92722),f775(f775(f242(x92721),x92722),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9273]~P75(x92731)+E(f775(f775(f242(x92731),x92732),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f83(x92731),x92732),x92732)) % 186.05/186.62 [9275]~P88(x92751)+E(f775(f775(f83(x92751),x92752),f775(f106(x92751),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f82(x92751),x92752),x92752)) % 186.05/186.62 [9508]~P133(x95081)+E(f775(f775(f242(x95081),f775(f81(x95081),x95082)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f242(x95081),x95082),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9509]~P110(x95091)+E(f775(f775(f242(x95091),f775(f77(x95091),x95092)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f242(x95091),x95092),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9505]~P88(x95051)+E(f775(f775(f83(x95051),f775(f106(x95051),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x95052),f775(f775(f82(x95051),x95052),x95052)) % 186.05/186.62 [9619]~P110(x96191)+E(f775(f77(x96191),f775(f775(f242(x96191),x96192),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x96191),x96192),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9669]~P110(x96691)+P1(f775(f775(f232(x96691),f2(x96691)),f775(f775(f242(x96691),x96692),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.62 [9845]~E(f775(a114,x98452),f775(f106(a850),x98451))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98451),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),a330),a107)),x98452))))) % 186.05/186.62 [9846]~E(f775(f106(a850),x98461),f775(a114,x98462))+P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98461),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),a330),a107)),x98462))))) % 186.05/186.62 [9889]E(f775(a114,x98891),f775(f106(a850),x98892))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98892),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),a330),a107)),x98891))))) % 186.05/186.62 [9890]E(f775(f106(a850),x98901),f775(a114,x98902))+~P1(f775(f775(f88(a1,a844),f775(f106(a1),f775(f775(f82(a1),x98901),a99))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a335),f775(f775(f10(a844,a844,a1),a328),a186))),f775(f775(f9(a1,a850,a844),f775(f775(f10(a850,f857(a850,a844),a1),a330),a107)),x98902))))) % 186.05/186.62 [9667]~P88(x96671)+E(f775(f775(f242(x96671),f775(f106(x96671),a99)),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x96672)),f80(x96671)) % 186.05/186.62 [9668]~P133(x96681)+E(f775(f775(f242(x96681),f775(f81(x96681),f80(x96681))),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x96682)),f80(x96681)) % 186.05/186.62 [9671]~P75(x96711)+E(f775(f775(f242(x96711),x96712),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),a99))),f775(f775(f83(x96711),f775(f775(f83(x96711),x96712),x96712)),x96712)) % 186.05/186.62 [9869]~P1(f775(f775(f232(a1),f2(a1)),x98692))+E(f52(a1,f775(f775(f82(a1),f80(a1)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98691)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98692)),f775(f775(f82(a1),f80(a1)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a1,x98691,x98692)))) % 186.05/186.62 [9892]~P1(f775(f775(f232(a1),f2(a1)),x98922))+E(f775(f775(f43(a1),f775(f775(f82(a1),f80(a1)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98921))),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98922)),f775(f775(f43(a1),x98921),x98922)) % 186.05/186.62 [9894]~P1(f775(f775(f232(a1),x98942),f2(a1)))+E(f775(f775(f43(a1),f775(f775(f82(a1),f80(a1)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98941))),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98942)),f775(f775(f43(a1),f775(f775(f82(a1),x98941),f80(a1))),x98942)) % 186.05/186.62 [9895]~P1(f775(f775(f232(a1),x98952),f2(a1)))+E(f52(a1,f775(f775(f82(a1),f80(a1)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98951)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98952)),f775(f775(f3(a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f52(a1,f775(f775(f82(a1),x98951),f80(a1)),x98952))),f80(a1))) % 186.05/186.62 [9764]~P88(x97641)+E(f775(f775(f242(x97641),f775(f106(x97641),a99)),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97642))),f775(f106(x97641),a99)) % 186.05/186.62 [9766]~P133(x97661)+E(f775(f775(f242(x97661),f775(f81(x97661),f80(x97661))),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97662))),f775(f81(x97661),f80(x97661))) % 186.05/186.62 [5992]E(x59921,x59922)+~P39(a25,x59921,x59923,x59922) % 186.05/186.62 [5004]~P36(x50041,x50043)+P36(x50041,f327(x50041,x50042,x50043)) % 186.05/186.62 [5168]P31(x51681,x51682,x51683)+~P31(x51681,f775(a114,x51682),x51683) % 186.05/186.62 [5251]~P12(x52511,x52512,x52513)+P12(f851(x52511),f149(x52511,x52512),f147(x52511,x52513)) % 186.05/186.62 [5252]~P47(x52521,x52522,x52523)+P47(f851(x52521),f149(x52521,x52522),f147(x52521,x52523)) % 186.05/186.62 [5361]P54(x53611,x53612,x53613)+~E(f627(x53613,x53612,x53611),f628(x53613,x53612,x53611)) % 186.05/186.62 [5362]P53(x53621,x53622,x53623)+~E(f640(x53623,x53622,x53621),f641(x53623,x53622,x53621)) % 186.05/186.62 [6314]P32(x63141,x63142,x63143)+~P31(x63141,f841(x63143,x63142,x63141),f345(x63143,x63142,x63141)) % 186.05/186.62 [4561]~E(x45611,f183(x45612))+~E(x45611,f775(f227(x45612),x45613)) % 186.05/186.62 [4610]~E(f775(f142(x46102),x46101),x46103)+E(x46101,f775(f142(x46102),x46103)) % 186.05/186.62 [4611]~E(x46112,f775(f142(x46111),x46113))+E(f775(f142(x46111),x46112),x46113) % 186.05/186.62 [4655]E(x46551,x46552)+~E(f775(f227(x46553),x46551),f775(f227(x46553),x46552)) % 186.05/186.62 [4656]E(x46561,x46562)+~E(f775(f142(x46563),x46561),f775(f142(x46563),x46562)) % 186.05/186.62 [4854]~P11(x48543,x48541)+P1(f775(f775(x48541,x48542),x48542)) % 186.05/186.62 [4855]~P49(x48553,x48551)+P1(f775(f775(x48551,x48552),x48552)) % 186.05/186.62 [4857]~P58(x48571,x48572)+P1(f775(f321(x48571,x48572),x48573)) % 186.05/186.62 [4919]~P36(x49191,x49192)+P36(f851(x49191),f775(f133(x49191,x49192),x49193)) % 186.05/186.62 [4923]~P1(f775(x49232,x49233))+~E(f775(f256(x49231),x49232),f180(f857(x49231,a844))) % 186.05/186.62 [4924]~P1(f775(x49242,x49243))+~E(f180(f857(x49241,a844)),f775(f256(x49241),x49242)) % 186.05/186.62 [4960]~P1(f775(x49601,x49603))+P1(f775(x49601,f92(x49602,x49601))) % 186.05/186.62 [5084]~E(x50842,x50843)+P1(f775(f775(f334(x50841),x50842),f775(a330,x50843))) % 186.05/186.62 [5137]E(f775(f142(x51371),x51372),f775(f775(f140(x51371),x51373),f115(x51371)))+~E(x51372,f775(f775(f140(x51371),x51373),f115(x51371))) % 186.05/186.62 [5138]~E(x51383,f775(f775(f140(x51381),x51382),f115(x51381)))+E(f775(f775(f140(x51381),x51382),f115(x51381)),f775(f142(x51381),x51383)) % 186.05/186.62 [5163]~E(x51633,f775(f18(f854(x51632),x51631),f183(x51632)))+E(f169(x51631,x51632,x51633),f180(f857(x51631,a844))) % 186.05/186.62 [5184]E(f775(f42(x51841),f374(x51842,x51843,x51841)),x51842)+~E(f775(f42(x51841),x51843),f775(a114,x51842)) % 186.05/186.62 [5190]~P36(x51901,x51903)+P1(f775(f775(f334(x51901),x51902),f322(x51901,x51903))) % 186.05/186.62 [5193]~E(f775(f142(x51932),x51931),f775(f775(f140(x51932),x51933),f115(x51932)))+E(x51931,f775(f775(f140(x51932),x51933),f115(x51932))) % 186.05/186.62 [5194]~E(f775(f775(f140(x51942),x51943),f115(x51942)),f775(f142(x51942),x51941))+E(x51941,f775(f775(f140(x51942),x51943),f115(x51942))) % 186.05/186.62 [5209]E(x52091,f775(f18(f854(x52092),x52093),f183(x52092)))+~E(f169(x52093,x52092,x52091),f180(f857(x52093,a844))) % 186.05/186.62 [5215]E(f87(f856(a850,a850),f55(x52151,x52152)),x52153)+~P1(f775(f55(x52151,x52152),x52153)) % 186.05/186.62 [5223]~E(x52233,f775(f227(x52231),x52232))+P1(f775(f775(f334(x52231),x52232),f226(x52231,x52233))) % 186.05/186.62 [5313]~E(x53132,f115(x53131))+P1(f775(f775(f334(f851(x53131)),x53132),f149(x53131,x53133))) % 186.05/186.62 [5321]~P47(x53211,x53212,x53213)+P47(x53211,x53212,f775(f278(x53211,x53211),x53213)) % 186.05/186.62 [5322]~P54(x53221,x53222,x53223)+P54(x53221,x53222,f775(f278(x53221,x53221),x53223)) % 186.05/186.62 [5342]~P7(x53421)+E(f52(x53421,f52(x53421,x53422,x53423),x53423),f52(x53421,x53422,x53423)) % 186.05/186.62 [5439]E(x54391,x54392)+~P1(f775(f775(f334(x54393),x54391),f775(a330,x54392))) % 186.05/186.62 [5482]~P2(x54821)+E(f182(x54821,x54822,f2(a850),x54823),x54823) % 186.05/186.62 [5502]P47(x55021,x55022,x55023)+~P47(x55021,x55022,f775(f278(x55021,x55021),x55023)) % 186.05/186.62 [5503]P54(x55031,x55032,x55033)+~P54(x55031,x55032,f775(f278(x55031,x55031),x55033)) % 186.05/186.62 [5524]E(x55241,f775(f227(x55242),x55243))+~P1(f775(f775(f334(x55242),x55243),f226(x55242,x55241))) % 186.05/186.62 [5606]~P1(f775(a26,x56063))+P1(f775(a26,f32(x56061,x56062,x56063))) % 186.05/186.62 [5618]E(f775(f126(x56181,x56182),x56183),f115(x56181))+P1(f775(x56182,f747(x56183,x56182,x56181))) % 186.05/186.62 [5774]~P1(f775(f127(x57741),x57743))+P1(f775(f127(x57741),f151(x57741,x57742,x57743))) % 186.05/186.62 [5775]~P1(f775(f127(x57751),x57752))+P1(f775(f127(x57751),f160(x57751,x57752,x57753))) % 186.05/186.62 [5776]~P1(f775(f127(x57761),x57763))+P1(f775(f127(x57761),f162(x57761,x57762,x57763))) % 186.05/186.62 [5777]~P140(x57771,x57773,x57772)+P1(f775(x57771,f52(a1,x57772,x57773))) % 186.05/186.62 [5876]P1(f775(a26,f31(x58761,x58762,x58763)))+~P1(f775(a26,f775(a27,x58762))) % 186.05/186.62 [5888]~P99(x58881)+E(f775(f775(f104(f857(x58881,a844)),f775(f257(x58881),x58882)),f295(x58881,x58882,x58883)),f180(f857(x58881,a844))) % 186.05/186.62 [5889]~P99(x58891)+E(f775(f775(f104(f857(x58891,a844)),f775(f293(x58891),x58892)),f297(x58891,x58892,x58893)),f180(f857(x58891,a844))) % 186.05/186.62 [5890]~P99(x58901)+E(f775(f775(f104(f857(x58901,a844)),f775(f293(x58901),x58902)),f298(x58901,x58902,x58903)),f180(f857(x58901,a844))) % 186.05/186.62 [6041]P1(f775(a26,x60411))+~P1(f775(a26,f32(x60412,x60413,x60411))) % 186.05/186.62 [6043]P1(f775(a26,x60431))+~P1(f775(a26,f33(x60432,x60433,x60431))) % 186.05/186.62 [6045]P1(f775(a26,x60451))+~P1(f775(a26,f33(x60452,x60451,x60453))) % 186.05/186.62 [6125]E(f775(f126(x61251,x61252),x61253),x61253)+~P1(f775(x61252,f759(x61253,x61252,x61251))) % 186.05/186.62 [6127]E(f775(f775(f302(x61271),f414(x61272,x61273,x61271)),f374(x61272,x61273,x61271)),x61273)+~E(f775(f42(x61271),x61273),f775(a114,x61272)) % 186.05/186.62 [6142]P140(x61421,x61422,x61423)+~P1(f775(x61421,f52(a1,x61423,x61422))) % 186.05/186.62 [6194]E(f162(x61941,x61942,x61943),x61943)+~P1(f775(x61942,f768(x61943,x61942,x61941))) % 186.05/186.62 [6235]~P1(f775(a26,f31(x62352,x62351,x62353)))+P1(f775(a26,f775(a27,x62351))) % 186.05/186.62 [6283]~P1(f775(x62832,f820(x62833,x62832,x62831)))+P1(f775(f245(x62831,x62832),x62833)) % 186.05/186.62 [6543]~P1(f775(f321(x65431,x65432),f821(x65433,x65432,x65431)))+P1(f775(f321(x65431,x65432),x65433)) % 186.05/186.62 [6544]~P1(f775(f321(x65441,x65442),f822(x65443,x65442,x65441)))+P1(f775(f321(x65441,x65442),x65443)) % 186.05/186.62 [7175]~P7(x71751)+E(f775(f775(f82(x71751),f775(f775(f83(x71751),x71752),f775(f775(f43(x71751),x71753),x71752))),f52(x71751,x71753,x71752)),x71753) % 186.05/186.62 [7663]E(f775(f775(f241(x76631,x76631),f472(x76632,x76633,x76631)),f472(x76632,x76633,x76631)),x76633)+~P1(f775(f775(f334(f856(x76631,x76631)),x76633),f260(x76631,x76632))) % 186.05/186.62 [7782]~P1(f775(f775(f334(x77821),f526(x77823,x77822,x77821)),f322(x77821,x77823)))+P1(f775(f775(f334(x77821),x77822),f322(x77821,x77823))) % 186.05/186.62 [7783]~P1(f775(f775(f334(x77831),f620(x77833,x77832,x77831)),f322(x77831,x77833)))+P1(f775(f775(f334(x77831),x77832),f322(x77831,x77833))) % 186.05/186.62 [7784]~P1(f775(f775(f334(x77841),f622(x77843,x77842,x77841)),f322(x77841,x77843)))+P1(f775(f775(f334(x77841),x77842),f322(x77841,x77843))) % 186.05/186.62 [7970]~P7(x79701)+E(f775(f775(f82(x79701),f775(f775(f83(x79701),f775(f775(f43(x79701),x79702),x79703)),x79703)),f52(x79701,x79702,x79703)),x79702) % 186.05/186.62 [8011]~E(f775(f42(x80111),x80112),f775(a114,x80113))+~P1(f775(f775(f334(x80111),f414(x80113,x80112,x80111)),f374(x80113,x80112,x80111))) % 186.05/186.62 [8612]P1(f775(f775(f232(f857(f856(x86121,x86121),a844)),f300(x86121,x86122)),f300(x86121,x86123)))+~P1(f775(f775(f232(f857(f856(x86121,x86121),a844)),x86122),f300(x86121,x86123))) % 186.05/186.62 [8850]E(x88501,f115(x88502))+~P1(f775(f775(f334(f856(f851(x88502),f851(x88502))),f775(f775(f241(f851(x88502),f851(x88502)),x88501),f115(x88502))),f147(x88502,x88503))) % 186.05/186.62 [8876]E(x88761,f115(x88762))+~P1(f775(f775(f334(f856(f851(x88762),f851(x88762))),f775(f775(f241(f851(x88762),f851(x88762)),f115(x88762)),x88761)),f147(x88762,x88763))) % 186.05/186.62 [9003]E(f775(f775(f140(x90031),f750(x90032,x90033,x90031)),f751(x90032,x90033,x90031)),x90033)+~P1(f775(f775(f334(f856(f851(x90031),f851(x90031))),f775(f775(f241(f851(x90031),f851(x90031)),f115(x90031)),x90033)),f137(x90031,x90032))) % 186.05/186.62 [9202]~P118(x92021)+~P1(f775(f775(f233(x92021),f775(f775(f82(x92021),f775(f775(f83(x92021),x92022),x92022)),f775(f775(f83(x92021),x92023),x92023))),f2(x92021))) % 186.05/186.62 [9251]P1(f775(f63(x92511),x92512))+~P1(f775(f775(f334(f856(f857(x92511,a844),f857(x92511,a844))),f775(f775(f241(f857(x92511,a844),f857(x92511,a844)),x92513),x92512)),f299(x92511))) % 186.05/186.62 [9529]~P45(x95291,x95292,x95293)+P1(f775(f775(f233(a1),f775(f775(f75(f856(a1,a1),a1,x95291,f240(a1,a1)),f207(x95291)),f224(x95291,x95292,f221(x95291,x95293)))),f2(a1))) % 186.05/186.62 [9530]~P46(x95301,x95302,x95303)+P1(f775(f775(f232(a1),f775(f775(f75(f856(a1,a1),a1,x95301,f240(a1,a1)),f207(x95301)),f224(x95301,x95302,f221(x95301,x95303)))),f2(a1))) % 186.05/186.62 [9644]P45(x96441,x96442,x96443)+~P1(f775(f775(f233(a1),f775(f775(f75(f856(a1,a1),a1,x96441,f240(a1,a1)),f207(x96441)),f224(x96441,x96442,f221(x96441,x96443)))),f2(a1))) % 186.05/186.62 [9645]P46(x96451,x96452,x96453)+~P1(f775(f775(f232(a1),f775(f775(f75(f856(a1,a1),a1,x96451,f240(a1,a1)),f207(x96451)),f224(x96451,x96452,f221(x96451,x96453)))),f2(a1))) % 186.05/186.62 [9975]~P110(x99751)+~P1(f775(f775(f233(x99751),f775(f775(f82(x99751),f775(f775(f242(x99751),x99752),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99751),x99753),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f2(x99751))) % 186.05/186.62 [4639]~E(x46393,f115(x46391))+E(f775(f775(f125(x46391),x46392),x46393),x46392) % 186.05/186.62 [4640]~E(x46402,f115(x46401))+E(f775(f775(f125(x46401),x46402),x46403),x46403) % 186.05/186.62 [4646]~E(x46462,f2(a850))+E(f775(f775(f159(x46461),x46462),x46463),f115(x46461)) % 186.05/186.62 [4650]~E(x46503,f115(x46501))+E(f775(f775(f159(x46501),x46502),x46503),f115(x46501)) % 186.05/186.62 [4689]~E(x46891,x46893)+E(x46891,f775(f775(f125(x46892),f115(x46892)),x46893)) % 186.05/186.62 [4770]~P106(x47702)+E(f775(f239(f857(x47701,x47702)),x47703),f239(x47702)) % 186.05/186.62 [4772]~P101(x47722)+E(f775(f180(f857(x47721,x47722)),x47723),f180(x47722)) % 186.05/186.62 [4791]E(x47911,f115(x47912))+~E(f775(f775(f125(x47912),x47913),x47911),x47913) % 186.05/186.62 [4792]E(x47921,f115(x47922))+~E(f775(f775(f125(x47922),x47921),x47923),x47923) % 186.05/186.62 [4800]E(x48001,f115(x48002))+~E(f775(f775(f125(x48002),x48003),x48001),f115(x48002)) % 186.05/186.62 [4801]E(x48011,f115(x48012))+~E(f775(f775(f125(x48012),x48011),x48013),f115(x48012)) % 186.05/186.62 [4826]~E(x48262,f2(a850))+E(f775(f775(f83(a850),x48261),x48262),f775(f775(f83(a850),x48263),x48262)) % 186.05/186.62 [4828]~E(x48281,f2(a850))+E(f775(f775(f83(a850),x48281),x48282),f775(f775(f83(a850),x48281),x48283)) % 186.05/186.62 [4881]~P85(x48811)+E(f775(f775(f82(x48811),x48812),x48813),f775(f775(f82(x48811),x48813),x48812)) % 186.05/186.62 [4882]~P85(x48821)+E(f775(f775(f83(x48821),x48822),x48823),f775(f775(f83(x48821),x48823),x48822)) % 186.05/186.62 [4884]~P100(x48841)+E(f775(f775(f236(x48841),x48842),x48843),f775(f775(f236(x48841),x48843),x48842)) % 186.05/186.62 [4886]~P100(x48861)+E(f775(f775(f179(x48861),x48862),x48863),f775(f775(f179(x48861),x48863),x48862)) % 186.05/186.62 [4888]~P92(x48881)+E(f775(f775(f103(x48881),x48882),x48883),f775(f775(f103(x48881),x48883),x48882)) % 186.05/186.62 [4889]~P93(x48891)+E(f775(f775(f103(x48891),x48892),x48893),f775(f775(f103(x48891),x48893),x48892)) % 186.05/186.62 [4890]~P93(x48901)+E(f775(f775(f104(x48901),x48902),x48903),f775(f775(f104(x48901),x48903),x48902)) % 186.05/186.62 [4892]~P98(x48921)+E(f775(f775(f104(x48921),x48922),x48923),f775(f775(f104(x48921),x48923),x48922)) % 186.05/186.62 [4955]E(f52(a850,x49551,x49552),f2(a850))+~E(x49551,f775(f775(f83(a850),x49552),x49553)) % 186.05/186.62 [4956]E(f52(a1,x49561,x49562),f2(a1))+~E(x49561,f775(f775(f83(a1),x49562),x49563)) % 186.05/186.62 [5016]E(x50161,x50162)+~E(f775(f775(f82(a850),x50163),x50161),f775(f775(f82(a850),x50163),x50162)) % 186.05/186.62 [5017]E(x50171,x50172)+~E(f775(f775(f82(a850),x50171),x50173),f775(f775(f82(a850),x50172),x50173)) % 186.05/186.62 [5027]~P69(x50271)+E(f775(f775(f82(x50271),x50272),f775(f81(x50271),x50273)),f775(f775(f3(x50271),x50272),x50273)) % 186.05/186.62 [5028]~P104(x50281)+E(f775(f775(f82(x50281),x50282),f775(f81(x50281),x50283)),f775(f775(f3(x50281),x50282),x50283)) % 186.05/186.62 [5029]~P6(x50291)+E(f775(f775(f82(x50291),x50292),f775(f81(x50291),x50293)),f775(f775(f3(x50291),x50292),x50293)) % 186.05/186.62 [5030]~P90(x50301)+E(f775(f775(f104(x50301),x50302),f775(f81(x50301),x50303)),f775(f775(f3(x50301),x50302),x50303)) % 186.05/186.62 [5031]~P69(x50311)+E(f775(f775(f3(x50311),x50312),f775(f81(x50311),x50313)),f775(f775(f82(x50311),x50312),x50313)) % 186.05/186.62 [5078]~P1(f775(x50783,x50782))+P1(f775(f775(f334(x50781),x50782),x50783)) % 186.05/186.62 [5080]~P66(x50802)+E(f775(f775(f8(x50801,x50802),x50803),f180(f857(x50801,a844))),f2(x50802)) % 186.05/186.62 [5082]~P70(x50822)+E(f775(f775(f11(x50821,x50822),x50823),f180(f857(x50821,a844))),f80(x50822)) % 186.05/186.62 [5127]~E(x51272,f775(f775(f82(a850),x51271),x51273))+P1(f775(f775(f232(a850),x51271),x51272)) % 186.05/186.62 [5129]~E(x51292,f180(f857(x51291,a844)))+E(f775(f775(f61(x51291),x51292),x51293),f180(f857(f857(x51291,a844),a844))) % 186.05/186.62 [5130]~E(x51302,f180(f857(x51301,a844)))+E(f180(f857(f857(x51301,a844),a844)),f775(f775(f61(x51301),x51302),x51303)) % 186.05/186.62 [5197]~E(f775(f259(x51972,x51973),x51971),f180(f857(x51973,a844)))+E(x51971,f180(f857(f856(x51972,x51973),a844))) % 186.05/186.62 [5198]~E(f775(f261(x51982,x51983),x51981),f180(f857(x51982,a844)))+E(x51981,f180(f857(f856(x51982,x51983),a844))) % 186.05/186.62 [5229]E(f775(f259(x52291,x52292),x52293),f180(f857(x52292,a844)))+~E(x52293,f180(f857(f856(x52291,x52292),a844))) % 186.05/186.62 [5230]E(f775(f261(x52301,x52302),x52303),f180(f857(x52301,a844)))+~E(x52303,f180(f857(f856(x52301,x52302),a844))) % 186.05/186.62 [5233]E(f269(x52331,x52332,x52333),f775(f775(f3(a101),x52332),x52333))+P1(f775(f775(f233(a101),x52332),x52333)) % 186.05/186.62 [5249]P1(f775(x52491,x52492))+~P1(f775(f775(f334(x52493),x52492),x52491)) % 186.05/186.62 [5285]E(x52851,x52852)+~E(f775(f81(f857(x52853,a844)),x52851),f775(f81(f857(x52853,a844)),x52852)) % 186.05/186.62 [5290]E(f307(x52901,x52902,x52903),f183(f851(a842)))+~P1(f775(f775(f233(a1),x52902),x52903)) % 186.05/186.62 [5295]~E(x52951,f180(f857(x52952,a844)))+~P1(f775(f775(f334(x52952),x52953),x52951)) % 186.05/186.62 [5323]~E(x53232,f775(f775(f82(a1),x53231),f775(f102(a1),x53233)))+P1(f775(f775(f232(a1),x53231),x53232)) % 186.05/186.62 [5339]E(f775(f775(f302(x53391),x53392),x53393),x53393)+~P1(f775(f775(f334(x53391),x53392),x53393)) % 186.05/186.62 [5351]E(x53511,f180(f857(x53512,a844)))+~E(f775(f775(f61(x53512),x53511),x53513),f180(f857(f857(x53512,a844),a844))) % 186.05/186.62 [5352]E(x53521,f180(f857(x53522,a844)))+~E(f180(f857(f857(x53522,a844),a844)),f775(f775(f61(x53522),x53521),x53523)) % 186.05/186.62 [5358]~P121(x53581)+E(f775(f775(f83(x53581),f775(f81(x53581),x53582)),f775(f81(x53581),x53583)),f775(f775(f83(x53581),x53582),x53583)) % 186.05/186.62 [5360]~P60(x53601)+E(f775(f775(f283(x53601),f775(f81(x53601),x53602)),f775(f81(x53601),x53603)),f775(f775(f283(x53601),x53602),x53603)) % 186.05/186.62 [5392]~P1(f775(x53923,x53922))+P1(f775(f775(f334(x53921),x53922),f775(f256(x53921),x53923))) % 186.05/186.62 [5432]E(f151(x54321,x54322,x54323),x54323)+P1(f775(f775(f334(x54321),x54322),f775(f158(x54321),x54323))) % 186.05/186.62 [5510]~P1(f775(f127(x55101),x55103))+P1(f775(f127(x55101),f775(f126(x55101,x55102),x55103))) % 186.05/186.62 [5552]~P7(x55521)+E(f775(f775(f43(x55521),f52(x55521,x55522,x55523)),x55523),f2(x55521)) % 186.05/186.62 [5570]E(f160(x55701,f775(f775(f140(x55701),x55702),f115(x55701)),x55703),f115(x55701))+P1(f775(f775(f334(a850),f2(a850)),x55703)) % 186.05/186.62 [5635]E(x56351,x56352)+~E(f775(f775(f83(a850),f775(a114,x56353)),x56351),f775(f775(f83(a850),f775(a114,x56353)),x56352)) % 186.05/186.62 [5636]~E(x56362,f775(f775(f82(a1),x56361),f775(f102(a1),f775(a114,x56363))))+P1(f775(f775(f233(a1),x56361),x56362)) % 186.05/186.62 [5754]~E(x57543,f115(x57541))+E(f775(f775(f775(f173(f851(x57541),f851(x57541)),x57542),f141(x57541)),x57543),f115(x57541)) % 186.05/186.62 [5758]P1(f775(x57581,x57582))+~P1(f775(f775(f334(x57583),x57582),f775(f256(x57583),x57581))) % 186.05/186.62 [5792]E(x57921,x57922)+~E(f775(f775(f302(x57923),x57921),f180(f857(x57923,a844))),f775(f775(f302(x57923),x57922),f180(f857(x57923,a844)))) % 186.05/186.62 [5802]~P99(x58021)+E(f775(f775(f104(f857(x58021,a844)),f775(f257(x58021),x58022)),f775(f294(x58021,x58022),x58023)),f180(f857(x58021,a844))) % 186.05/186.62 [5862]~P77(x58621)+E(f775(f303(x58621,x58621,f81(x58621)),f775(f294(x58621,x58622),x58623)),f297(x58621,f775(f81(x58621),x58623),f775(f81(x58621),x58622))) % 186.05/186.62 [5870]E(f775(f181(f851(x58701)),f151(x58701,x58702,x58703)),f775(f181(f851(x58701)),x58703))+P1(f775(f775(f334(x58701),x58702),f775(f158(x58701),x58703))) % 186.05/186.62 [5927]~P99(x59271)+E(f775(f775(f104(f857(x59271,a844)),f775(f294(x59271,x59272),x59273)),f775(f258(x59271),x59273)),f180(f857(x59271,a844))) % 186.05/186.62 [5948]~P77(x59481)+E(f775(f303(x59481,x59481,f81(x59481)),f295(x59481,x59482,x59483)),f295(x59481,f775(f81(x59481),x59483),f775(f81(x59481),x59482))) % 186.05/186.62 [5949]~P77(x59491)+E(f775(f303(x59491,x59491,f81(x59491)),f298(x59491,x59492,x59493)),f298(x59491,f775(f81(x59491),x59493),f775(f81(x59491),x59492))) % 186.05/186.62 [6008]E(f160(x60081,f775(f775(f140(x60081),x60082),f115(x60081)),x60083),f775(f775(f140(x60081),x60082),f115(x60081)))+~P1(f775(f775(f334(a850),f2(a850)),x60083)) % 186.05/186.62 [6016]~P77(x60161)+E(f775(f303(x60161,x60161,f81(x60161)),f297(x60161,x60162,x60163)),f775(f294(x60161,f775(f81(x60161),x60163)),f775(f81(x60161),x60162))) % 186.05/186.62 [6036]~P8(x60361)+E(f52(x60361,f775(f81(x60361),f52(x60361,x60362,x60363)),x60363),f52(x60361,f775(f81(x60361),x60362),x60363)) % 186.05/186.62 [6140]~P1(f775(f63(f856(x61402,x61401)),x61403))+P1(f775(f63(x61401),f775(f259(x61402,x61401),x61403))) % 186.05/186.62 [6141]~P1(f775(f63(f856(x61411,x61412)),x61413))+P1(f775(f63(x61411),f775(f261(x61411,x61412),x61413))) % 186.05/186.62 [6146]~P99(x61461)+E(f775(f775(f104(f857(x61461,a844)),f295(x61461,x61462,x61463)),f775(f296(x61461),x61463)),f180(f857(x61461,a844))) % 186.05/186.62 [6147]~P99(x61471)+E(f775(f775(f104(f857(x61471,a844)),f297(x61471,x61472,x61473)),f775(f296(x61471),x61473)),f180(f857(x61471,a844))) % 186.05/186.62 [6148]~P99(x61481)+E(f775(f775(f104(f857(x61481,a844)),f298(x61481,x61482,x61483)),f775(f258(x61481),x61483)),f180(f857(x61481,a844))) % 186.05/186.62 [6217]E(f775(f775(f153(x62171),x62172),f730(x62172,x62173,x62171)),x62173)+~P1(f775(f775(f334(x62171),x62173),f775(f158(x62171),x62172))) % 186.05/186.62 [6369]E(x63691,f115(x63692))+~E(f775(f775(f775(f173(f851(x63692),f851(x63692)),x63693),f141(x63692)),x63691),f115(x63692)) % 186.05/186.62 [6448]P39(x64481,x64482,f407(x64483,x64482,x64481),x64483)+~P1(f775(f775(f187(x64481),x64482),x64483)) % 186.05/186.62 [6449]P39(x64491,x64492,f521(x64493,x64492,x64491),x64493)+~P1(f775(f775(f187(x64491),x64492),x64493)) % 186.05/186.62 [6479]~P1(f775(f63(f856(x64792,x64791)),x64793))+P1(f775(f63(f856(x64791,x64792)),f775(f278(x64792,x64791),x64793))) % 186.05/186.62 [6501]E(x65011,x65012)+~E(f282(a850,f279(a850),x65013,x65011),f775(f775(f302(a850),x65012),f180(f857(a850,a844)))) % 186.05/186.62 [6502]E(x65021,x65022)+~E(f282(a850,f279(a850),x65021,x65022),f775(f775(f302(a850),x65023),f180(f857(a850,a844)))) % 186.05/186.62 [6638]P54(x66381,x66382,x66383)+P1(f775(f775(f334(x66381),f628(x66383,x66382,x66381)),x66382)) % 186.05/186.62 [6639]P54(x66391,x66392,x66393)+P1(f775(f775(f334(x66391),f627(x66393,x66392,x66391)),x66392)) % 186.05/186.62 [6651]P1(f775(f321(x66511,x66512),x66513))+P1(f775(f775(x66512,f821(x66513,x66512,x66511)),x66513)) % 186.05/186.62 [6652]P1(f775(f321(x66521,x66522),x66523))+P1(f775(f775(x66522,f822(x66523,x66522,x66521)),x66523)) % 186.05/186.62 [6683]E(f775(f181(f851(x66831)),f151(x66831,x66832,x66833)),f775(f775(f3(a850),f775(f181(f851(x66831)),x66833)),f80(a850)))+~P1(f775(f775(f334(x66831),x66832),f775(f158(x66831),x66833))) % 186.05/186.62 [6723]P1(f775(f245(x67231,x67232),x67233))+P1(f775(f775(f334(x67231),f820(x67233,x67232,x67231)),x67233)) % 186.05/186.62 [6736]~P1(f775(f63(f856(x67362,x67361)),f775(f278(x67361,x67362),x67363)))+P1(f775(f63(f856(x67361,x67362)),x67363)) % 186.05/186.62 [6797]~P1(f775(f775(f334(x67971),x67972),f775(f158(x67971),f116(x67971,x67973))))+P1(f775(f775(f334(x67971),x67972),f775(f158(x67971),x67973))) % 186.05/186.62 [6804]P32(x68041,x68042,x68043)+P1(f775(f775(f334(f849(x68041)),f345(x68043,x68042,x68041)),x68043)) % 186.05/186.62 [6833]E(f775(f126(x68331,x68332),x68333),x68333)+P1(f775(f775(f334(x68331),f759(x68333,x68332,x68331)),f775(f158(x68331),x68333))) % 186.05/186.62 [6850]E(f775(f126(x68501,x68502),x68503),f115(x68501))+P1(f775(f775(f334(x68501),f747(x68503,x68502,x68501)),f775(f158(x68501),x68503))) % 186.05/186.62 [6878]E(f162(x68781,x68782,x68783),x68783)+P1(f775(f775(f334(x68781),f768(x68783,x68782,x68781)),f775(f158(x68781),x68783))) % 186.05/186.62 [6999]P1(f775(f775(f334(x69991),x69992),f697(x69993,x69992,x69991)))+~P1(f775(f775(f334(x69991),x69992),f44(f857(x69991,a844),x69993))) % 186.05/186.62 [7001]~P66(x70011)+E(f775(f775(f82(x70011),f775(f775(f8(a850,x70011),x70012),f775(f257(a850),x70013))),f775(x70012,x70013)),f775(f775(f8(a850,x70011),x70012),f775(f257(a850),f775(a114,x70013)))) % 186.05/186.62 [7105]~P1(f775(f775(f334(x71051),x71052),f686(x71052,x71053,x71051)))+P1(f775(f775(f334(x71051),x71052),f45(f857(x71051,a844),x71053))) % 186.05/186.62 [7134]~P66(x71341)+E(f775(f775(f82(x71341),f775(f775(f8(a850,x71341),x71342),f775(f293(a850),x71343))),f775(x71342,f775(a114,x71343))),f775(f775(f8(a850,x71341),x71342),f775(f293(a850),f775(a114,x71343)))) % 186.05/186.62 [7288]P1(f775(f775(f334(f851(x72881)),x72882),f149(x72881,x72883)))+P1(f775(f775(f334(x72881),f746(x72883,x72882,x72881)),f775(f158(x72881),x72882))) % 186.05/186.62 [7305]~P1(f775(f775(f334(f851(x73051)),x73052),f149(x73051,f322(x73051,x73053))))+P1(f775(f775(f334(f851(x73051)),x73052),f322(f851(x73051),f146(x73051,x73053)))) % 186.05/186.62 [7333]~P1(f775(f775(f334(f851(x73331)),x73332),f322(f851(x73331),f146(x73331,x73333))))+P1(f775(f775(f334(f851(x73331)),x73332),f149(x73331,f322(x73331,x73333)))) % 186.05/186.62 [7373]E(f775(f775(f775(f173(f851(x73731),f851(x73731)),x73732),f141(x73731)),x73733),x73733)+~P1(f775(f775(f232(a850),f775(f181(f851(x73731)),x73733)),f80(a850))) % 186.05/186.62 [7427]~P29(x74271,x74272,x74273,f239(f857(x74271,a844)))+P29(f851(x74271),f851(x74272),f775(f143(x74271,x74272),x74273),f239(f857(f851(x74271),a844))) % 186.05/186.62 [7584]E(x75841,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x75842)),x75843)),f775(f250(a850,a850),x75842)))+~P1(f775(f55(x75841,x75843),x75842)) % 186.05/186.62 [7592]P29(x75921,x75922,x75923,f239(f857(x75921,a844)))+~P29(f851(x75921),f851(x75922),f775(f143(x75921,x75922),x75923),f239(f857(f851(x75921),a844))) % 186.05/186.62 [7635]P1(f775(f775(f334(f857(x76351,a844)),f686(x76352,x76353,x76351)),x76353))+P1(f775(f775(f334(x76351),x76352),f45(f857(x76351,a844),x76353))) % 186.05/186.62 [7724]P1(f775(f775(f334(f851(x77241)),x77242),f149(x77241,x77243)))+~P1(f775(f775(f334(x77241),f746(x77243,x77242,x77241)),x77243)) % 186.05/186.62 [7855]E(x78551,x78552)+~E(f775(f775(f9(x78553,f857(x78553,a844),a844),f334(x78553)),x78551),f775(f775(f9(x78553,f857(x78553,a844),a844),f334(x78553)),x78552)) % 186.05/186.62 [7861]~P1(f775(f775(f334(f856(x78611,x78611)),x78613),f260(x78611,x78612)))+P1(f775(f775(f334(x78611),f472(x78612,x78613,x78611)),x78612)) % 186.05/186.62 [7863]~P1(f775(f775(f334(x78631),x78633),f44(f857(x78631,a844),x78632)))+P1(f775(f775(f334(f857(x78631,a844)),f697(x78632,x78633,x78631)),x78632)) % 186.05/186.62 [8123]E(f775(f229(f854(f851(a842)),f851(a842),f307(x81231,x81232,f775(f775(f82(a1),x81233),f80(a1))),f227(f851(a842))),f775(x81231,x81233)),f307(x81231,x81232,x81233))+P1(f775(f775(f233(a1),x81232),x81233)) % 186.05/186.62 [8222]E(x82221,f115(x82222))+P1(f775(f775(f334(x82222),f775(f240(x82222,f856(a101,a101)),f775(f270(x82222,x82221),x82223))),f775(f158(x82222),x82221))) % 186.05/186.62 [8320]~P5(x83201)+E(f775(f132(x83201,x83201,f775(f9(x83201,x83201,x83201),f82(x83201)),x83202),f775(f142(x83201),x83203)),f775(f132(x83201,x83201,f82(x83201),x83202),x83203)) % 186.05/186.62 [8781]~P100(x87811)+E(f775(f158(x87811),f139(x87811,x87811,f7(x87811),x87812,x87813)),f775(f775(f302(x87811),x87812),f775(f158(x87811),x87813))) % 186.05/186.62 [8790]P1(f775(f775(f233(a850),f2(a850)),f639(x87901,x87902,x87903)))+~P1(f775(f775(f334(f856(x87903,x87903)),x87902),f775(f775(f281(x87903,x87903,x87903),x87901),f300(x87903,x87901)))) % 186.05/186.62 [9053]~P56(x90531,x90532)+~P1(f775(f775(f334(f856(x90531,x90531)),f775(f775(f241(x90531,x90531),x90533),x90533)),f775(f775(f281(x90531,x90531,x90531),x90532),f300(x90531,x90532)))) % 186.05/186.62 [9164]~E(f775(f775(f104(f857(f856(x91641,x91641),a844)),f775(f278(x91641,x91641),x91642)),f300(x91641,x91642)),f180(f857(f856(x91641,x91641),a844)))+~P1(f775(f775(f334(f856(x91641,x91641)),f775(f775(f241(x91641,x91641),x91643),x91643)),f775(f775(f281(x91641,x91641,x91641),x91642),f300(x91641,x91642)))) % 186.05/186.62 [9338]~P1(f775(f63(x93381),x93382))+P1(f775(f775(f232(a850),f775(f42(x93381),f775(f775(f3(f857(x93381,a844)),x93382),f775(f775(f302(x93381),x93383),f180(f857(x93381,a844)))))),f775(f42(x93381),x93382))) % 186.05/186.62 [4939]~E(x49393,f115(x49391))+E(f134(x49391,f775(f775(f140(x49391),x49392),x49393)),x49392) % 186.05/186.62 [4952]~E(x49523,f115(x49521))+E(f116(x49521,f775(f775(f140(x49521),x49522),x49523)),f115(x49521)) % 186.05/186.62 [4981]E(x49811,f115(x49812))+E(f134(x49812,f775(f775(f140(x49812),x49813),x49811)),f134(x49812,x49811)) % 186.05/186.62 [4983]E(x49831,f115(x49832))+E(f134(x49832,f775(f775(f125(x49832),x49833),x49831)),f134(x49832,x49831)) % 186.05/186.62 [4990]~E(x49903,f115(x49901))+E(f134(x49901,f775(f775(f125(x49901),x49902),x49903)),f134(x49901,x49902)) % 186.05/186.62 [4991]~E(x49913,f115(x49911))+E(f116(x49911,f775(f775(f125(x49911),x49912),x49913)),f116(x49911,x49912)) % 186.05/186.62 [5021]E(x50211,f115(x50212))+E(f775(f131(x50212),f775(f775(f125(x50212),x50211),x50213)),f775(f131(x50212),x50211)) % 186.05/186.62 [5052]~E(x50522,f115(x50521))+E(f775(f131(x50521),f775(f775(f125(x50521),x50522),x50523)),f775(f131(x50521),x50523)) % 186.05/186.62 [5103]~P100(x51031)+E(f775(f775(f236(x51031),x51032),f775(f775(f179(x51031),x51032),x51033)),x51032) % 186.05/186.62 [5104]~P100(x51041)+E(f775(f775(f179(x51041),x51042),f775(f775(f236(x51041),x51042),x51043)),x51042) % 186.05/186.62 [5105]~P93(x51051)+E(f775(f775(f103(x51051),x51052),f775(f775(f104(x51051),x51052),x51053)),x51052) % 186.05/186.62 [5106]~P93(x51061)+E(f775(f775(f104(x51061),x51062),f775(f775(f103(x51061),x51062),x51063)),x51062) % 186.05/186.62 [5125]~P7(x51251)+E(f52(x51251,f775(f775(f83(x51251),x51252),x51253),x51253),f2(x51251)) % 186.05/186.62 [5126]~P7(x51261)+E(f52(x51261,f775(f775(f83(x51261),x51262),x51263),x51262),f2(x51261)) % 186.05/186.62 [5192]~P6(x51921)+E(f775(f81(x51921),f775(f775(f3(x51921),x51922),x51923)),f775(f775(f3(x51921),x51923),x51922)) % 186.05/186.62 [5253]E(x52531,f115(x52532))+E(f116(x52532,f775(f775(f140(x52532),x52533),x52531)),f775(f775(f140(x52532),x52533),f116(x52532,x52531))) % 186.05/186.62 [5254]E(x52541,f115(x52542))+E(f116(x52542,f775(f775(f125(x52542),x52543),x52541)),f775(f775(f125(x52542),x52543),f116(x52542,x52541))) % 186.05/186.62 [5255]~P9(x52551)+E(f45(x52551,f775(f775(f302(x52551),x52552),x52553)),f775(f775(f104(x52551),x52552),f45(x52551,x52553))) % 186.05/186.62 [5256]~P9(x52561)+E(f44(x52561,f775(f775(f302(x52561),x52562),x52563)),f775(f775(f103(x52561),x52562),f44(x52561,x52563))) % 186.05/186.62 [5299]~P91(x52991)+E(f775(f775(f83(x52991),x52992),f775(f775(f83(x52991),x52992),x52993)),f775(f775(f83(x52991),x52992),x52993)) % 186.05/186.62 [5301]~P100(x53011)+E(f775(f775(f236(x53011),x53012),f775(f775(f236(x53011),x53012),x53013)),f775(f775(f236(x53011),x53012),x53013)) % 186.05/186.62 [5303]~P100(x53031)+E(f775(f775(f179(x53031),x53032),f775(f775(f179(x53031),x53032),x53033)),f775(f775(f179(x53031),x53032),x53033)) % 186.05/186.62 [5305]~P92(x53051)+E(f775(f775(f103(x53051),x53052),f775(f775(f103(x53051),x53052),x53053)),f775(f775(f103(x53051),x53052),x53053)) % 186.05/186.62 [5306]~P93(x53061)+E(f775(f775(f103(x53061),x53062),f775(f775(f103(x53061),x53062),x53063)),f775(f775(f103(x53061),x53062),x53063)) % 186.05/186.62 [5307]~P93(x53071)+E(f775(f775(f104(x53071),x53072),f775(f775(f104(x53071),x53072),x53073)),f775(f775(f104(x53071),x53072),x53073)) % 186.05/186.62 [5309]~P98(x53091)+E(f775(f775(f104(x53091),x53092),f775(f775(f104(x53091),x53092),x53093)),f775(f775(f104(x53091),x53092),x53093)) % 186.05/186.62 [5316]~P7(x53161)+E(f52(x53161,f775(f775(f82(x53161),x53162),x53163),x53163),f52(x53161,x53162,x53163)) % 186.05/186.62 [5317]~P7(x53171)+E(f52(x53171,f775(f775(f82(x53171),x53172),x53173),x53172),f52(x53171,x53173,x53172)) % 186.05/186.62 [5324]~P121(x53241)+E(f775(f775(f83(x53241),x53242),f775(f81(x53241),x53243)),f775(f81(x53241),f775(f775(f83(x53241),x53242),x53243))) % 186.05/186.62 [5325]~P60(x53251)+E(f775(f775(f283(x53251),x53252),f775(f81(x53251),x53253)),f775(f81(x53251),f775(f775(f283(x53251),x53252),x53253))) % 186.05/186.62 [5326]~P67(x53261)+E(f775(f775(f82(x53261),x53262),f775(f155(x53261),x53263)),f775(f155(x53261),f775(f775(f140(x53261),x53262),x53263))) % 186.05/186.62 [5357]~P121(x53571)+E(f775(f775(f83(x53571),f775(f81(x53571),x53572)),x53573),f775(f775(f83(x53571),x53572),f775(f81(x53571),x53573))) % 186.05/186.62 [5363]~P12(x53631,x53632,x53633)+E(f44(f857(x53631,a844),f775(f775(f61(x53631),x53632),x53633)),x53632) % 186.05/186.62 [5424]~P105(x54241)+E(f775(f775(f83(x54241),x54242),f775(f775(f242(x54241),x54242),x54243)),f775(f775(f242(x54241),x54242),f775(a114,x54243))) % 186.05/186.62 [5425]~P85(x54251)+E(f775(f775(f83(x54251),x54252),f775(f775(f242(x54251),x54252),x54253)),f775(f775(f242(x54251),x54252),f775(a114,x54253))) % 186.05/186.62 [5435]~P69(x54351)+E(f775(f775(f82(x54351),f775(f81(x54351),x54352)),f775(f775(f82(x54351),x54352),x54353)),x54353) % 186.05/186.62 [5454]~P2(x54541)+E(f775(f775(f242(x54541),f775(f102(x54541),x54542)),x54543),f775(f102(x54541),f775(f775(f242(a850),x54542),x54543))) % 186.05/186.62 [5455]~P133(x54551)+E(f775(f775(f242(x54551),f775(f105(x54551),x54552)),x54553),f775(f105(x54551),f775(f775(f242(a1),x54552),x54553))) % 186.05/186.62 [5460]~P79(x54601)+E(f775(f77(x54601),f775(f775(f3(x54601),x54602),x54603)),f775(f77(x54601),f775(f775(f3(x54601),x54603),x54602))) % 186.05/186.62 [5463]~P110(x54631)+E(f775(f775(f83(x54631),f84(x54631,x54632)),f84(x54631,x54633)),f84(x54631,f775(f775(f83(x54631),x54632),x54633))) % 186.05/186.62 [5467]E(x54671,f115(x54672))+E(f775(f775(f125(x54672),f775(f157(x54672),x54671)),x54673),f775(f157(x54672),f775(f775(f125(x54672),x54671),x54673))) % 186.05/186.62 [5473]~E(x54732,f775(a114,f775(f775(f82(a850),x54731),x54733)))+P1(f775(f775(f233(a850),x54731),x54732)) % 186.05/186.62 [5474]~P121(x54741)+E(f775(f775(f83(x54741),f775(f81(x54741),x54742)),x54743),f775(f81(x54741),f775(f775(f83(x54741),x54742),x54743))) % 186.05/186.62 [5475]~P113(x54751)+E(f775(f775(f283(x54751),f775(f81(x54751),x54752)),x54753),f775(f81(x54751),f775(f775(f283(x54751),x54752),x54753))) % 186.05/186.62 [5476]~P110(x54761)+E(f775(f775(f242(x54761),f775(f77(x54761),x54762)),x54763),f775(f77(x54761),f775(f775(f242(x54761),x54762),x54763))) % 186.05/186.62 [5569]E(f493(x55691,x55692,x55693),f497(x55691,x55692,x55693))+E(f775(f775(f104(f857(x55693,a844)),x55692),x55691),f180(f857(x55693,a844))) % 186.05/186.62 [5583]~P66(x55832)+E(f775(f775(f8(x55831,x55832),f775(f18(x55832,x55831),f2(x55832))),x55833),f2(x55832)) % 186.05/186.62 [5584]~P70(x55842)+E(f775(f775(f11(x55841,x55842),f775(f18(x55842,x55841),f80(x55842))),x55843),f80(x55842)) % 186.05/186.62 [5586]~P2(x55861)+E(f775(f775(f82(x55861),f775(f102(x55861),x55862)),f775(f102(x55861),x55863)),f775(f102(x55861),f775(f775(f82(a850),x55862),x55863))) % 186.05/186.62 [5587]~P2(x55871)+E(f775(f775(f83(x55871),f775(f102(x55871),x55872)),f775(f102(x55871),x55873)),f775(f102(x55871),f775(f775(f83(a850),x55872),x55873))) % 186.05/186.62 [5588]~P133(x55881)+E(f775(f775(f82(x55881),f775(f105(x55881),x55882)),f775(f105(x55881),x55883)),f775(f105(x55881),f775(f775(f82(a1),x55882),x55883))) % 186.05/186.62 [5589]~P133(x55891)+E(f775(f775(f83(x55891),f775(f105(x55891),x55892)),f775(f105(x55891),x55893)),f775(f105(x55891),f775(f775(f83(a1),x55892),x55893))) % 186.05/186.62 [5590]~P133(x55901)+E(f775(f775(f3(x55901),f775(f105(x55901),x55902)),f775(f105(x55901),x55903)),f775(f105(x55901),f775(f775(f3(a1),x55902),x55903))) % 186.05/186.62 [5593]~P88(x55931)+E(f775(f775(f3(x55931),f775(f106(x55931),x55932)),f775(f106(x55931),x55933)),f775(f106(x55931),f775(f775(f3(a1),x55932),x55933))) % 186.05/186.62 [5594]~P88(x55941)+E(f775(f775(f82(x55941),f775(f106(x55941),x55942)),f775(f106(x55941),x55943)),f775(f106(x55941),f775(f775(f82(a1),x55942),x55943))) % 186.05/186.62 [5595]~P88(x55951)+E(f775(f775(f83(x55951),f775(f106(x55951),x55952)),f775(f106(x55951),x55953)),f775(f106(x55951),f775(f775(f83(a1),x55952),x55953))) % 186.05/186.62 [5642]~E(x56423,x56422)+P1(f775(f775(f232(f857(x56421,a844)),x56422),x56423)) % 186.05/186.62 [5648]~E(x56482,x56483)+P1(f775(f775(f232(f857(x56481,a844)),x56482),x56483)) % 186.05/186.62 [5653]~P69(x56531)+E(f775(f775(f82(x56531),f775(f81(x56531),x56532)),f775(f81(x56531),x56533)),f775(f81(x56531),f775(f775(f82(x56531),x56533),x56532))) % 186.05/186.62 [5654]~P6(x56541)+E(f775(f775(f82(x56541),f775(f81(x56541),x56542)),f775(f81(x56541),x56543)),f775(f81(x56541),f775(f775(f82(x56541),x56542),x56543))) % 186.05/186.62 [5655]~P68(x56551)+E(f775(f775(f179(x56551),f775(f81(x56551),x56552)),f775(f81(x56551),x56553)),f775(f81(x56551),f775(f775(f236(x56551),x56552),x56553))) % 186.05/186.62 [5656]~P68(x56561)+E(f775(f775(f236(x56561),f775(f81(x56561),x56562)),f775(f81(x56561),x56563)),f775(f81(x56561),f775(f775(f179(x56561),x56562),x56563))) % 186.05/186.62 [5657]~P90(x56571)+E(f775(f775(f104(x56571),f775(f81(x56571),x56572)),f775(f81(x56571),x56573)),f775(f81(x56571),f775(f775(f103(x56571),x56572),x56573))) % 186.05/186.62 [5658]~P90(x56581)+E(f775(f775(f103(x56581),f775(f81(x56581),x56582)),f775(f81(x56581),x56583)),f775(f81(x56581),f775(f775(f104(x56581),x56582),x56583))) % 186.05/186.62 [5659]~P110(x56591)+E(f775(f775(f83(x56591),f775(f77(x56591),x56592)),f775(f77(x56591),x56593)),f775(f77(x56591),f775(f775(f83(x56591),x56592),x56593))) % 186.05/186.62 [5660]~P62(x56601)+E(f775(f775(f283(x56601),f775(f77(x56601),x56602)),f775(f77(x56601),x56603)),f775(f77(x56601),f775(f775(f283(x56601),x56602),x56603))) % 186.05/186.62 [5661]~P67(x56611)+E(f775(f775(f82(x56611),f775(f155(x56611),x56612)),f775(f155(x56611),x56613)),f775(f155(x56611),f775(f775(f125(x56611),x56612),x56613))) % 186.05/186.62 [5662]E(x56621,f180(f857(x56622,a844)))+~E(f775(f775(f103(f857(x56622,a844)),x56623),x56621),f180(f857(x56622,a844))) % 186.05/186.62 [5663]E(x56631,f180(f857(x56632,a844)))+~E(f775(f775(f103(f857(x56632,a844)),x56631),x56633),f180(f857(x56632,a844))) % 186.05/186.62 [5664]~P141(x56641,x56643,x56642)+P1(f775(x56641,f775(f775(f43(a1),x56642),x56643))) % 186.05/186.62 [5726]~P1(f775(f63(x57261),x57263))+P1(f775(f63(x57261),f775(f775(f302(x57261),x57262),x57263))) % 186.05/186.62 [5727]~P1(f775(f127(x57271),x57273))+P1(f775(f127(x57271),f775(f775(f159(x57271),x57272),x57273))) % 186.05/186.62 [5728]~P1(f775(f127(x57281),x57283))+P1(f775(f127(x57281),f775(f775(f128(x57281),x57282),x57283))) % 186.05/186.62 [5759]~P100(x57591)+P1(f775(f775(f232(x57591),x57592),f775(f775(f179(x57591),x57593),x57592))) % 186.05/186.62 [5760]~P100(x57601)+P1(f775(f775(f232(x57601),x57602),f775(f775(f179(x57601),x57602),x57603))) % 186.05/186.62 [5761]~P92(x57611)+P1(f775(f775(f232(x57611),x57612),f775(f775(f103(x57611),x57613),x57612))) % 186.05/186.62 [5762]~P93(x57621)+P1(f775(f775(f232(x57621),x57622),f775(f775(f103(x57621),x57623),x57622))) % 186.05/186.62 [5763]~P92(x57631)+P1(f775(f775(f232(x57631),x57632),f775(f775(f103(x57631),x57632),x57633))) % 186.05/186.62 [5764]~P93(x57641)+P1(f775(f775(f232(x57641),x57642),f775(f775(f103(x57641),x57642),x57643))) % 186.05/186.62 [5765]~P85(x57651)+P1(f775(f775(f279(x57651),x57652),f775(f775(f83(x57651),x57653),x57652))) % 186.05/186.62 [5766]~P85(x57661)+P1(f775(f775(f279(x57661),x57662),f775(f775(f83(x57661),x57662),x57663))) % 186.05/186.62 [5779]~E(x57791,f2(a850))+E(f775(f775(f43(a850),f775(f775(f83(a850),x57791),x57792)),f775(f775(f83(a850),x57791),x57793)),f2(a850)) % 186.05/186.62 [5843]P1(f775(x58431,x58432))+P1(f775(f775(f187(f35(x58431,x58433)),x58432),x58432)) % 186.05/186.62 [5855]~P88(x58551)+E(f775(f775(f3(x58551),f775(f106(x58551),x58552)),f775(f106(x58551),x58553)),f775(f106(x58551),f775(f775(f82(a1),x58552),f775(f81(a1),x58553)))) % 186.05/186.62 [5911]E(x59111,f2(a850))+E(f775(f775(f43(a850),f775(f775(f83(a850),x59111),x59112)),f775(f775(f83(a850),x59111),x59113)),f775(f775(f43(a850),x59112),x59113)) % 186.05/186.62 [5980]P141(x59801,x59802,x59803)+~P1(f775(x59801,f775(f775(f43(a1),x59803),x59802))) % 186.05/186.62 [6057]E(x60571,f115(x60572))+E(f775(f775(f140(x60572),f775(f131(x60572),x60571)),f775(f775(f159(x60572),x60573),f775(f157(x60572),x60571))),f775(f775(f159(x60572),f775(a114,x60573)),x60571)) % 186.05/186.62 [6065]E(f775(f775(f3(f857(x60651,a844)),x60652),x60653),x60652)+~E(f775(f775(f104(f857(x60651,a844)),x60652),x60653),f180(f857(x60651,a844))) % 186.05/186.62 [6109]~P1(f775(f775(f233(a850),x61091),x61093))+P1(f775(f775(f233(a850),x61091),f775(f775(f82(a850),x61092),x61093))) % 186.05/186.62 [6111]~P1(f775(f775(f233(a850),x61111),x61112))+P1(f775(f775(f233(a850),x61111),f775(f775(f82(a850),x61112),x61113))) % 186.05/186.62 [6113]~P1(f775(f775(f232(a850),x61131),x61133))+P1(f775(f775(f232(a850),x61131),f775(f775(f82(a850),x61132),x61133))) % 186.05/186.62 [6115]~P1(f775(f775(f232(a850),x61151),x61152))+P1(f775(f775(f232(a850),x61151),f775(f775(f82(a850),x61152),x61153))) % 186.05/186.62 [6154]P1(f775(f63(x61541),x61542))+~P1(f775(f63(x61541),f775(f775(f302(x61541),x61543),x61542))) % 186.05/186.62 [6155]P1(f775(f127(x61551),x61552))+~P1(f775(f127(x61551),f775(f775(f140(x61551),x61553),x61552))) % 186.05/186.62 [6156]P1(f775(f127(x61561),x61562))+~P1(f775(f127(x61561),f775(f775(f125(x61561),x61563),x61562))) % 186.05/186.62 [6157]P1(f775(f127(x61571),x61572))+~P1(f775(f127(x61571),f775(f775(f125(x61571),x61572),x61573))) % 186.05/186.62 [6202]~E(f52(a1,x62022,x62021),f52(a1,x62023,x62021))+P1(f775(f775(f279(a1),x62021),f775(f775(f3(a1),x62022),x62023))) % 186.05/186.62 [6207]~P85(x62071)+E(f775(f775(f82(x62071),x62072),f775(f775(f83(x62071),x62073),x62072)),f775(f775(f83(x62071),f775(f775(f82(x62071),x62073),f80(x62071))),x62072)) % 186.05/186.62 [6256]~E(x62561,x62562)+~P1(f775(f775(f233(f857(x62563,a844)),x62561),x62562)) % 186.05/186.62 [6304]P1(f775(f775(f334(x63041),x63042),x63043))+P1(f775(f775(f334(x63041),x63042),f775(f81(f857(x63041,a844)),x63043))) % 186.05/186.62 [6311]E(f134(x63111,f775(f775(f128(x63111),x63112),x63113)),f134(x63111,x63113))+~P1(f775(f775(f233(a850),x63112),f775(f181(f851(x63111)),x63113))) % 186.05/186.62 [6312]E(f775(f775(f159(x63121),x63122),f116(x63121,x63123)),f775(f775(f159(x63121),x63122),x63123))+~P1(f775(f775(f233(a850),x63122),f775(f181(f851(x63121)),x63123))) % 186.05/186.62 [6371]E(f775(f775(f775(f173(f851(x63711),f851(x63711)),x63712),f141(x63711)),x63713),x63713)+~E(f52(a850,x63712,f775(f181(f851(x63711)),x63713)),f2(a850)) % 186.05/186.62 [6380]~P12(x63801,x63803,x63802)+E(f775(f775(f281(x63801,x63801,x63801),f775(f278(x63801,x63801),x63802)),x63802),x63802) % 186.05/186.62 [6423]~E(f775(f775(f103(f857(x64231,a844)),x64232),x64233),x64233)+P1(f775(f775(f232(f857(x64231,a844)),x64232),x64233)) % 186.05/186.62 [6428]~P53(x64281,x64281,x64283)+P53(x64281,x64281,f775(f775(f173(f856(x64281,x64281),a844),x64282),x64283)) % 186.05/186.62 [6430]~P1(f775(f775(f334(x64301),x64303),f775(f158(x64301),x64302)))+P1(f775(f775(f233(a850),f2(a850)),f775(f181(f851(x64301)),x64302))) % 186.05/186.62 [6460]~P79(x64601)+E(f775(f77(x64601),f775(f775(f82(x64601),f775(f77(x64601),x64602)),f775(f77(x64601),x64603))),f775(f775(f82(x64601),f775(f77(x64601),x64602)),f775(f77(x64601),x64603))) % 186.05/186.62 [6472]E(f775(f775(f43(a850),f775(f775(f83(a850),x64721),x64722)),f775(f775(f83(a850),x64721),x64723)),f775(f775(f43(a850),x64722),x64723))+~P1(f775(f775(f233(a850),f2(a850)),x64721)) % 186.05/186.62 [6499]E(f52(a1,x64991,x64992),f52(a1,x64993,x64992))+~P1(f775(f775(f279(a1),x64992),f775(f775(f3(a1),x64991),x64993))) % 186.05/186.62 [6613]~P1(f775(f63(x66131),x66133))+E(f775(f775(f66(x66131,f857(x66131,a844),f302(x66131)),x66132),x66133),f775(f775(f103(f857(x66131,a844)),x66133),x66132)) % 186.05/186.62 [6676]E(f775(f775(f103(f857(x66761,a844)),x66762),x66763),x66762)+~P1(f775(f775(f232(f857(x66761,a844)),x66763),x66762)) % 186.05/186.62 [6678]E(f775(f775(f103(f857(x66781,a844)),x66782),x66783),x66783)+~P1(f775(f775(f232(f857(x66781,a844)),x66782),x66783)) % 186.05/186.62 [6679]E(f775(f775(f104(f857(x66791,a844)),x66792),x66793),x66793)+~P1(f775(f775(f232(f857(x66791,a844)),x66793),x66792)) % 186.05/186.62 [6680]E(f775(f775(f104(f857(x66801,a844)),x66802),x66803),x66802)+~P1(f775(f775(f232(f857(x66801,a844)),x66802),x66803)) % 186.05/186.62 [6733]~P1(f775(f127(x67331),x67332))+E(f775(f775(f3(f857(x67331,a844)),f775(f158(x67331),x67332)),f775(f775(f302(x67331),x67333),f180(f857(x67331,a844)))),f775(f158(x67331),f151(x67331,x67333,x67332))) % 186.05/186.62 [6792]P36(x67921,x67922)+~P36(x67921,f775(f775(f173(f856(x67921,x67921),a844),x67923),x67922)) % 186.05/186.62 [6808]~E(x68081,f2(a850))+P1(f775(f775(f279(a850),f775(f775(f83(a850),x68081),x68082)),f775(f775(f83(a850),x68081),x68083))) % 186.05/186.62 [6862]P1(f775(f56(x68621,x68622),f775(a58,x68623)))+~P1(f775(f56(f775(f81(a1),x68621),f775(f81(a1),x68622)),x68623)) % 186.05/186.62 [6867]E(f775(f775(f3(f857(x68671,a844)),f775(f775(f302(x68671),x68672),x68673)),f775(f775(f302(x68671),x68672),f180(f857(x68671,a844)))),x68673)+P1(f775(f775(f334(x68671),x68672),x68673)) % 186.05/186.62 [6886]E(f775(f775(f104(f857(x68861,a844)),f775(f158(x68861),x68862)),f775(f158(x68861),x68863)),f180(f857(x68861,a844)))+~P1(f775(f127(x68861),f775(f775(f125(x68861),x68862),x68863))) % 186.05/186.62 [6903]~P1(f775(f775(f334(x69031),x69032),f775(f158(x69031),x69033)))+~P1(f775(f127(x69031),f775(f775(f140(x69031),x69032),x69033))) % 186.05/186.62 [6980]E(f775(f775(f104(f857(x69801,a844)),x69802),x69803),f180(f857(x69801,a844)))+P1(f775(f775(f334(x69801),f493(x69803,x69802,x69801)),x69802)) % 186.05/186.62 [6981]E(f775(f775(f104(f857(x69811,a844)),x69812),x69813),f180(f857(x69811,a844)))+P1(f775(f775(f334(x69811),f497(x69813,x69812,x69811)),x69813)) % 186.05/186.62 [6985]E(f116(x69851,f775(f775(f159(x69851),x69852),x69853)),f775(f775(f159(x69851),f775(f775(f3(a850),x69852),f80(a850))),x69853))+~P1(f775(f775(f232(a850),x69852),f775(f181(f851(x69851)),x69853))) % 186.05/186.62 [7067]P1(f775(f775(f233(a850),f2(a850)),x70671))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x70672),x70671)),f775(f775(f83(a850),x70673),x70671))) % 186.05/186.62 [7068]P1(f775(f775(f233(a850),f2(a850)),x70681))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x70681),x70682)),f775(f775(f83(a850),x70681),x70683))) % 186.05/186.62 [7071]~P1(f775(f775(f334(x70711),x70712),x70713))+~P1(f775(f775(f334(x70711),x70712),f775(f81(f857(x70711,a844)),x70713))) % 186.05/186.62 [7077]~P1(f775(f775(f233(f857(x70771,a844)),x70772),x70773))+P1(f775(f775(f232(f857(x70771,a844)),x70772),x70773)) % 186.05/186.62 [7182]~P1(f775(f775(f233(a850),x71822),x71823))+P1(f775(f775(f233(a850),f775(f775(f82(a850),x71821),x71822)),f775(f775(f82(a850),x71821),x71823))) % 186.05/186.62 [7183]~P1(f775(f775(f233(a850),x71831),x71833))+P1(f775(f775(f233(a850),f775(f775(f82(a850),x71831),x71832)),f775(f775(f82(a850),x71833),x71832))) % 186.05/186.62 [7184]~P1(f775(f775(f233(a1),x71841),x71843))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x71841),x71842)),f775(f775(f82(a1),x71843),x71842))) % 186.05/186.62 [7187]~P1(f775(f775(f232(a850),x71872),x71873))+P1(f775(f775(f232(a850),f775(f775(f82(a850),x71871),x71872)),f775(f775(f82(a850),x71871),x71873))) % 186.05/186.62 [7188]~P1(f775(f775(f232(a850),x71881),x71883))+P1(f775(f775(f232(a850),f775(f775(f82(a850),x71881),x71882)),f775(f775(f82(a850),x71883),x71882))) % 186.05/186.62 [7190]~P1(f775(f775(f232(a850),x71902),x71903))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x71901),x71902)),f775(f775(f83(a850),x71901),x71903))) % 186.05/186.62 [7192]~P1(f775(f775(f232(a850),x71921),x71923))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x71921),x71922)),f775(f775(f83(a850),x71923),x71922))) % 186.05/186.62 [7193]~P1(f775(f775(f232(a850),x71931),x71933))+P1(f775(f775(f232(a850),f775(f775(f43(a850),x71931),x71932)),f775(f775(f43(a850),x71933),x71932))) % 186.05/186.62 [7194]~P1(f775(f775(f232(a850),x71943),x71942))+P1(f775(f775(f232(a850),f775(f775(f3(a850),x71941),x71942)),f775(f775(f3(a850),x71941),x71943))) % 186.05/186.62 [7195]~P1(f775(f775(f232(a850),x71951),x71953))+P1(f775(f775(f232(a850),f775(f775(f3(a850),x71951),x71952)),f775(f775(f3(a850),x71953),x71952))) % 186.05/186.62 [7196]~P1(f775(f775(f232(a1),x71962),x71963))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x71961),x71962)),f775(f775(f82(a1),x71961),x71963))) % 186.05/186.62 [7199]~P1(f775(f775(f279(a850),x71992),x71993))+P1(f775(f775(f279(a850),f775(f775(f83(a850),x71991),x71992)),f775(f775(f83(a850),x71991),x71993))) % 186.05/186.62 [7287]E(x72871,x72872)+~P1(f775(f775(f334(x72873),x72871),f775(f775(f302(x72873),x72872),f180(f857(x72873,a844))))) % 186.05/186.62 [7289]~E(f775(f775(f104(f857(x72891,a844)),x72892),x72893),f180(f857(x72891,a844)))+P1(f775(f775(f232(f857(x72891,a844)),x72892),f775(f81(f857(x72891,a844)),x72893))) % 186.05/186.62 [7296]P1(f775(f775(f334(f857(x72961,a844)),x72962),f775(f301(x72961),x72963)))+~P1(f775(f775(f232(f857(x72961,a844)),x72962),x72963)) % 186.05/186.62 [7353]E(f775(f775(f140(x73531),f775(f775(f153(x73531),x73532),x73533)),f775(f775(f128(x73531),f775(a114,x73533)),x73532)),f775(f775(f128(x73531),x73533),x73532))+~P1(f775(f775(f233(a850),x73533),f775(f181(f851(x73531)),x73532))) % 186.05/186.62 [7383]P1(f775(f775(f334(f856(x73831,x73831)),x73832),f300(x73831,x73833)))+~P1(f775(f775(f334(f856(x73831,x73831)),x73832),x73833)) % 186.05/186.62 [7393]~P1(f775(f775(f334(f857(x73931,a844)),x73932),f775(f301(x73931),x73933)))+P1(f775(f775(f232(f857(x73931,a844)),x73932),x73933)) % 186.05/186.62 [7435]P1(f775(f775(f232(f857(x74351,a844)),x74352),f44(f857(x74351,a844),x74353)))+~P1(f775(f775(f334(f857(x74351,a844)),x74352),x74353)) % 186.05/186.62 [7463]~P133(x74631)+E(f775(f775(f83(x74631),f775(f775(f242(x74631),f775(f81(x74631),f80(x74631))),x74632)),f775(f775(f242(x74631),x74633),x74632)),f775(f775(f242(x74631),f775(f81(x74631),x74633)),x74632)) % 186.05/186.62 [7485]E(f775(f775(f153(x74851),x74852),f775(f775(f3(a850),f775(f181(f851(x74851)),x74852)),f775(a114,x74853))),f775(f775(f153(x74851),f775(f142(x74851),x74852)),x74853))+~P1(f775(f775(f233(a850),x74853),f775(f181(f851(x74851)),x74852))) % 186.05/186.62 [7502]~E(f775(f775(f104(f857(x75021,a844)),f651(x75023,x75022,x75021)),x75023),f180(f857(x75021,a844)))+E(f775(f775(f104(f857(x75021,a844)),f44(f857(x75021,a844),x75022)),x75023),f180(f857(x75021,a844))) % 186.05/186.62 [7566]~P1(f775(f775(f334(x75663),x75662),f775(f158(x75663),x75661)))+P1(f775(f775(f233(a850),f730(x75661,x75662,x75663)),f775(f181(f851(x75663)),x75661))) % 186.05/186.62 [7574]P1(f775(f775(f334(x75741),f775(f775(f153(x75741),x75742),x75743)),f775(f158(x75741),x75742)))+~P1(f775(f775(f233(a850),x75743),f775(f181(f851(x75741)),x75742))) % 186.05/186.62 [7683]P1(f775(f775(f232(f857(f851(x76831),a844)),f149(x76831,x76832)),f149(x76831,x76833)))+~P1(f775(f775(f232(f857(x76831,a844)),x76832),x76833)) % 186.05/186.62 [7712]E(f775(f775(f104(f857(x77121,a844)),f44(f857(x77121,a844),x77122)),x77123),f180(f857(x77121,a844)))+P1(f775(f775(f334(f857(x77121,a844)),f651(x77123,x77122,x77121)),x77122)) % 186.05/186.62 [7714]~P1(f775(f775(f334(f857(x77141,a844)),x77143),x77142))+P1(f775(f775(f232(f857(x77141,a844)),f45(f857(x77141,a844),x77142)),x77143)) % 186.05/186.62 [7716]E(f775(f775(f104(f857(x77161,a844)),x77162),x77163),f180(f857(x77161,a844)))+~P1(f775(f775(f232(f857(x77161,a844)),x77162),f775(f81(f857(x77161,a844)),x77163))) % 186.05/186.62 [7769]E(f775(f775(f3(a850),f775(f775(f82(a850),f775(f155(a850),x77691)),x77692)),f775(f775(f153(a850),x77691),x77693)),f775(f155(a850),f775(f775(f148(a850,x77691),x77693),x77692)))+~P1(f775(f775(f233(a850),x77693),f775(f181(f851(a850)),x77691))) % 186.05/186.62 [7819]P1(f775(f775(f233(a850),x78191),x78192))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),x78193),x78191)),f775(f775(f82(a850),x78193),x78192))) % 186.05/186.62 [7820]P1(f775(f775(f233(a850),x78201),x78202))+~P1(f775(f775(f233(a850),f775(f775(f83(a850),x78203),x78201)),f775(f775(f83(a850),x78203),x78202))) % 186.05/186.62 [7821]P1(f775(f775(f233(a850),x78211),x78212))+~P1(f775(f775(f233(a850),f775(f775(f83(a850),x78211),x78213)),f775(f775(f83(a850),x78212),x78213))) % 186.05/186.62 [7824]P1(f775(f775(f232(a850),x78241),x78242))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x78243),x78241)),f775(f775(f82(a850),x78243),x78242))) % 186.05/186.62 [7853]P1(f775(f775(f233(a850),f2(a850)),x78531))+~P1(f775(f775(f233(a850),f775(f775(f83(a850),x78532),x78531)),f775(f775(f83(a850),x78533),x78531))) % 186.05/186.62 [7854]P1(f775(f775(f233(a850),f2(a850)),x78541))+~P1(f775(f775(f233(a850),f775(f775(f83(a850),x78541),x78542)),f775(f775(f83(a850),x78541),x78543))) % 186.05/186.62 [7927]E(f244(x79271,x79272,x79273),x79272)+~P1(f775(f775(f232(f857(x79271,a844)),x79273),f775(f775(f302(x79271),x79272),f180(f857(x79271,a844))))) % 186.05/186.62 [8006]E(f775(f775(f125(x80061),f775(f775(f159(x80061),x80062),x80063)),f775(f775(f140(x80061),f775(f775(f153(x80061),x80063),x80062)),f115(x80061))),f775(f775(f159(x80061),f775(a114,x80062)),x80063))+~P1(f775(f775(f233(a850),x80062),f775(f181(f851(x80061)),x80063))) % 186.05/186.62 [8075]P1(f775(f775(f232(f857(f857(x80751,a844),a844)),f245(x80751,x80752)),f245(x80751,x80753)))+~P1(f775(f775(f232(f857(x80751,a844)),x80752),x80753)) % 186.05/186.62 [8114]~P1(f775(f127(x81141),x81143))+P1(f775(f127(x81141),f775(f775(f775(f173(f851(x81141),f851(x81141)),x81142),f141(x81141)),x81143))) % 186.05/186.62 [8119]~P1(f775(f775(f233(a850),x81192),x81193))+P1(f775(f775(f233(a850),f775(f775(f83(a850),f775(a114,x81191)),x81192)),f775(f775(f83(a850),f775(a114,x81191)),x81193))) % 186.05/186.62 [8142]P1(f775(f775(f232(f857(f857(x81421,a844),a844)),f775(f301(x81421),x81422)),f775(f301(x81421),x81423)))+~P1(f775(f775(f232(f857(x81421,a844)),x81422),x81423)) % 186.05/186.62 [8299]~P1(f775(f775(f232(f857(x82991,a844)),x82993),x82992))+P1(f775(f775(f232(f857(x82991,a844)),f775(f81(f857(x82991,a844)),x82992)),f775(f81(f857(x82991,a844)),x82993))) % 186.05/186.62 [8338]E(f775(f303(a850,a850,f775(f775(f9(a850,a850,a850),f3(a850)),x83381)),f775(f294(a850,x83382),x83383)),f775(f294(a850,f775(f775(f3(a850),x83382),x83381)),f775(f775(f3(a850),x83383),x83381)))+~P1(f775(f775(f233(a850),x83381),x83383)) % 186.05/186.62 [8364]~P67(x83641)+E(f775(f775(f82(x83641),x83642),f775(f132(x83641,x83641,f82(x83641),f2(x83641)),x83643)),f775(f132(x83641,x83641,f82(x83641),x83642),x83643)) % 186.05/186.62 [8445]~P79(x84451)+P1(f775(f775(f232(x84451),f775(f77(x84451),f775(f775(f82(x84451),x84452),x84453))),f775(f775(f82(x84451),f775(f77(x84451),x84452)),f775(f77(x84451),x84453)))) % 186.05/186.62 [8446]~P79(x84461)+P1(f775(f775(f232(x84461),f775(f77(x84461),f775(f775(f3(x84461),x84462),x84463))),f775(f775(f82(x84461),f775(f77(x84461),x84462)),f775(f77(x84461),x84463)))) % 186.05/186.62 [8456]E(f775(f775(f82(a1),f775(f775(f83(a1),x84561),f52(a1,f775(f775(f43(a1),x84562),x84561),x84563))),f52(a1,x84562,x84561)),f52(a1,x84562,f775(f775(f83(a1),x84561),x84563)))+~P1(f775(f775(f233(a1),f2(a1)),x84563)) % 186.05/186.62 [8465]E(f775(f775(f125(x84651),f775(f775(f159(x84651),x84652),x84653)),f775(f775(f140(x84651),f775(f131(x84651),f775(f775(f128(x84651),x84652),x84653))),f115(x84651))),f775(f775(f159(x84651),f775(a114,x84652)),x84653))+~P1(f775(f775(f233(a850),x84652),f775(f181(f851(x84651)),x84653))) % 186.05/186.62 [8484]E(f775(f265(x84841,f775(f775(f143(x84841,f856(a101,x84841)),f775(f241(a101,x84841),f80(a101))),x84842)),f775(a5,x84843)),f775(f775(f153(x84841),x84842),x84843))+~P1(f775(f775(f233(a850),x84843),f775(f181(f851(x84841)),x84842))) % 186.05/186.62 [8541]P1(f775(f775(f334(f856(x85411,x85411)),x85412),f775(f775(f281(x85411,x85411,x85411),x85413),f300(x85411,x85413))))+~P1(f775(f775(f334(f856(x85411,x85411)),x85412),x85413)) % 186.05/186.62 [8558]P1(f775(f775(f232(a850),x85581),x85582))+~P1(f775(f775(f232(a850),f775(f775(f83(a850),f775(a114,x85583)),x85581)),f775(f775(f83(a850),f775(a114,x85583)),x85582))) % 186.05/186.62 [8569]P1(f775(f775(f232(f857(x85691,a844)),x85692),x85693))+~P1(f775(f775(f232(f857(x85691,a844)),f775(f81(f857(x85691,a844)),x85693)),f775(f81(f857(x85691,a844)),x85692))) % 186.05/186.62 [8587]P1(f775(f127(x85871),x85872))+~P1(f775(f127(x85871),f775(f775(f775(f173(f851(x85871),f851(x85871)),x85873),f141(x85871)),x85872))) % 186.05/186.62 [8653]E(f775(f277(x86531,x86531,f300(x86531,x86532)),x86533),x86533)+~P1(f775(f775(f232(f857(x86531,a844)),f775(f277(x86531,x86531,x86532),x86533)),x86533)) % 186.05/186.62 [8655]E(f775(f303(f856(x86551,x86552),x86552,f250(x86551,x86552)),f775(f158(f856(x86551,x86552)),x86553)),f171(x86551,x86552,f166(x86551,x86552,x86553)))+~P1(f775(f127(x86551),f775(f775(f143(f856(x86551,x86552),x86551),f240(x86551,x86552)),x86553))) % 186.05/186.62 [8694]~P100(x86941)+P18(x86941,f775(f126(x86941,f775(f775(f9(x86941,x86941,a844),a330),f775(x86942,x86943))),x86943)) % 186.05/186.62 [8699]~P1(f775(f775(f232(a850),x86991),x86992))+P1(f775(f775(f232(a850),x86991),f775(f132(a850,a850,f82(a850),x86992),x86993))) % 186.05/186.62 [8770]~P1(f775(f775(f334(f856(x87701,x87701)),x87702),f300(x87701,x87703)))+P1(f775(f775(f334(f856(x87701,x87701)),x87702),f775(f775(f173(f856(x87701,x87701),a844),f634(x87703,x87702,x87701)),x87703))) % 186.05/186.62 [8839]~P67(x88391)+E(f775(f775(f82(x88391),x88392),f775(f132(x88391,x88391,f775(f9(x88391,x88391,x88391),f82(x88391)),f2(x88391)),f775(f142(x88391),x88393))),f775(f132(x88391,x88391,f82(x88391),x88392),x88393)) % 186.05/186.62 [9098]P53(x90981,x90982,x90983)+P1(f775(f775(f334(f856(x90981,x90982)),f775(f775(f241(x90981,x90982),f647(x90983,x90982,x90981)),f641(x90983,x90982,x90981))),x90983)) % 186.05/186.62 [9099]P53(x90991,x90992,x90993)+P1(f775(f775(f334(f856(x90991,x90992)),f775(f775(f241(x90991,x90992),f647(x90993,x90992,x90991)),f640(x90993,x90992,x90991))),x90993)) % 186.05/186.62 [9154]~P1(f775(f775(f334(f856(x91541,x91541)),x91542),f775(f775(f281(x91541,x91541,x91541),x91543),f300(x91541,x91543))))+P1(f775(f775(f334(f856(x91541,x91541)),x91542),f775(f775(f173(f856(x91541,x91541),a844),f639(x91543,x91542,x91541)),x91543))) % 186.05/186.62 [9155]~P1(f775(x91551,f775(f775(f153(x91552),x91553),f775(f181(f851(x91552)),f162(x91552,x91551,x91553)))))+~P1(f775(f775(f233(a850),f775(f181(f851(x91552)),f162(x91552,x91551,x91553))),f775(f181(f851(x91552)),x91553))) % 186.05/186.62 [9231]~P1(f775(f775(f232(f857(x92311,a844)),x92312),x92313))+P1(f775(f775(f232(f857(x92311,a844)),f775(f775(f9(x92311,f857(x92311,a844),a844),f334(x92311)),x92312)),f775(f775(f9(x92311,f857(x92311,a844),a844),f334(x92311)),x92313))) % 186.05/186.62 [9287]~P1(f775(f775(f334(f856(f857(x92871,a844),f857(x92871,a844))),f775(f775(f241(f857(x92871,a844),f857(x92871,a844)),x92872),x92873)),f299(x92871)))+P1(f775(f775(f233(f857(x92871,a844)),x92872),x92873)) % 186.05/186.62 [9313]P54(x93131,x93132,x93133)+~P1(f775(f775(f334(f856(x93131,x93131)),f775(f775(f241(x93131,x93131),f628(x93133,x93132,x93131)),f627(x93133,x93132,x93131))),x93133)) % 186.05/186.62 [9314]P54(x93141,x93142,x93143)+~P1(f775(f775(f334(f856(x93141,x93141)),f775(f775(f241(x93141,x93141),f627(x93143,x93142,x93141)),f628(x93143,x93142,x93141))),x93143)) % 186.05/186.62 [9348]~P1(f775(f775(f334(f856(f851(x93481),f851(x93481))),f775(f775(f241(f851(x93481),f851(x93481)),x93482),x93482)),f137(x93481,x93483)))+P1(f775(f775(f334(f856(x93481,x93481)),f775(f775(f241(x93481,x93481),f755(x93482,x93483,x93481)),f755(x93482,x93483,x93481))),x93483)) % 186.05/186.62 [9393]P1(f775(f775(f232(f857(x93931,a844)),x93932),x93933))+~P1(f775(f775(f232(f857(x93931,a844)),f775(f775(f9(x93931,f857(x93931,a844),a844),f334(x93931)),x93932)),f775(f775(f9(x93931,f857(x93931,a844),a844),f334(x93931)),x93933))) % 186.05/186.62 [9479]E(f775(f775(f3(a850),f775(f775(f8(a850,a850),x94791),f775(f257(a850),x94792))),f775(f775(f8(a850,a850),x94793),f775(f257(a850),x94792))),f775(f775(f8(a850,a850),f775(f775(f20(a850,a850,a850),f775(f775(f10(a850,f857(a850,a850),a850),f3(a850)),x94791)),x94793)),f775(f257(a850),x94792)))+~P1(f775(f775(f232(a850),f775(x94793,f341(x94792,x94791,x94793))),f775(x94791,f341(x94792,x94791,x94793)))) % 186.05/186.62 [9761]E(f775(f256(f856(x97611,x97612)),f775(f251(x97611,x97612,a844),f775(f775(f9(x97611,f857(x97612,f854(x97612)),f857(x97612,a844)),f775(f775(f10(f857(f854(x97612),a844),f857(f857(x97612,f854(x97612)),f857(x97612,a844)),x97611),f10(f854(x97612),a844,x97612)),f775(f775(f10(f854(x97612),f857(f854(x97612),a844),x97611),a330),f166(x97611,x97612,x97613)))),f227(x97612)))),f775(f158(f856(x97611,x97612)),x97613))+~P1(f775(f127(x97611),f775(f775(f143(f856(x97611,x97612),x97611),f240(x97611,x97612)),x97613))) % 186.05/186.62 [5507]~P69(x55071)+E(f775(f775(f82(x55071),f775(f775(f3(x55071),x55072),x55073)),x55073),x55072) % 186.05/186.62 [5508]~P69(x55081)+E(f775(f775(f3(x55081),f775(f775(f82(x55081),x55082),x55083)),x55083),x55082) % 186.05/186.62 [5734]~P69(x57341)+E(f775(f775(f82(x57341),x57342),f775(f775(f82(x57341),f775(f81(x57341),x57342)),x57343)),x57343) % 186.05/186.62 [5817]~P75(x58171)+E(f775(f775(f83(x58171),f775(f775(f242(x58171),x58172),x58173)),x58172),f775(f775(f242(x58171),x58172),f775(a114,x58173))) % 186.05/186.62 [5818]~P85(x58181)+E(f775(f775(f83(x58181),f775(f775(f242(x58181),x58182),x58183)),x58182),f775(f775(f242(x58181),x58182),f775(a114,x58183))) % 186.05/186.62 [6033]~P110(x60331)+E(f775(f77(x60331),f775(f775(f242(x60331),f775(f81(x60331),x60332)),x60333)),f775(f77(x60331),f775(f775(f242(x60331),x60332),x60333))) % 186.05/186.62 [6085]~P75(x60851)+E(f775(f775(f83(x60851),f775(f775(f242(x60851),x60852),x60853)),x60852),f775(f775(f83(x60851),x60852),f775(f775(f242(x60851),x60852),x60853))) % 186.05/186.62 [6145]E(f775(f775(f3(a101),f775(f775(f82(a101),x61451),x61452)),x61453),f269(x61451,x61452,x61453))+~P1(f775(f775(f233(a101),x61452),x61453)) % 186.05/186.62 [6167]~E(f775(f775(f128(x61671),x61673),x61672),f115(x61671))+P1(f775(f775(f232(a850),f775(f181(f851(x61671)),x61672)),x61673)) % 186.05/186.62 [6309]E(f775(f775(f83(a850),f775(f106(a850),x63091)),f775(f775(f83(a850),f775(f106(a850),x63092)),x63093)),f2(a850))+~P1(f775(f775(f233(a1),x63091),a85)) % 186.05/186.62 [6325]~P60(x63251)+E(f775(f775(f242(x63251),f775(f775(f283(x63251),f80(x63251)),x63252)),x63253),f775(f775(f283(x63251),f80(x63251)),f775(f775(f242(x63251),x63252),x63253))) % 186.05/186.62 [6410]E(f775(f775(f3(a850),f775(f775(f82(a850),x64101),x64102)),x64103),f775(f775(f3(a850),x64101),f775(f775(f3(a850),x64103),x64102)))+~P1(f775(f775(f232(a850),x64102),x64103)) % 186.05/186.62 [6411]E(f775(f775(f3(a850),f775(f775(f82(a850),x64111),x64112)),x64113),f775(f775(f82(a850),x64111),f775(f775(f3(a850),x64112),x64113)))+~P1(f775(f775(f232(a850),x64113),x64112)) % 186.05/186.62 [6451]~P100(x64511)+P1(f775(f775(f232(x64511),f775(f775(f236(x64511),x64512),x64513)),x64513)) % 186.05/186.62 [6452]~P100(x64521)+P1(f775(f775(f232(x64521),f775(f775(f236(x64521),x64522),x64523)),x64522)) % 186.05/186.62 [6453]~P93(x64531)+P1(f775(f775(f232(x64531),f775(f775(f104(x64531),x64532),x64533)),x64533)) % 186.05/186.62 [6454]~P98(x64541)+P1(f775(f775(f232(x64541),f775(f775(f104(x64541),x64542),x64543)),x64543)) % 186.05/186.62 [6455]~P93(x64551)+P1(f775(f775(f232(x64551),f775(f775(f104(x64551),x64552),x64553)),x64552)) % 186.05/186.62 [6456]~P98(x64561)+P1(f775(f775(f232(x64561),f775(f775(f104(x64561),x64562),x64563)),x64562)) % 186.05/186.62 [6471]E(f775(f775(f43(a1),f775(f775(f43(a1),x64711),x64712)),x64713),f775(f775(f43(a1),x64711),f775(f775(f83(a1),x64712),x64713)))+~P1(f775(f775(f233(a1),f2(a1)),x64713)) % 186.05/186.62 [6524]~P85(x65241)+E(f775(f775(f82(x65241),f775(f775(f83(x65241),x65242),x65243)),x65243),f775(f775(f83(x65241),f775(f775(f82(x65241),x65242),f80(x65241))),x65243)) % 186.05/186.62 [6525]~P88(x65251)+E(f775(f775(f83(x65251),f775(f81(x65251),f775(f106(x65251),x65252))),x65253),f775(f775(f83(x65251),f775(f106(x65251),f775(f81(a1),x65252))),x65253)) % 186.05/186.62 [6598]~P67(x65981)+E(f775(f155(x65981),f775(f775(f143(x65982,x65981),f775(f18(x65981,x65982),f2(x65981))),x65983)),f2(x65981)) % 186.05/186.62 [6617]E(f775(f775(f82(a850),f775(f106(a850),x66171)),f775(f775(f82(a850),f775(f106(a850),x66172)),x66173)),f775(f775(f82(a850),f775(f106(a850),x66172)),x66173))+~P1(f775(a186,f775(f106(a1),x66171))) % 186.05/186.62 [6632]~P9(x66321)+E(f45(x66321,f775(f775(f302(x66321),x66322),f775(f775(f302(x66321),x66323),f180(f857(x66321,a844))))),f775(f775(f104(x66321),x66322),x66323)) % 186.05/186.62 [6633]~P9(x66331)+E(f44(x66331,f775(f775(f302(x66331),x66332),f775(f775(f302(x66331),x66333),f180(f857(x66331,a844))))),f775(f775(f103(x66331),x66332),x66333)) % 186.05/186.62 [6658]E(f775(f775(f159(x66581),x66582),x66583),x66583)+~P1(f775(f775(f232(a850),f775(f181(f851(x66581)),x66583)),x66582)) % 186.05/186.62 [6670]E(f775(f775(f128(x66701),x66702),x66703),f115(x66701))+~P1(f775(f775(f232(a850),f775(f181(f851(x66701)),x66703)),x66702)) % 186.05/186.62 [6682]E(f775(f775(f3(a850),f775(f775(f82(a850),x66821),x66822)),x66823),f775(f775(f82(a850),f775(f775(f3(a850),x66821),x66823)),x66822))+~P1(f775(f775(f232(a850),x66823),x66821)) % 186.05/186.62 [6696]~P1(f775(f775(f233(a850),x66961),x66963))+P1(f775(f775(f233(a850),f775(f775(f3(a850),x66961),x66962)),x66963)) % 186.05/186.62 [6724]~P100(x67241)+E(f151(x67241,x67242,f775(f775(f138(x67241,x67241,f7(x67241)),x67242),x67243)),x67243) % 186.05/186.62 [6822]E(f775(f775(f3(a850),f775(f775(f82(a850),x68221),x68222)),f775(a114,x68223)),f775(f775(f3(a850),x68221),f775(a114,f775(f775(f3(a850),x68223),x68222))))+~P1(f775(f775(f232(a850),x68222),x68223)) % 186.05/186.62 [6823]~P110(x68231)+P1(f775(f775(f232(x68231),f2(x68231)),f775(f775(f242(x68231),f775(f77(x68231),x68232)),x68233))) % 186.05/186.62 [6874]P28(x68741,x68742,x68743)+~P1(f775(f775(f232(f857(f849(x68741),a844)),x68743),x68742)) % 186.05/186.62 [6915]~P1(f775(f63(x69151),x69152))+P1(f775(f63(x69151),f775(f775(f3(f857(x69151,a844)),x69152),x69153))) % 186.05/186.62 [6916]~P1(f775(f63(x69161),x69163))+P1(f775(f63(x69161),f775(f775(f104(f857(x69161,a844)),x69162),x69163))) % 186.05/186.62 [6917]~P1(f775(f63(x69171),x69172))+P1(f775(f63(x69171),f775(f775(f104(f857(x69171,a844)),x69172),x69173))) % 186.05/186.62 [7056]~P36(x70561,x70563)+P36(x70561,f775(f775(f104(f857(f856(x70561,x70561),a844)),x70562),x70563)) % 186.05/186.62 [7057]~P36(x70571,x70572)+P36(x70571,f775(f775(f104(f857(f856(x70571,x70571),a844)),x70572),x70573)) % 186.05/186.62 [7177]~P93(x71771)+E(f15(x71771,f775(f158(x71771),f775(f775(f140(x71771),x71772),x71773))),f775(f132(x71771,x71771,f103(x71771),x71772),x71773)) % 186.05/186.62 [7178]~P100(x71781)+E(f16(x71781,f775(f158(x71781),f775(f775(f140(x71781),x71782),x71783))),f775(f132(x71781,x71781,f179(x71781),x71782),x71783)) % 186.05/186.62 [7179]~P100(x71791)+E(f17(x71791,f775(f158(x71791),f775(f775(f140(x71791),x71792),x71793))),f775(f132(x71791,x71791,f236(x71791),x71792),x71793)) % 186.05/186.62 [7180]~P93(x71801)+E(f12(x71801,f775(f158(x71801),f775(f775(f140(x71801),x71802),x71803))),f775(f132(x71801,x71801,f104(x71801),x71802),x71803)) % 186.05/186.62 [7181]~P1(f775(f775(f279(a1),x71811),x71812))+P1(f775(f775(f279(a1),x71811),f775(f775(f82(a1),x71812),f775(f775(f83(a1),x71811),x71813)))) % 186.05/186.62 [7251]~P1(f775(f63(x72511),x72512))+P1(f775(f775(f232(a850),f775(f42(x72511),x72512)),f775(f42(x72511),f775(f775(f302(x72511),x72513),x72512)))) % 186.05/186.62 [7258]E(f775(f775(f103(f857(a850,a844)),f775(f294(a850,x72581),x72582)),f775(f294(a850,x72582),f775(f775(f82(a850),x72582),x72583))),f775(f294(a850,x72581),f775(f775(f82(a850),x72582),x72583)))+~P1(f775(f775(f232(a850),x72581),x72582)) % 186.05/186.62 [7268]P1(f775(f775(f233(a850),x72681),x72682))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),x72681),x72683)),x72682)) % 186.05/186.62 [7271]P1(f775(f775(f232(a850),x72711),x72712))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x72713),x72711)),x72712)) % 186.05/186.62 [7272]P1(f775(f775(f232(a850),x72721),x72722))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x72721),x72723)),x72722)) % 186.05/186.62 [7314]~P100(x73141)+E(f13(x73141,f179(x73141),f775(f158(x73141),f775(f775(f140(x73141),x73142),x73143))),f775(f132(x73141,x73141,f179(x73141),x73142),x73143)) % 186.05/186.62 [7315]~P100(x73151)+E(f14(x73151,f236(x73151),f775(f158(x73151),f775(f775(f140(x73151),x73152),x73153))),f775(f132(x73151,x73151,f236(x73151),x73152),x73153)) % 186.05/186.62 [7319]~E(x73192,f180(f857(f856(x73191,x73191),a844)))+P1(f775(f775(f232(f857(f856(x73191,x73191),a844)),x73192),x73193)) % 186.05/186.62 [7428]E(f775(f775(f103(f857(x74281,a844)),x74282),f775(f775(f3(f857(x74281,a844)),x74283),x74282)),x74283)+~P1(f775(f775(f232(f857(x74281,a844)),x74282),x74283)) % 186.05/186.62 [7431]~P1(f775(f775(f233(a850),x74311),f775(f775(f3(a850),x74313),x74312)))+P1(f775(f775(f233(a850),f775(f775(f82(a850),x74311),x74312)),x74313)) % 186.05/186.62 [7432]~P1(f775(f775(f232(a850),x74321),f775(f775(f82(a850),x74323),x74322)))+P1(f775(f775(f232(a850),f775(f775(f3(a850),x74321),x74322)),x74323)) % 186.05/186.62 [7492]E(x74921,f115(x74922))+E(f775(f131(x74922),f775(f775(f775(f173(f851(x74922),f851(x74922)),x74923),f141(x74922)),x74921)),f775(f775(f153(x74922),x74921),f52(a850,x74923,f775(f181(f851(x74922)),x74921)))) % 186.05/186.62 [7501]E(f775(f775(f302(x75011),x75012),f775(f775(f3(f857(x75011,a844)),x75013),f775(f775(f302(x75011),x75012),f180(f857(x75011,a844))))),x75013)+~P1(f775(f775(f334(x75011),x75012),x75013)) % 186.05/186.62 [7665]P1(f775(f775(f233(a850),x76651),f775(f775(f3(a850),x76652),x76653)))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),x76651),x76653)),x76652)) % 186.05/186.62 [7666]P1(f775(f775(f232(a850),x76661),f775(f775(f82(a850),x76662),x76663)))+~P1(f775(f775(f232(a850),f775(f775(f3(a850),x76661),x76663)),x76662)) % 186.05/186.62 [7686]P1(f775(f63(x76861),x76862))+~P1(f775(f63(x76861),f775(f775(f103(f857(x76861,a844)),x76863),x76862))) % 186.05/186.62 [7687]P1(f775(f63(x76871),x76872))+~P1(f775(f63(x76871),f775(f775(f103(f857(x76871,a844)),x76872),x76873))) % 186.05/186.62 [7768]~P44(x77681,x77683)+P1(f775(f775(f334(f856(x77681,x77681)),f775(f775(f241(x77681,x77681),x77682),x77682)),x77683)) % 186.05/186.62 [7818]P1(f775(f775(f279(a1),x78181),x78182))+~P1(f775(f775(f279(a1),x78181),f775(f775(f82(a1),x78182),f775(f775(f83(a1),x78181),x78183)))) % 186.05/186.62 [7898]E(f775(f775(f153(a850),f130(a850,f775(f294(a850,x78981),x78982))),x78983),f775(f775(f82(a850),x78981),x78983))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),x78981),x78983)),x78982)) % 186.05/186.62 [7968]~P1(f775(f775(f187(f775(a27,x79681)),x79682),x79683))+P1(f775(f775(f187(f775(f231(a845),f775(a30,x79681))),x79682),x79683)) % 186.05/186.62 [7972]E(f775(f775(f159(a850),x79721),f130(a850,f775(f294(a850,x79722),x79723))),f130(a850,f775(f294(a850,x79722),f775(f775(f82(a850),x79722),x79721))))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x79722),x79721)),x79723)) % 186.05/186.62 [8021]~P88(x80211)+E(f775(f775(f242(x80211),x80212),f775(f106(a850),f775(f775(f82(a1),x80213),x80213))),f775(f775(f88(x80211,x80211),f775(f775(f242(x80211),x80212),f775(f106(a850),x80213))),f775(f775(f20(x80211,x80211,x80211),f83(x80211)),f7(x80211)))) % 186.05/186.62 [8221]P1(f775(f775(f187(f775(a27,x82211)),x82212),x82213))+~P1(f775(f775(f187(f775(f231(a845),f775(a30,x82211))),x82212),x82213)) % 186.05/186.62 [8278]E(f775(f775(f125(x82781),f775(f775(f159(x82781),x82782),x82783)),f775(f775(f140(x82781),f775(f775(f153(x82781),x82783),x82782)),f775(f775(f128(x82781),f775(a114,x82782)),x82783))),x82783)+~P1(f775(f775(f233(a850),x82782),f775(f181(f851(x82781)),x82783))) % 186.05/186.62 [8285]P1(f775(f775(f232(f857(x82851,a844)),f321(x82851,x82852)),f321(x82851,x82853)))+~P1(f775(f775(f232(f857(x82851,f857(x82851,a844))),x82853),x82852)) % 186.05/186.62 [8286]~P54(x82861,x82862,x82863)+P54(x82861,x82862,f775(f775(f3(f857(f856(x82861,x82861),a844)),x82863),f300(x82861,f180(f857(f856(x82861,x82861),a844))))) % 186.05/186.62 [8308]P1(f775(f775(f232(f857(x83081,a844)),f322(x83081,x83082)),f322(x83081,x83083)))+~P1(f775(f775(f232(f857(f856(x83081,x83081),a844)),x83083),x83082)) % 186.05/186.62 [8315]~P118(x83151)+P1(f775(f775(f232(x83151),f2(x83151)),f775(f775(f82(x83151),f775(f775(f83(x83151),x83152),x83152)),f775(f775(f83(x83151),x83153),x83153)))) % 186.05/186.62 [8352]P1(f775(f775(f232(f857(x83521,a844)),f775(f276(x83521),x83522)),f775(f276(x83521),x83523)))+~P1(f775(f775(f232(f857(f856(x83521,x83521),a844)),x83522),x83523)) % 186.05/186.62 [8384]~P48(x83841,x83842)+~P1(f775(f775(f334(f856(x83841,x83841)),f775(f775(f241(x83841,x83841),x83843),x83843)),x83842)) % 186.05/186.62 [8386]~P36(x83861,x83862)+~P1(f775(f775(f334(f856(x83861,x83861)),f775(f775(f241(x83861,x83861),x83863),x83863)),x83862)) % 186.05/186.62 [8447]P1(f775(f775(f232(f857(x84471,a844)),f45(f857(x84471,a844),x84472)),f45(f857(x84471,a844),x84473)))+~P1(f775(f775(f232(f857(f857(x84471,a844),a844)),x84473),x84472)) % 186.05/186.62 [8448]P1(f775(f775(f232(f857(x84481,a844)),f44(f857(x84481,a844),x84482)),f44(f857(x84481,a844),x84483)))+~P1(f775(f775(f232(f857(f857(x84481,a844),a844)),x84482),x84483)) % 186.05/186.62 [8503]~P12(x85031,x85033,x85032)+P1(f775(f775(f232(f857(f856(x85031,x85031),a844)),x85032),f775(f775(f248(x85031,x85031),x85033),f775(f18(f857(x85031,a844),x85031),x85033)))) % 186.05/186.62 [8504]~P47(x85041,x85043,x85042)+P1(f775(f775(f232(f857(f856(x85041,x85041),a844)),x85042),f775(f775(f248(x85041,x85041),x85043),f775(f18(f857(x85041,a844),x85041),x85043)))) % 186.05/186.62 [8542]~P79(x85421)+P1(f775(f775(f232(x85421),f775(f775(f3(x85421),f775(f77(x85421),x85422)),f775(f77(x85421),x85423))),f775(f77(x85421),f775(f775(f3(x85421),x85423),x85422)))) % 186.05/186.62 [8543]~P79(x85431)+P1(f775(f775(f232(x85431),f775(f775(f3(x85431),f775(f77(x85431),x85432)),f775(f77(x85431),x85433))),f775(f77(x85431),f775(f775(f3(x85431),x85432),x85433)))) % 186.05/186.62 [8567]P1(f775(f775(f232(f857(f856(x85671,x85671),a844)),f300(x85671,x85672)),f300(x85671,x85673)))+~P1(f775(f775(f232(f857(f856(x85671,x85671),a844)),x85672),x85673)) % 186.05/186.62 [8713]P54(x87131,x87132,x87133)+~P54(x87131,x87132,f775(f775(f3(f857(f856(x87131,x87131),a844)),x87133),f300(x87131,f180(f857(f856(x87131,x87131),a844))))) % 186.05/186.62 [8732]P1(f775(f775(f232(f857(f856(f851(x87321),f851(x87321)),a844)),f147(x87321,x87322)),f147(x87321,x87323)))+~P1(f775(f775(f232(f857(f856(x87321,x87321),a844)),x87322),x87323)) % 186.05/186.62 [8733]P1(f775(f775(f232(f857(f856(f851(x87331),f851(x87331)),a844)),f146(x87331,x87332)),f146(x87331,x87333)))+~P1(f775(f775(f232(f857(f856(x87331,x87331),a844)),x87332),x87333)) % 186.05/186.62 [8750]~P47(x87501,x87503,x87502)+P1(f775(f775(f232(f857(f856(x87501,x87501),a844)),x87502),f775(f775(f281(x87501,x87501,x87501),f775(f278(x87501,x87501),x87502)),x87502))) % 186.05/186.62 [8791]~P1(f775(f127(x87911),x87912))+E(f775(f126(x87911,f775(f775(f9(x87911,f857(x87911,a844),a844),f334(x87911)),f775(f158(x87911),f160(x87911,x87912,x87913)))),x87912),f160(x87911,x87912,x87913)) % 186.05/186.62 [8837]E(x88371,x88372)+~P1(f775(f775(f334(f856(x88373,x88373)),f775(f775(f241(x88373,x88373),x88371),x88372)),f300(x88373,f180(f857(f856(x88373,x88373),a844))))) % 186.05/186.62 [8919]P1(f775(f775(f334(x89191),x89192),f322(x89191,x89193)))+P1(f775(f775(f334(f856(x89191,x89191)),f775(f775(f241(x89191,x89191),f526(x89193,x89192,x89191)),x89192)),x89193)) % 186.05/186.62 [8920]P1(f775(f775(f334(x89201),x89202),f322(x89201,x89203)))+P1(f775(f775(f334(f856(x89201,x89201)),f775(f775(f241(x89201,x89201),f620(x89203,x89202,x89201)),x89202)),x89203)) % 186.05/186.62 [8921]P1(f775(f775(f334(x89211),x89212),f322(x89211,x89213)))+P1(f775(f775(f334(f856(x89211,x89211)),f775(f775(f241(x89211,x89211),f622(x89213,x89212,x89211)),x89212)),x89213)) % 186.05/186.62 [9025]P1(f775(x90253,x90252))+E(f775(f256(x90251),f775(f775(f20(x90251,a844,a844),f775(f775(f10(a844,f857(a844,a844),x90251),a331),f775(a330,x90252))),x90253)),f180(f857(x90251,a844))) % 186.05/186.62 [9044]~P79(x90441)+P1(f775(f775(f232(x90441),f775(f77(x90441),f775(f775(f3(x90441),f775(f77(x90441),x90442)),f775(f77(x90441),x90443)))),f775(f77(x90441),f775(f775(f3(x90441),x90442),x90443)))) % 186.05/186.62 [9057]~P1(f775(x90573,x90572))+E(f775(f256(x90571),f775(f775(f20(x90571,a844,a844),f775(f775(f10(a844,f857(a844,a844),x90571),a331),f775(a330,x90572))),x90573)),f775(f775(f302(x90571),x90572),f180(f857(x90571,a844)))) % 186.05/186.62 [9063]~P1(f775(f775(f334(f857(x90631,a844)),x90633),f775(f301(x90631),x90632)))+P1(f775(f245(x90631,f775(f775(f9(x90631,f857(x90631,a844),a844),f334(x90631)),x90632)),x90633)) % 186.05/186.62 [9097]P36(x90971,x90972)+P1(f775(f775(f334(f856(x90971,x90971)),f775(f775(f241(x90971,x90971),f775(f589(x90972,x90971),f775(a114,x90973))),f775(f589(x90972,x90971),x90973))),x90972)) % 186.05/186.62 [9223]P1(f775(f775(f334(f857(x92231,a844)),x92232),f775(f301(x92231),x92233)))+~P1(f775(f245(x92231,f775(f775(f9(x92231,f857(x92231,a844),a844),f334(x92231)),x92233)),x92232)) % 186.05/186.62 [9283]P1(f775(f775(f334(x92831),f775(f265(x92831,x92832),x92833)),f775(f158(x92831),f775(f775(f143(f856(a101,x92831),x92831),f250(a101,x92831)),x92832))))+~P1(f775(f775(f233(a101),x92833),f775(f155(a101),f775(f775(f143(f856(a101,x92831),a101),f240(a101,x92831)),x92832)))) % 186.05/186.62 [9331]P1(f775(f775(f232(f857(f856(f851(x93311),f851(x93311)),a844)),f147(x93311,x93312)),f775(f775(f248(f851(x93311),f851(x93311)),f149(x93311,x93313)),f775(f18(f857(f851(x93311),a844),f851(x93311)),f149(x93311,x93313)))))+~P1(f775(f775(f232(f857(f856(x93311,x93311),a844)),x93312),f775(f775(f248(x93311,x93311),x93313),f775(f18(f857(x93311,a844),x93311),x93313)))) % 186.05/186.62 [9351]P1(f775(f775(f334(x93511),f775(f240(x93511,f856(a101,a101)),f775(f263(x93511,x93512),x93513))),f775(f158(x93511),f775(f775(f143(f856(a101,x93511),x93511),f250(a101,x93511)),x93512))))+~P1(f775(f775(f233(a101),f2(a101)),f775(f155(a101),f775(f775(f143(f856(a101,x93511),a101),f240(a101,x93511)),x93512)))) % 186.05/186.62 [9366]~P1(f775(f775(f232(f857(f856(x93661,x93661),a844)),x93662),f775(f775(f248(x93661,x93661),x93663),f775(f18(f857(x93661,a844),x93661),x93663))))+P1(f775(f775(f232(f857(f856(x93661,x93661),a844)),f775(f775(f281(x93661,x93661,x93661),x93662),f300(x93661,x93662))),f775(f775(f248(x93661,x93661),x93663),f775(f18(f857(x93661,a844),x93661),x93663)))) % 186.05/186.62 [9647]~P36(x96471,x96472)+~P1(f775(f775(f334(f856(x96471,x96471)),f775(f775(f241(x96471,x96471),f775(x96473,f775(a114,f590(x96472,x96471,x96473)))),f775(x96473,f590(x96472,x96471,x96473)))),x96472)) % 186.05/186.62 [9648]~P36(x96481,x96482)+~P1(f775(f775(f334(f856(x96481,x96481)),f775(f775(f241(x96481,x96481),f775(x96483,f775(a114,f636(x96483,x96482,x96481)))),f775(x96483,f636(x96483,x96482,x96481)))),x96482)) % 186.05/186.62 [9903]P1(f775(f775(f232(f857(f856(f857(x99031,a844),f857(x99031,a844)),a844)),f775(f775(f281(f857(x99031,a844),f857(x99031,a844),f857(x99031,a844)),f326(x99031,x99032)),f775(f775(f103(f857(f856(f857(x99031,a844),f857(x99031,a844)),a844)),f326(x99031,x99033)),f775(f775(f302(f856(f857(x99031,a844),f857(x99031,a844))),f775(f775(f241(f857(x99031,a844),f857(x99031,a844)),f180(f857(x99031,a844))),f180(f857(x99031,a844)))),f180(f857(f856(f857(x99031,a844),f857(x99031,a844)),a844)))))),f326(x99031,x99032)))+~P1(f775(f775(f232(f857(f856(x99031,x99031),a844)),f775(f775(f281(x99031,x99031,x99031),x99032),x99033)),x99032)) % 186.05/186.62 [9904]P1(f775(f775(f232(f857(f856(f857(x99041,a844),f857(x99041,a844)),a844)),f775(f775(f281(f857(x99041,a844),f857(x99041,a844),f857(x99041,a844)),f324(x99041,x99042)),f775(f775(f103(f857(f856(f857(x99041,a844),f857(x99041,a844)),a844)),f324(x99041,x99043)),f775(f775(f302(f856(f857(x99041,a844),f857(x99041,a844))),f775(f775(f241(f857(x99041,a844),f857(x99041,a844)),f180(f857(x99041,a844))),f180(f857(x99041,a844)))),f180(f857(f856(f857(x99041,a844),f857(x99041,a844)),a844)))))),f324(x99041,x99042)))+~P1(f775(f775(f232(f857(f856(x99041,x99041),a844)),f775(f775(f281(x99041,x99041,x99041),x99042),x99043)),x99042)) % 186.05/186.62 [7176]~P1(f775(f775(f232(a850),x71762),x71761))+E(f775(f775(f3(a850),f775(a114,f775(f775(f3(a850),x71761),x71762))),x71763),f775(f775(f3(a850),f775(a114,x71761)),f775(f775(f82(a850),x71762),x71763))) % 186.05/186.62 [7216]~P7(x72161)+E(f775(f775(f82(x72161),f52(x72161,x72162,x72163)),f775(f775(f83(x72161),f775(f775(f43(x72161),x72162),x72163)),x72163)),x72162) % 186.05/186.62 [7436]E(f775(f775(f83(a850),f775(f106(a850),x74361)),f775(f775(f83(a850),f775(f106(a850),x74362)),x74363)),f775(f775(f83(a850),f775(f106(a850),f775(f775(f83(a1),x74361),x74362))),x74363))+P1(f775(f775(f233(a1),x74361),a85)) % 186.05/186.62 [7909]~P1(f775(f775(f232(a850),x79093),x79092))+P1(f775(f775(f232(a850),x79091),f775(f775(f3(a850),f775(f775(f82(a850),x79092),x79091)),x79093))) % 186.05/186.62 [8104]~P1(f775(f775(f232(a850),x81041),x81042))+E(f775(f775(f125(a850),f130(a850,f775(f294(a850,x81041),x81042))),f130(a850,f775(f294(a850,x81042),f775(f775(f82(a850),x81042),x81043)))),f130(a850,f775(f294(a850,x81041),f775(f775(f82(a850),x81042),x81043)))) % 186.05/186.62 [8361]~P1(f775(f63(x83611),x83612))+E(f775(a114,f775(f42(x83611),f775(f775(f3(f857(x83611,a844)),x83612),f775(f775(f302(x83611),x83613),f180(f857(x83611,a844)))))),f775(f42(x83611),f775(f775(f302(x83611),x83613),x83612))) % 186.05/186.62 [8405]~P1(f775(f63(x84051),x84052))+E(f775(f775(f82(a850),f80(a850)),f775(f42(x84051),f775(f775(f3(f857(x84051,a844)),x84052),f775(f775(f302(x84051),x84053),f180(f857(x84051,a844)))))),f775(f42(x84051),f775(f775(f302(x84051),x84053),x84052))) % 186.05/186.62 [8576]E(f775(f775(f3(a850),f775(f42(x85761),x85762)),f775(f42(x85761),f775(f775(f104(f857(x85761,a844)),x85762),x85763))),f775(f42(x85761),f775(f775(f3(f857(x85761,a844)),x85762),x85763)))+~P1(f775(f63(x85761),f775(f775(f104(f857(x85761,a844)),x85762),x85763))) % 186.05/186.62 [8788]~P10(f775(x87882,f425(x87882,x87883,x87881)))+E(f775(f102(a1),f775(f775(f8(x87881,a850),f775(f775(f10(a1,a850,x87881),a107),x87882)),x87883)),f775(f775(f8(x87881,a1),x87882),x87883)) % 186.05/186.62 [8789]~P10(f775(x87892,f462(x87892,x87893,x87891)))+E(f775(f102(a1),f775(f775(f11(x87891,a850),f775(f775(f10(a1,a850,x87891),a107),x87892)),x87893)),f775(f775(f11(x87891,a1),x87892),x87893)) % 186.05/186.62 [8821]~P1(f775(f63(x88211),x88213))+P1(f775(f775(f232(a850),f775(f775(f3(a850),f775(f42(x88211),x88212)),f775(f42(x88211),x88213))),f775(f42(x88211),f775(f775(f3(f857(x88211,a844)),x88212),x88213)))) % 186.05/186.62 [8845]P1(f775(f775(f334(x88451),f425(x88452,x88453,x88451)),x88453))+E(f775(f102(a1),f775(f775(f8(x88451,a850),f775(f775(f10(a1,a850,x88451),a107),x88452)),x88453)),f775(f775(f8(x88451,a1),x88452),x88453)) % 186.05/186.62 [8846]P1(f775(f775(f334(x88461),f462(x88462,x88463,x88461)),x88463))+E(f775(f102(a1),f775(f775(f11(x88461,a850),f775(f775(f10(a1,a850,x88461),a107),x88462)),x88463)),f775(f775(f11(x88461,a1),x88462),x88463)) % 186.05/186.62 [8913]E(f87(x89131,f775(f775(f9(x89131,f857(x89131,a844),a844),f334(x89131)),f775(f775(f3(f857(x89131,a844)),x89132),f775(f775(f302(x89131),x89133),f180(f857(x89131,a844)))))),f244(x89131,x89133,x89132))+P1(f775(f775(f232(f857(x89131,a844)),x89132),f775(f775(f302(x89131),x89133),f180(f857(x89131,a844))))) % 186.05/186.62 [9224]E(f775(f775(f143(f851(x92241),x92241),f775(f775(f9(f851(x92241),a850,x92241),f153(x92241)),x92242)),f775(f126(f851(x92241),f775(f775(f10(a850,a844,f851(x92241)),f775(f233(a850),x92242)),f181(f851(x92241)))),x92243)),f775(f775(f153(f851(x92241)),f164(x92241,x92243)),x92242))+~P1(f775(f775(f233(a850),x92242),f775(f181(f851(f851(x92241))),f164(x92241,x92243)))) % 186.05/186.62 [9523]~P1(f775(f775(f334(f856(x95231,x95231)),x95232),f300(x95231,x95233)))+P1(f775(f775(f334(f856(x95231,x95231)),x95232),f775(f775(f46(a850,f857(f856(x95231,x95231),a844)),f239(f857(a850,a844))),f775(f775(f9(a850,f857(f856(x95231,x95231),a844),f857(f856(x95231,x95231),a844)),f173(f856(x95231,x95231),a844)),x95233)))) % 186.05/186.62 [9576]~P1(f775(f775(f232(f857(x95761,a844)),f775(f775(f46(a850,f857(x95761,a844)),f775(f294(a850,f2(a850)),f397(x95763,x95762,x95761))),x95762)),x95763))+P1(f775(f775(f232(f857(x95761,a844)),f775(f775(f46(a850,f857(x95761,a844)),f239(f857(a850,a844))),x95762)),x95763)) % 186.05/186.62 [9624]~P1(f775(f775(f233(a1),f2(a1)),x96243))+P1(f775(f775(f233(a1),x96241),f775(f775(f82(a1),x96242),f775(f775(f83(a1),f775(f775(f82(a1),f775(f77(a1),f775(f775(f3(a1),x96242),x96241))),f80(a1))),x96243)))) % 186.05/186.62 [9634]~P36(x96341,f775(f775(f103(f857(f856(x96341,x96341),a844)),x96342),x96343))+P36(x96341,f775(f775(f103(f857(f856(x96341,x96341),a844)),f775(f775(f103(f857(f856(x96341,x96341),a844)),f775(f775(f281(x96341,x96341,x96341),x96342),x96342)),f775(f775(f281(x96341,x96341,x96341),x96343),x96342))),x96343)) % 186.05/186.62 [9700]P36(x97001,f775(f775(f103(f857(f856(x97001,x97001),a844)),x97002),x97003))+~P36(x97001,f775(f775(f103(f857(f856(x97001,x97001),a844)),f775(f775(f103(f857(f856(x97001,x97001),a844)),f775(f775(f281(x97001,x97001,x97001),x97002),x97002)),f775(f775(f281(x97001,x97001,x97001),x97003),x97002))),x97003)) % 186.05/186.62 [9305]~P133(x93051)+E(f775(f105(x93051),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x93052),x93053)),f180(f857(f856(a850,a850),a844)))))),f775(f775(f3(x93051),f775(f102(x93051),x93052)),f775(f102(x93051),x93053))) % 186.05/186.62 [9384]P1(f775(x93843,x93842))+E(f775(f256(x93841),f775(f775(f20(x93841,a844,a844),f775(f775(f10(a844,f857(a844,a844),x93841),a331),f775(f775(f9(x93841,x93841,a844),a330),x93842))),x93843)),f180(f857(x93841,a844))) % 186.05/186.62 [9386]~P1(f775(x93863,x93862))+E(f775(f256(x93861),f775(f775(f20(x93861,a844,a844),f775(f775(f10(a844,f857(a844,a844),x93861),a331),f775(f775(f9(x93861,x93861,a844),a330),x93862))),x93863)),f775(f775(f302(x93861),x93862),f180(f857(x93861,a844)))) % 186.05/186.62 [9692]~P1(f775(f63(x96921),x96923))+E(f775(f775(f66(x96921,f857(x96921,a844),f775(f775(f10(f857(x96921,a844),f857(f857(x96921,a844),f857(x96921,a844)),x96921),f775(f9(f857(x96921,a844),f857(x96921,a844),f857(x96921,a844)),f3(f857(x96921,a844)))),f775(f775(f9(x96921,f857(x96921,a844),f857(x96921,a844)),f302(x96921)),f180(f857(x96921,a844))))),x96922),x96923),f775(f775(f3(f857(x96921,a844)),x96922),x96923)) % 186.05/186.62 [9725]~P1(f775(f775(f233(a1),f2(a1)),x97253))+P1(f775(f775(f233(a1),f775(f775(f3(a1),x97251),f775(f775(f83(a1),f775(f775(f82(a1),f775(f77(a1),f775(f775(f3(a1),x97251),x97252))),f80(a1))),x97253))),x97252)) % 186.05/186.62 [9971]~P1(f775(f775(f334(x99711),x99713),f322(x99711,x99712)))+P1(f775(f321(x99711,f775(f775(f9(x99711,f857(f856(x99711,x99711),a844),f857(x99711,a844)),f775(f775(f10(f857(x99711,f857(f857(f856(x99711,x99711),a844),a844)),f857(f857(f856(x99711,x99711),a844),f857(x99711,a844)),x99711),f9(x99711,f857(f856(x99711,x99711),a844),a844)),f775(f775(f10(f857(x99711,f856(x99711,x99711)),f857(x99711,f857(f857(f856(x99711,x99711),a844),a844)),x99711),f775(f10(f856(x99711,x99711),f857(f857(f856(x99711,x99711),a844),a844),x99711),f334(f856(x99711,x99711)))),f241(x99711,x99711)))),x99712)),x99713)) % 186.05/186.62 [9983]P1(f775(f775(f334(x99831),x99832),f322(x99831,x99833)))+~P1(f775(f321(x99831,f775(f775(f9(x99831,f857(f856(x99831,x99831),a844),f857(x99831,a844)),f775(f775(f10(f857(x99831,f857(f857(f856(x99831,x99831),a844),a844)),f857(f857(f856(x99831,x99831),a844),f857(x99831,a844)),x99831),f9(x99831,f857(f856(x99831,x99831),a844),a844)),f775(f775(f10(f857(x99831,f856(x99831,x99831)),f857(x99831,f857(f857(f856(x99831,x99831),a844),a844)),x99831),f775(f10(f856(x99831,x99831),f857(f857(f856(x99831,x99831),a844),a844),x99831),f334(f856(x99831,x99831)))),f241(x99831,x99831)))),x99833)),x99832)) % 186.05/186.62 [9574]~P1(f775(f63(x95741),f775(f256(x95741),x95743)))+P1(f775(f63(x95741),f775(f256(x95741),f775(f775(f20(x95741,a844,a844),f775(f775(f10(a844,f857(a844,a844),x95741),a331),x95742)),x95743)))) % 186.05/186.62 [9575]~P1(f775(f63(x95751),f775(f256(x95751),x95752)))+P1(f775(f63(x95751),f775(f256(x95751),f775(f775(f20(x95751,a844,a844),f775(f775(f10(a844,f857(a844,a844),x95751),a331),x95752)),x95753)))) % 186.05/186.62 [9659]P1(f775(f63(x96591),f775(f256(x96591),x96592)))+~P1(f775(f63(x96591),f775(f256(x96591),f775(f775(f20(x96591,a844,a844),f775(f775(f10(a844,f857(a844,a844),x96591),a332),x96593)),x96592)))) % 186.05/186.62 [9660]P1(f775(f63(x96601),f775(f256(x96601),x96602)))+~P1(f775(f63(x96601),f775(f256(x96601),f775(f775(f20(x96601,a844,a844),f775(f775(f10(a844,f857(a844,a844),x96601),a332),x96602)),x96603)))) % 186.05/186.62 [9956]~P1(f775(f63(x99561),x99562))+P1(f775(f63(f851(x99561)),f775(f256(f851(x99561)),f775(f775(f20(f851(x99561),a844,a844),f775(f775(f10(a844,f857(a844,a844),f851(x99561)),a331),f775(f775(f9(f851(x99561),f857(x99561,a844),a844),f775(f775(f10(f857(x99561,a844),f857(f857(x99561,a844),a844),f851(x99561)),f232(f857(x99561,a844))),f158(x99561))),x99562))),f775(f775(f9(f851(x99561),a850,a844),f775(f775(f10(a850,f857(a850,a844),f851(x99561)),a330),f181(f851(x99561)))),x99563))))) % 186.05/186.62 [9957]~P1(f775(f63(x99571),x99572))+P1(f775(f63(f851(x99571)),f775(f256(f851(x99571)),f775(f775(f20(f851(x99571),a844,a844),f775(f775(f10(a844,f857(a844,a844),f851(x99571)),a331),f775(f775(f9(f851(x99571),f857(x99571,a844),a844),f775(f775(f10(f857(x99571,a844),f857(f857(x99571,a844),a844),f851(x99571)),f232(f857(x99571,a844))),f158(x99571))),x99572))),f775(f775(f9(f851(x99571),a850,a844),f775(f775(f10(a850,f857(a850,a844),f851(x99571)),f232(a850)),f181(f851(x99571)))),x99573))))) % 186.05/186.62 [9673]~P85(x96731)+E(f775(f775(f242(x96731),x96732),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x96733)),f775(f775(f83(x96731),f775(f775(f242(x96731),x96732),x96733)),f775(f775(f242(x96731),x96732),x96733))) % 186.05/186.62 [9704]~P75(x97041)+E(f775(f775(f242(x97041),f775(f775(f242(x97041),x97042),x97043)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f242(x97041),x97042),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97043))) % 186.05/186.62 [9765]~P133(x97651)+E(f775(f775(f242(x97651),f775(f81(x97651),x97652)),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97653)),f775(f775(f242(x97651),x97652),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97653))) % 186.05/186.62 [9908]~P110(x99081)+P1(f775(f775(f232(x99081),f2(x99081)),f775(f775(f82(x99081),f775(f775(f242(x99081),x99082),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99081),x99083),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))) % 186.05/186.62 [9775]~P85(x97751)+E(f775(f775(f242(x97751),x97752),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97753))),f775(f775(f83(x97751),x97752),f775(f775(f83(x97751),f775(f775(f242(x97751),x97752),x97753)),f775(f775(f242(x97751),x97752),x97753)))) % 186.05/186.62 [9824]~P75(x98241)+E(f775(f775(f83(x98241),x98242),f775(f775(f242(x98241),f775(f775(f242(x98241),x98242),x98243)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x98241),x98242),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98243)))) % 186.05/186.62 [9868]~P110(x98681)+P1(f775(f775(f232(x98681),f2(x98681)),f775(f775(f242(x98681),x98682),f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x98683)))) % 186.05/186.62 [9937]~P88(x99371)+E(f775(f775(f82(x99371),f775(f775(f82(x99371),f775(f775(f242(x99371),x99372),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99371),x99373),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f775(f775(f83(x99371),f775(f775(f83(x99371),f775(f106(x99371),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x99372)),x99373)),f775(f775(f242(x99371),f775(f775(f82(x99371),x99372),x99373)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9938]~P88(x99381)+E(f775(f775(f3(x99381),f775(f775(f82(x99381),f775(f775(f242(x99381),x99382),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99381),x99383),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f775(f775(f83(x99381),f775(f775(f83(x99381),f775(f106(x99381),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x99382)),x99383)),f775(f775(f242(x99381),f775(f775(f3(x99381),x99382),x99383)),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [4577]E(x45771,x45772)+~E(f35(x45773,x45771),f35(x45774,x45772)) % 186.05/186.62 [4578]E(x45781,x45782)+~E(f35(x45781,x45783),f35(x45782,x45784)) % 186.05/186.62 [4579]E(x45791,x45792)+~E(f36(x45793,x45791),f36(x45794,x45792)) % 186.05/186.62 [4580]E(x45801,x45802)+~E(f36(x45801,x45803),f36(x45802,x45804)) % 186.05/186.62 [4581]E(x45811,x45812)+~E(f28(x45813,x45811),f28(x45814,x45812)) % 186.05/186.62 [4582]E(x45821,x45822)+~E(f28(x45821,x45823),f28(x45822,x45824)) % 186.05/186.62 [5699]P39(f35(x56991,x56993),x56992,x56994,x56992)+P1(f775(x56991,x56992)) % 186.05/186.62 [6861]~P39(x68611,x68612,x68613,x68614)+P39(x68611,x68612,f775(a114,x68613),x68614) % 186.05/186.62 [7706]P29(x77061,x77062,x77063,x77064)+~E(f505(x77064,x77063,x77062,x77061),f519(x77064,x77063,x77062,x77061)) % 186.05/186.62 [8206]~P29(x82061,f854(x82062),x82064,f169(x82061,x82062,x82064))+P29(x82061,f854(x82062),f170(x82061,x82062,x82063,x82064),f169(x82061,x82062,x82064)) % 186.05/186.62 [8420]~P29(x84201,f854(x84202),f170(x84201,x84202,x84204,x84203),f169(x84201,x84202,x84203))+P29(x84201,f854(x84202),x84203,f169(x84201,x84202,x84203)) % 186.05/186.62 [4944]~P21(x49443,x49441,x49444)+E(f775(f775(x49441,x49442),x49442),x49442) % 186.05/186.62 [4947]E(x49471,x49472)+~E(f775(f304(x49473,x49474),x49471),f775(f304(x49473,x49474),x49472)) % 186.05/186.62 [4949]E(x49491,x49492)+~E(f775(f313(x49493,x49494),x49491),f775(f313(x49493,x49494),x49492)) % 186.05/186.62 [5226]~E(x52264,f180(f857(x52261,a844)))+E(f775(f303(x52261,x52262,x52263),x52264),f180(f857(x52262,a844))) % 186.05/186.62 [5489]~E(f775(f303(x54892,x54893,x54894),x54891),f180(f857(x54893,a844)))+E(x54891,f180(f857(x54892,a844))) % 186.05/186.62 [5780]~P100(x57802)+E(f775(f775(f138(x57801,x57802,x57803),x57804),f115(x57801)),f775(f775(f140(x57801),x57804),f115(x57801))) % 186.05/186.62 [5815]E(f775(x58151,x58152),f183(x58153))+P1(f775(f775(f334(x58154),x58152),f169(x58154,x58153,x58151))) % 186.05/186.62 [6139]~E(x61391,f180(f857(x61392,a844)))+~P1(f775(f64(x61392,x61393,x61391),x61394)) % 186.05/186.62 [6160]~P57(x61601,x61603,x61604,x61602)+P1(f775(f63(x61601),x61602)) % 186.05/186.62 [6161]~P57(x61611,x61613,x61612,x61614)+P1(f775(f63(x61611),x61612)) % 186.05/186.62 [6168]~P57(x61682,x61683,x61684,x61681)+~E(x61681,f180(f857(x61682,a844))) % 186.05/186.62 [6200]~P99(x62001)+E(f775(f775(f104(f857(x62001,a844)),f775(f294(x62001,x62002),x62003)),f295(x62001,x62003,x62004)),f180(f857(x62001,a844))) % 186.05/186.62 [6229]~P1(f775(f775(x62293,x62294),x62292))+P1(f775(f775(f334(x62291),x62292),f287(x62291,x62293,x62294))) % 186.05/186.62 [6230]~P1(f775(f775(x62303,x62304),x62302))+P1(f775(f775(f334(x62301),x62302),f286(x62301,x62303,x62304))) % 186.05/186.62 [6231]~P1(f775(f775(x62313,x62312),x62314))+P1(f775(f775(f334(x62311),x62312),f290(x62311,x62313,x62314))) % 186.05/186.62 [6232]~P1(f775(f775(x62323,x62322),x62324))+P1(f775(f775(f334(x62321),x62322),f288(x62321,x62323,x62324))) % 186.05/186.62 [6384]~P99(x63841)+E(f775(f775(f104(f857(x63841,a844)),f295(x63841,x63842,x63843)),f297(x63841,x63843,x63844)),f180(f857(x63841,a844))) % 186.05/186.62 [6385]~P99(x63851)+E(f775(f775(f104(f857(x63851,a844)),f295(x63851,x63852,x63853)),f298(x63851,x63853,x63854)),f180(f857(x63851,a844))) % 186.05/186.62 [6386]~P99(x63861)+E(f775(f775(f104(f857(x63861,a844)),f297(x63861,x63862,x63863)),f297(x63861,x63863,x63864)),f180(f857(x63861,a844))) % 186.05/186.62 [6387]~P99(x63871)+E(f775(f775(f104(f857(x63871,a844)),f297(x63871,x63872,x63873)),f298(x63871,x63873,x63874)),f180(f857(x63871,a844))) % 186.05/186.62 [6388]~P99(x63881)+E(f775(f775(f104(f857(x63881,a844)),f298(x63881,x63882,x63883)),f295(x63881,x63883,x63884)),f180(f857(x63881,a844))) % 186.05/186.62 [6426]P1(f775(f775(x64261,x64262),f596(x64262,x64261)))+~P1(f775(f246(x64263,x64264,x64261),x64262)) % 186.05/186.62 [6480]~E(f775(x64801,x64802),f183(x64803))+~P1(f775(f775(f334(x64804),x64802),f169(x64804,x64803,x64801))) % 186.05/186.62 [6562]~P2(x65621)+E(f182(x65621,x65622,f775(a114,x65623),x65624),f182(x65621,x65622,x65623,f775(x65622,x65624))) % 186.05/186.62 [6626]~P1(f775(f775(f334(x66264),x66263),f287(x66264,x66261,x66262)))+P1(f775(f775(x66261,x66262),x66263)) % 186.05/186.62 [6627]~P1(f775(f775(f334(x66274),x66273),f286(x66274,x66271,x66272)))+P1(f775(f775(x66271,x66272),x66273)) % 186.05/186.62 [6628]~P1(f775(f775(f334(x66284),x66282),f290(x66284,x66281,x66283)))+P1(f775(f775(x66281,x66282),x66283)) % 186.05/186.62 [6629]~P1(f775(f775(f334(x66294),x66292),f288(x66294,x66291,x66293)))+P1(f775(f775(x66291,x66292),x66293)) % 186.05/186.62 [6711]E(f775(f42(f858(x67111,x67112)),f314(x67111,x67112,x67113,x67114)),f2(a850))+P1(f775(f63(x67112),x67114)) % 186.05/186.62 [6712]E(f775(f42(f858(x67121,x67122)),f314(x67121,x67122,x67123,x67124)),f2(a850))+P1(f775(f63(x67121),x67123)) % 186.05/186.62 [6923]~P19(x69234,x69231,x69232)+E(f775(f75(x69231,x69231,x69231,f775(x69232,x69233)),f775(x69232,x69233)),f775(x69232,x69233)) % 186.05/186.62 [7161]E(f272(x71611,x71612,x71613,x71614),f775(f241(f857(a101,f857(a844,f854(f852(x71611)))),f856(a101,a101)),f48(x71611)))+~P1(f775(f775(f232(a101),x71613),f2(a101))) % 186.05/186.62 [7227]~P39(f775(a27,x72271),x72272,f775(a114,x72273),x72274)+P39(f775(f231(a845),f775(a30,x72271)),x72272,x72273,x72274) % 186.05/186.62 [7264]P39(f775(a27,x72641),x72642,f775(a114,x72643),x72644)+~P39(f775(f231(a845),f775(a30,x72641)),x72642,x72643,x72644) % 186.05/186.62 [7564]~P39(f775(a27,x75644),x75643,x75642,x75641)+E(f775(a114,f442(x75641,x75642,x75643,x75644)),x75642) % 186.05/186.62 [7834]~E(x78342,x78343)+P1(f775(f775(f334(f856(x78341,x78341)),f775(f775(f241(x78341,x78341),x78342),x78343)),f300(x78341,x78344))) % 186.05/186.62 [7860]~P29(x78601,x78602,x78603,f239(f857(x78601,a844)))+E(f775(f79(x78601,x78602,f239(f857(x78601,a844)),x78603),f775(x78603,x78604)),x78604) % 186.05/186.62 [7952]~P1(f775(f775(f334(f851(x79521)),f775(f775(f140(x79521),x79524),x79522)),f149(x79521,x79523)))+P1(f775(f775(f334(f851(x79521)),x79522),f149(x79521,x79523))) % 186.05/186.62 [7953]~P1(f775(f775(f334(f851(x79531)),f775(f775(f125(x79531),x79534),x79532)),f149(x79531,x79533)))+P1(f775(f775(f334(f851(x79531)),x79532),f149(x79531,x79533))) % 186.05/186.62 [7954]~P1(f775(f775(f334(f851(x79541)),f775(f775(f125(x79541),x79542),x79544)),f149(x79541,x79543)))+P1(f775(f775(f334(f851(x79541)),x79542),f149(x79541,x79543))) % 186.05/186.62 [8028]~P39(f775(a27,x80281),x80282,x80284,x80283)+P39(f775(f231(a845),f775(a30,x80281)),x80282,f442(x80283,x80284,x80282,x80281),x80283) % 186.05/186.62 [8065]P29(x80654,x80653,x80651,x80652)+E(f775(x80651,f505(x80652,x80651,x80653,x80654)),f775(x80651,f519(x80652,x80651,x80653,x80654))) % 186.05/186.62 [8074]E(f170(x80741,x80742,x80743,x80744),f170(x80741,x80742,x80744,x80743))+~E(f775(f775(f104(f857(x80741,a844)),f169(x80741,x80742,x80743)),f169(x80741,x80742,x80744)),f180(f857(x80741,a844))) % 186.05/186.62 [8171]~P29(x81712,x81711,x81714,x81713)+P29(x81711,x81712,f79(x81712,x81711,x81713,x81714),f775(f303(x81712,x81711,x81714),x81713)) % 186.05/186.62 [8306]P36(f856(x83062,x83064),f275(x83062,x83064,x83061,x83063))+P1(f775(x83061,f593(x83062,x83063,x83064,x83061))) % 186.05/186.62 [8427]E(x84271,x84272)+~P1(f775(f775(f334(f856(x84273,x84273)),f775(f775(f241(x84273,x84273),x84271),x84272)),f260(x84273,x84274))) % 186.05/186.62 [8461]~E(f775(x84611,f515(x84613,x84612,x84614,x84611)),f775(f174(x84614,x84612,x84613),f515(x84613,x84612,x84614,x84611)))+E(f775(x84611,f2(a850)),x84612) % 186.05/186.62 [8495]~P1(f775(f63(f858(x84953,x84951)),f314(x84953,x84951,x84954,x84952)))+P1(f775(f63(x84951),x84952)) % 186.05/186.62 [8496]~P1(f775(f63(f858(x84961,x84963)),f314(x84961,x84963,x84962,x84964)))+P1(f775(f63(x84961),x84962)) % 186.05/186.62 [8657]P36(f856(x86571,x86572),f275(x86571,x86572,x86573,x86574))+~P36(x86572,f775(x86574,f593(x86571,x86574,x86572,x86573))) % 186.05/186.62 [9158]E(f775(f775(f148(x91581,x91582),f738(x91583,x91584,x91582,x91581)),f739(x91583,x91584,x91582,x91581)),x91584)+~P1(f775(f775(f334(f856(f851(x91581),f851(x91581))),f775(f775(f241(f851(x91581),f851(x91581)),x91582),x91584)),f146(x91581,x91583))) % 186.05/186.62 [9162]~P1(f775(f775(f334(f856(f851(x91621),f851(x91621))),f775(f775(f241(f851(x91621),f851(x91621)),x91622),x91623)),f135(x91621,x91624)))+P1(f775(f775(f334(f856(f851(x91621),f851(x91621))),f775(f775(f241(f851(x91621),f851(x91621)),x91622),x91623)),f137(x91621,x91624))) % 186.05/186.62 [9259]P1(f775(f63(x92591),x92592))+~P1(f775(f775(f334(f856(f857(x92591,a844),f857(x92591,a844))),f775(f775(f241(f857(x92591,a844),f857(x92591,a844)),x92593),x92592)),f324(x92591,x92594))) % 186.05/186.62 [9260]P1(f775(f63(x92601),x92602))+~P1(f775(f775(f334(f856(f857(x92601,a844),f857(x92601,a844))),f775(f775(f241(f857(x92601,a844),f857(x92601,a844)),x92602),x92603)),f324(x92601,x92604))) % 186.05/186.62 [9263]~E(x92631,f180(f857(x92632,a844)))+~P1(f775(f775(f334(f856(f857(x92632,a844),f857(x92632,a844))),f775(f775(f241(f857(x92632,a844),f857(x92632,a844)),x92633),x92631)),f324(x92632,x92634))) % 186.05/186.62 [9879]P16(x98791,x98792,x98793,x98794)+~P1(f775(f775(f251(x98791,x98791,a844),f775(f775(f9(x98791,f857(x98791,x98792),f857(x98791,a844)),f775(f775(f10(f857(x98792,a844),f857(f857(x98791,x98792),f857(x98791,a844)),x98791),f10(x98792,a844,x98791)),f775(f775(f10(x98792,f857(x98792,a844),x98791),a330),x98794))),x98794)),f498(x98794,x98793,x98792,x98791))) % 186.05/186.62 [4847]~E(x48474,f115(x48471))+E(f775(f775(f143(x48471,x48472),x48473),x48474),f115(x48472)) % 186.05/186.62 [4848]~E(x48484,f183(x48481))+E(f775(f775(f196(x48481,x48482),x48483),x48484),f183(x48482)) % 186.05/186.62 [4849]~E(x48492,f115(x48491))+E(f775(f775(f148(x48491,x48492),x48493),x48494),f115(x48491)) % 186.05/186.62 [5086]E(x50861,f183(x50862))+~E(f775(f775(f196(x50862,x50863),x50864),x50861),f183(x50863)) % 186.05/186.62 [5087]E(x50871,f115(x50872))+~E(f775(f775(f143(x50872,x50873),x50874),x50871),f115(x50873)) % 186.05/186.62 [5088]E(x50881,f115(x50882))+~E(f775(f775(f148(x50882,x50881),x50883),x50884),f115(x50882)) % 186.05/186.62 [5118]E(x51181,x51182)+~E(f775(f775(f125(x51183),x51184),x51181),f775(f775(f125(x51183),x51184),x51182)) % 186.05/186.62 [5119]E(x51191,x51192)+~E(f775(f775(f125(x51193),x51191),x51194),f775(f775(f125(x51193),x51192),x51194)) % 186.05/186.62 [5261]P1(f775(x52613,x52612))+E(f151(x52611,x52612,f775(f126(x52611,x52613),x52614)),f775(f126(x52611,x52613),x52614)) % 186.05/186.62 [5272]E(x52721,x52722)+~E(f130(a850,f775(f294(a850,x52721),x52723)),f775(f775(f140(a850),x52722),x52724)) % 186.05/186.62 [5319]~P30(x53192,x53193)+P30(x53191,f775(f775(f76(x53192,x53191),x53193),x53194)) % 186.05/186.62 [5320]~P36(x53202,x53203)+P36(x53201,f775(f775(f280(x53202,x53201),x53203),x53204)) % 186.05/186.62 [5529]~E(x55291,f115(x55292))+~E(f775(f775(f125(x55292),x55293),f775(f775(f140(x55292),x55294),f115(x55292))),x55291) % 186.05/186.62 [5562]E(f134(x55621,x55622),x55623)+~E(f775(f775(f125(x55621),x55624),f775(f775(f140(x55621),x55623),f115(x55621))),x55622) % 186.05/186.62 [5563]E(f116(x55631,x55632),x55633)+~E(f775(f775(f125(x55631),x55633),f775(f775(f140(x55631),x55634),f115(x55631))),x55632) % 186.05/186.62 [5671]~E(f130(a850,f775(f294(a850,x56711),x56712)),f775(f775(f140(a850),x56713),x56714))+P1(f775(f775(f233(a850),x56711),x56712)) % 186.05/186.62 [5878]E(x58781,f775(f775(f125(x58782),f775(f142(x58782),x58783)),f775(f775(f140(x58782),x58784),f115(x58782))))+~E(f775(f142(x58782),x58781),f775(f775(f140(x58782),x58784),x58783)) % 186.05/186.62 [6061]~P99(x60611)+E(f775(f775(f104(f857(x60611,a844)),f775(f294(x60611,x60612),x60613)),f775(f294(x60611,x60613),x60614)),f180(f857(x60611,a844))) % 186.05/186.62 [6096]~P66(x60961)+E(f775(f155(x60961),f775(f775(f143(a1,x60961),x60962),f163(x60963,x60964))),f775(f775(f8(a1,x60961),x60962),f775(f158(a1),f163(x60963,x60964)))) % 186.05/186.62 [6097]~P66(x60971)+E(f775(f775(f8(a1,x60971),x60972),f775(f158(a1),f163(x60973,x60974))),f775(f155(x60971),f775(f775(f143(a1,x60971),x60972),f163(x60973,x60974)))) % 186.05/186.62 [6244]~E(x62442,f775(f775(f125(x62441),f775(f142(x62441),x62444)),f775(f775(f140(x62441),x62443),f115(x62441))))+E(f775(f142(x62441),x62442),f775(f775(f140(x62441),x62443),x62444)) % 186.05/186.62 [6260]~P23(x62602,x62603,x62604,x62601)+E(f775(x62601,f180(f857(x62602,a844))),f39(x62603)) % 186.05/186.62 [6290]~P99(x62901)+E(f775(f775(f104(f857(x62901,a844)),f298(x62901,x62902,x62903)),f775(f294(x62901,x62903),x62904)),f180(f857(x62901,a844))) % 186.05/186.62 [6377]~P39(x63771,x63772,x63774,x63773)+P1(f775(f775(f187(x63771),x63772),x63773)) % 186.05/186.62 [6511]E(x65111,f180(f857(x65112,a844)))+~E(f314(x65113,x65112,x65114,x65111),f180(f857(f858(x65113,x65112),a844))) % 186.05/186.62 [6512]E(x65121,f180(f857(x65122,a844)))+~E(f314(x65122,x65123,x65121,x65124),f180(f857(f858(x65122,x65123),a844))) % 186.05/186.62 [6592]~P1(f775(f247(x65923,x65924,x65921),x65922))+P1(f775(f775(x65921,f592(x65922,x65921)),x65922)) % 186.05/186.62 [6640]~P1(f775(f63(x66402),x66404))+P1(f775(f63(x66401),f775(f303(x66402,x66401,x66403),x66404))) % 186.05/186.62 [6882]~P29(x68822,x68821,x68823,x68824)+E(f775(f42(x68821),f775(f303(x68822,x68821,x68823),x68824)),f775(f42(x68822),x68824)) % 186.05/186.62 [6902]E(f775(f303(x69021,x69022,x69023),f775(f305(x69021,x69022,x69023),x69024)),x69024)+~E(f775(f303(x69021,x69022,x69023),f239(f857(x69021,a844))),f239(f857(x69022,a844))) % 186.05/186.62 [7328]~P29(x73281,x73282,x73283,f239(f857(x73281,a844)))+E(f775(f305(x73281,x73282,x73283),f775(f303(x73281,x73282,x73283),x73284)),x73284) % 186.05/186.62 [7668]P1(f775(x76681,x76682))+~P1(f775(f775(f334(x76683),x76682),f775(f158(x76683),f162(x76683,x76681,x76684)))) % 186.05/186.62 [7778]~P1(f775(f775(f334(f851(x77781)),f775(f775(f140(x77781),x77782),x77784)),f149(x77781,x77783)))+P1(f775(f775(f334(x77781),x77782),x77783)) % 186.05/186.62 [7905]~P1(f775(f775(f334(x79051),x79052),f775(f158(x79051),f151(x79051,x79054,x79053))))+P1(f775(f775(f334(x79051),x79052),f775(f158(x79051),x79053))) % 186.05/186.62 [7907]~P1(f775(f775(f334(x79071),x79072),f775(f158(x79071),f160(x79071,x79073,x79074))))+P1(f775(f775(f334(x79071),x79072),f775(f158(x79071),x79073))) % 186.05/186.62 [7908]~P1(f775(f775(f334(x79081),x79082),f775(f158(x79081),f162(x79081,x79084,x79083))))+P1(f775(f775(f334(x79081),x79082),f775(f158(x79081),x79083))) % 186.05/186.62 [8121]E(f775(f775(f153(x81211),f162(x81211,x81212,x81213)),x81214),f775(f775(f153(x81211),x81213),x81214))+~P1(f775(f775(f233(a850),x81214),f775(f181(f851(x81211)),f162(x81211,x81212,x81213)))) % 186.05/186.62 [8204]~P66(x82041)+E(f775(f775(f8(a850,x82041),f775(f775(f10(a850,x82041,a850),x82042),a114)),f775(f294(a850,x82043),x82044)),f775(f775(f8(a850,x82041),x82042),f775(f294(a850,f775(a114,x82043)),f775(a114,x82044)))) % 186.05/186.62 [8213]~P66(x82131)+E(f775(f775(f8(a850,x82131),f775(f775(f10(a850,x82131,a850),x82132),a114)),f295(a850,x82133,x82134)),f775(f775(f8(a850,x82131),x82132),f295(a850,f775(a114,x82133),f775(a114,x82134)))) % 186.05/186.62 [8345]~P29(x83451,x83453,x83454,f239(f857(x83451,a844)))+P29(x83451,f857(x83452,x83453),f775(f775(f10(x83453,f857(x83452,x83453),x83451),f18(x83453,x83452)),x83454),f239(f857(x83451,a844))) % 186.05/186.62 [8436]~P29(x84362,x84361,x84364,x84363)+E(f775(f303(x84361,x84362,f79(x84362,x84361,x84363,x84364)),f775(f303(x84362,x84361,x84364),x84363)),x84363) % 186.05/186.62 [8497]~P1(f775(f775(f334(f856(x84971,x84971)),f775(f775(f241(x84971,x84971),x84972),x84974)),f260(x84971,x84973)))+P1(f775(f775(f334(x84971),x84972),x84973)) % 186.05/186.62 [8572]E(f775(f775(f775(f74(x85721,f854(x85722)),f775(f18(f854(x85722),x85721),f183(x85722))),x85723),f775(f227(x85722),f529(x85723,x85724,x85722,x85721))),x85724)+~E(f169(x85721,x85722,x85724),f775(f775(f302(x85721),x85723),f180(f857(x85721,a844)))) % 186.05/186.62 [8690]~E(f775(f775(f8(x86901,a850),x86904),x86903),f775(a114,x86902))+P1(f775(f775(f334(x86901),f361(x86902,x86903,x86904,x86901)),x86903)) % 186.05/186.62 [8706]~E(f775(f775(f8(x87064,a850),x87061),x87063),f775(a114,x87062))+P1(f775(f775(f233(a850),f2(a850)),f775(x87061,f361(x87062,x87063,x87061,x87064)))) % 186.05/186.62 [8716]~P1(f775(f63(x87162),x87164))+P1(f775(f775(f232(a850),f775(f42(x87161),f775(f303(x87162,x87161,x87163),x87164))),f775(f42(x87162),x87164))) % 186.05/186.62 [8717]E(f775(f775(f241(x87171,x87172),f701(x87173,x87174,x87172,x87171)),f702(x87173,x87174,x87172,x87171)),x87174)+~P1(f775(f775(f334(f856(x87171,x87172)),x87174),f775(f278(x87172,x87171),x87173))) % 186.05/186.62 [8726]P29(x87261,x87262,x87263,x87264)+P1(f775(f775(f334(x87261),f505(x87264,x87263,x87262,x87261)),x87264)) % 186.05/186.62 [8727]P29(x87271,x87272,x87273,x87274)+P1(f775(f775(f334(x87271),f519(x87274,x87273,x87272,x87271)),x87274)) % 186.05/186.62 [8780]P16(x87801,x87802,x87803,x87804)+P1(f775(f775(f334(f856(x87801,x87801)),f498(x87804,x87803,x87802,x87801)),x87803)) % 186.05/186.62 [8827]P1(f775(x88271,x88272))+~P1(f775(x88271,f775(f775(f241(x88273,x88274),f831(x88274,x88273,x88271)),f832(x88274,x88273,x88271)))) % 186.05/186.62 [8840]E(f775(f181(f851(x88401)),x88402),f775(f181(f851(x88401)),x88403))+~P1(f775(f775(f334(f856(f851(x88401),f851(x88401))),f775(f775(f241(f851(x88401),f851(x88401)),x88402),x88403)),f135(x88401,x88404))) % 186.05/186.62 [8843]E(f775(f181(f851(x88431)),x88432),f775(f181(f851(x88431)),x88433))+~P1(f775(f775(f334(f856(f851(x88431),f851(x88431))),f775(f775(f241(f851(x88431),f851(x88431)),x88432),x88433)),f147(x88431,x88434))) % 186.05/186.62 [8844]E(f775(f181(f851(x88441)),x88442),f775(f181(f851(x88441)),x88443))+~P1(f775(f775(f334(f856(f851(x88441),f851(x88441))),f775(f775(f241(f851(x88441),f851(x88441)),x88442),x88443)),f146(x88441,x88444))) % 186.05/186.62 [8917]P1(f775(f775(f232(a850),f144(x89171,x89172,x89173)),f144(x89171,x89174,x89173)))+P1(f775(f775(f334(x89171),f758(x89174,x89172,x89173,x89171)),f775(f158(x89171),x89173))) % 186.05/186.62 [8918]E(f775(f181(f851(x89181)),x89182),f775(f181(f851(x89181)),x89183))+~P1(f775(f775(f334(f856(f851(x89181),f851(x89181))),f775(f775(f241(f851(x89181),f851(x89181)),x89182),x89183)),f300(f851(x89181),f146(x89181,x89184)))) % 186.05/186.62 [9030]P1(f775(f775(f279(a850),x90301),x90302))+P1(f775(f775(f232(f857(a850,a844)),f282(a850,f279(a850),x90301,x90302)),f282(a850,f279(a850),x90303,x90304))) % 186.05/186.62 [9138]~P29(x91381,x91382,x91383,x91384)+~P1(f775(f775(f233(a850),f775(f42(x91382),f775(f303(x91381,x91382,x91383),x91384))),f775(f42(x91381),x91384))) % 186.05/186.62 [9168]~P1(f775(f775(f334(f856(f851(x91681),f851(x91681))),f775(f775(f241(f851(x91681),f851(x91681)),x91682),x91683)),f146(x91681,x91684)))+P1(f775(f775(f334(f856(f851(x91681),f851(x91681))),f775(f775(f241(f851(x91681),f851(x91681)),x91682),x91683)),f147(x91681,f300(x91681,x91684)))) % 186.05/186.62 [9171]~P1(f775(f775(f334(f856(f851(x91711),f851(x91711))),f775(f775(f241(f851(x91711),f851(x91711)),x91712),x91713)),f147(x91711,x91714)))+P1(f775(f775(f334(f856(f851(x91711),f851(x91711))),f775(f775(f241(f851(x91711),f851(x91711)),x91712),x91713)),f300(f851(x91711),f146(x91711,x91714)))) % 186.05/186.62 [9186]P1(f775(f775(f334(f856(x91861,x91861)),f775(f775(f241(x91861,x91861),x91862),x91863)),f300(x91861,x91864)))+~P1(f775(f775(f334(f856(x91861,x91861)),f775(f775(f241(x91861,x91861),x91862),x91863)),f775(f775(f281(x91861,x91861,x91861),x91864),f300(x91861,x91864)))) % 186.05/186.62 [9255]P1(f775(f775(f279(a850),x92551),x92552))+~P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x92553,x92554)),f282(a850,f279(a850),x92551,x92552))) % 186.05/186.62 [9367]E(f775(f775(f125(x93671),f742(x93672,x93673,x93674,x93671)),f775(f775(f140(x93671),f743(x93672,x93673,x93674,x93671)),f745(x93672,x93673,x93674,x93671))),x93674)+~P1(f775(f775(f334(f856(f851(x93671),f851(x93671))),f775(f775(f241(f851(x93671),f851(x93671)),x93674),x93673)),f146(x93671,x93672))) % 186.05/186.62 [9368]E(f775(f775(f125(x93681),f742(x93682,x93683,x93684,x93681)),f775(f775(f140(x93681),f744(x93682,x93683,x93684,x93681)),f745(x93682,x93683,x93684,x93681))),x93683)+~P1(f775(f775(f334(f856(f851(x93681),f851(x93681))),f775(f775(f241(f851(x93681),f851(x93681)),x93684),x93683)),f146(x93681,x93682))) % 186.05/186.62 [9441]P1(f775(f775(f334(f856(x94411,x94411)),f775(f775(f241(x94411,x94411),x94412),f656(x94413,x94414,x94412,x94411))),f300(x94411,x94413)))+~P1(f775(f775(f334(f856(x94411,x94411)),f775(f775(f241(x94411,x94411),x94412),x94414)),f775(f775(f281(x94411,x94411,x94411),x94413),f300(x94411,x94413)))) % 186.05/186.62 [9506]P1(f775(f775(f232(a850),f144(x95061,x95062,x95063)),f144(x95061,x95064,x95063)))+~P1(f775(f775(f233(a850),f775(x95062,f758(x95064,x95062,x95063,x95061))),f775(x95064,f758(x95064,x95062,x95063,x95061)))) % 186.05/186.62 [9572]P1(f775(f775(f334(f856(x95721,x95721)),f775(f775(f241(x95721,x95721),f655(x95722,x95723,x95724,x95721)),x95723)),f300(x95721,x95722)))+~P1(f775(f775(f334(f856(x95721,x95721)),f775(f775(f241(x95721,x95721),x95724),x95723)),f775(f775(f281(x95721,x95721,x95721),x95722),f300(x95721,x95722)))) % 186.05/186.62 [5098]~E(x50982,x50983)+E(f151(x50981,x50982,f775(f775(f140(x50981),x50983),x50984)),x50984) % 186.05/186.62 [5218]P1(f775(x52182,x52183))+E(f162(x52181,x52182,f775(f775(f140(x52181),x52183),x52184)),f115(x52181)) % 186.05/186.62 [5284]~P84(x52842)+E(f775(f775(f81(f857(x52841,x52842)),x52843),x52844),f775(f81(x52842),f775(x52843,x52844))) % 186.05/186.62 [5296]~E(x52962,f2(a850))+E(f775(f775(f128(x52961),x52962),f775(f775(f140(x52961),x52963),x52964)),f775(f775(f140(x52961),x52963),x52964)) % 186.05/186.62 [5297]P1(f775(x52972,x52973))+E(f775(f126(x52971,x52972),f775(f775(f140(x52971),x52973),x52974)),f775(f126(x52971,x52972),x52974)) % 186.05/186.62 [5430]~E(x54302,x54304)+P1(f775(f775(f775(f302(x54301),x54302),x54303),x54304)) % 186.05/186.62 [5438]E(x54381,f115(x54382))+E(f134(x54383,f775(f775(f143(x54382,x54383),x54384),x54381)),f775(x54384,f134(x54382,x54381))) % 186.05/186.62 [5449]~E(x54491,f65(x54492,x54494))+E(f775(x54491,f775(f775(f302(x54492),x54493),f180(f857(x54492,a844)))),x54493) % 186.05/186.62 [5484]E(x54841,f115(x54842))+E(f775(f131(x54843),f775(f775(f143(x54842,x54843),x54844),x54841)),f775(x54844,f775(f131(x54842),x54841))) % 186.05/186.62 [5581]~P1(f775(x55813,x55814))+P1(f775(f775(f775(f302(x55811),x55812),x55813),x55814)) % 186.05/186.62 [5706]~P22(x57062,x57064,x57061)+E(f775(x57061,f775(f775(f302(x57062),x57063),f180(f857(x57062,a844)))),x57063) % 186.05/186.62 [5731]~E(x57312,x57313)+P1(f775(f775(f334(x57311),x57312),f775(f775(f302(x57311),x57313),x57314))) % 186.05/186.62 [5735]~P85(x57351)+E(f775(f775(f82(x57351),x57352),f775(f775(f82(x57351),x57353),x57354)),f775(f775(f82(x57351),x57353),f775(f775(f82(x57351),x57352),x57354))) % 186.05/186.62 [5736]~P85(x57361)+E(f775(f775(f83(x57361),x57362),f775(f775(f83(x57361),x57363),x57364)),f775(f775(f83(x57361),x57363),f775(f775(f83(x57361),x57362),x57364))) % 186.05/186.62 [5738]~P100(x57381)+E(f775(f775(f236(x57381),x57382),f775(f775(f236(x57381),x57383),x57384)),f775(f775(f236(x57381),x57383),f775(f775(f236(x57381),x57382),x57384))) % 186.05/186.62 [5740]~P100(x57401)+E(f775(f775(f179(x57401),x57402),f775(f775(f179(x57401),x57403),x57404)),f775(f775(f179(x57401),x57403),f775(f775(f179(x57401),x57402),x57404))) % 186.05/186.62 [5742]~P92(x57421)+E(f775(f775(f103(x57421),x57422),f775(f775(f103(x57421),x57423),x57424)),f775(f775(f103(x57421),x57423),f775(f775(f103(x57421),x57422),x57424))) % 186.05/186.62 [5743]~P93(x57431)+E(f775(f775(f103(x57431),x57432),f775(f775(f103(x57431),x57433),x57434)),f775(f775(f103(x57431),x57433),f775(f775(f103(x57431),x57432),x57434))) % 186.05/186.62 [5744]~P93(x57441)+E(f775(f775(f104(x57441),x57442),f775(f775(f104(x57441),x57443),x57444)),f775(f775(f104(x57441),x57443),f775(f775(f104(x57441),x57442),x57444))) % 186.05/186.62 [5746]~P98(x57461)+E(f775(f775(f104(x57461),x57462),f775(f775(f104(x57461),x57463),x57464)),f775(f775(f104(x57461),x57463),f775(f775(f104(x57461),x57462),x57464))) % 186.05/186.62 [5753]E(x57531,x57532)+E(f151(x57533,x57531,f775(f775(f140(x57533),x57532),x57534)),f775(f775(f140(x57533),x57532),f151(x57533,x57531,x57534))) % 186.05/186.62 [5768]~P1(f775(x57682,x57683))+E(f775(f126(x57681,x57682),f775(f775(f140(x57681),x57683),x57684)),f775(f775(f140(x57681),x57683),f775(f126(x57681,x57682),x57684))) % 186.05/186.62 [5899]~P1(f775(x58992,x58993))+E(f162(x58991,x58992,f775(f775(f140(x58991),x58993),x58994)),f775(f775(f140(x58991),x58993),f162(x58991,x58992,x58994))) % 186.05/186.62 [5951]P28(x59511,x59512,x59513)+~P28(x59511,x59512,f775(f775(f302(f849(x59511)),x59514),x59513)) % 186.05/186.62 [5964]E(x59641,f180(f857(x59642,a844)))+E(f775(f775(f46(x59642,f857(x59643,a844)),x59641),f775(f18(f857(x59643,a844),x59642),x59644)),x59644) % 186.05/186.62 [5965]E(x59651,f180(f857(x59652,a844)))+E(f775(f775(f47(x59652,f857(x59653,a844)),x59651),f775(f18(f857(x59653,a844),x59652),x59654)),x59654) % 186.05/186.62 [5974]~E(x59744,f180(f857(x59742,a844)))+E(f775(f775(f248(x59741,x59742),x59743),f775(f18(f857(x59742,a844),x59741),x59744)),f180(f857(f856(x59741,x59742),a844))) % 186.05/186.62 [5975]~E(x59753,f180(f857(x59751,a844)))+E(f775(f775(f248(x59751,x59752),x59753),f775(f18(f857(x59752,a844),x59751),x59754)),f180(f857(f856(x59751,x59752),a844))) % 186.05/186.62 [6026]E(x60261,f2(a850))+E(f775(f775(f128(x60262),x60261),f775(f775(f140(x60262),x60263),x60264)),f775(f775(f128(x60262),f775(f775(f3(a850),x60261),f80(a850))),x60264)) % 186.05/186.62 [6053]E(x60531,f180(f857(x60532,a844)))+E(f775(f303(x60532,x60533,f775(f18(x60533,x60532),x60534)),x60531),f775(f775(f302(x60533),x60534),f180(f857(x60533,a844)))) % 186.05/186.62 [6056]E(f775(f305(x60561,x60562,f775(f18(x60562,x60561),x60563)),x60564),f180(f857(x60561,a844)))+P1(f775(f775(f334(x60562),x60563),x60564)) % 186.05/186.62 [6123]~E(x61233,f180(f857(x61231,a844)))+E(f775(f775(f46(x61231,f857(x61232,a844)),x61233),f775(f18(f857(x61232,a844),x61231),x61234)),f180(f857(x61232,a844))) % 186.05/186.62 [6124]~E(x61243,f180(f857(x61241,a844)))+E(f775(f775(f47(x61241,f857(x61242,a844)),x61243),f775(f18(f857(x61242,a844),x61241),x61244)),f239(f857(x61242,a844))) % 186.05/186.62 [6126]~P7(x61261)+E(f52(x61261,f775(f775(f83(x61261),x61262),x61263),f775(f775(f83(x61261),x61262),x61264)),f775(f775(f83(x61261),x61262),f52(x61261,x61263,x61264))) % 186.05/186.62 [6300]E(f775(f305(x63001,x63002,f775(f18(x63002,x63001),x63003)),x63004),f239(f857(x63001,a844)))+~P1(f775(f775(f334(x63002),x63003),x63004)) % 186.05/186.62 [6323]~P1(f775(f775(f334(x63231),x63232),x63234))+P1(f775(f775(f334(x63231),x63232),f775(f775(f302(x63231),x63233),x63234))) % 186.05/186.62 [6336]~E(x63363,f775(f775(f3(a850),f775(f181(f851(x63361)),x63362)),f80(a850)))+E(f116(x63361,f775(f775(f148(x63361,x63362),x63363),x63364)),f116(x63361,x63362)) % 186.05/186.62 [6361]~P100(x63611)+E(f775(f775(f104(f857(x63611,a844)),f775(f293(x63611),x63612)),f295(x63611,x63613,x63614)),f295(x63611,x63613,f775(f775(f236(x63611),x63612),x63614))) % 186.05/186.62 [6362]~P100(x63621)+E(f775(f775(f104(f857(x63621,a844)),f775(f258(x63621),x63622)),f295(x63621,x63623,x63624)),f295(x63621,f775(f775(f179(x63621),x63622),x63623),x63624)) % 186.05/186.62 [6379]E(f775(f775(f104(f857(x63791,a844)),x63792),f775(f775(f302(x63791),x63793),x63794)),f775(f775(f104(f857(x63791,a844)),x63792),x63794))+P1(f775(f775(f334(x63791),x63793),x63792)) % 186.05/186.62 [6391]E(f151(x63911,x63912,f775(f775(f125(x63911),x63913),x63914)),f775(f775(f125(x63911),x63913),f151(x63911,x63912,x63914)))+P1(f775(f775(f334(x63911),x63912),f775(f158(x63911),x63913))) % 186.05/186.62 [6396]~P75(x63961)+E(f775(f775(f83(x63961),f775(f775(f242(x63961),x63962),x63963)),f775(f775(f242(x63961),x63962),x63964)),f775(f775(f242(x63961),x63962),f775(f775(f82(a850),x63963),x63964))) % 186.05/186.62 [6397]~P85(x63971)+E(f775(f775(f83(x63971),f775(f775(f242(x63971),x63972),x63973)),f775(f775(f242(x63971),x63972),x63974)),f775(f775(f242(x63971),x63972),f775(f775(f82(a850),x63973),x63974))) % 186.05/186.62 [6433]~P85(x64331)+E(f775(f775(f82(x64331),f775(f775(f83(x64331),x64332),x64333)),f775(f775(f83(x64331),x64332),x64334)),f775(f775(f83(x64331),x64332),f775(f775(f82(x64331),x64333),x64334))) % 186.05/186.62 [6434]~P100(x64341)+E(f775(f775(f179(x64341),f775(f775(f236(x64341),x64342),x64343)),f775(f775(f236(x64341),x64342),x64344)),f775(f775(f236(x64341),x64342),f775(f775(f179(x64341),x64343),x64344))) % 186.05/186.62 [6435]~P100(x64351)+E(f775(f775(f236(x64351),f775(f775(f179(x64351),x64352),x64353)),f775(f775(f179(x64351),x64352),x64354)),f775(f775(f179(x64351),x64352),f775(f775(f236(x64351),x64353),x64354))) % 186.05/186.62 [6436]~P97(x64361)+E(f775(f775(f104(x64361),f775(f775(f103(x64361),x64362),x64363)),f775(f775(f103(x64361),x64362),x64364)),f775(f775(f103(x64361),x64362),f775(f775(f104(x64361),x64363),x64364))) % 186.05/186.62 [6437]~P97(x64371)+E(f775(f775(f103(x64371),f775(f775(f104(x64371),x64372),x64373)),f775(f775(f104(x64371),x64372),x64374)),f775(f775(f104(x64371),x64372),f775(f775(f103(x64371),x64373),x64374))) % 186.05/186.62 [6474]~P7(x64741)+E(f52(x64741,f775(f775(f83(x64741),x64742),x64743),f775(f775(f83(x64741),x64744),x64743)),f775(f775(f83(x64741),f52(x64741,x64742,x64744)),x64743)) % 186.05/186.62 [6477]~E(f775(f181(f851(x64771)),x64773),f775(f181(f851(x64772)),x64774))+E(f775(f775(f143(f856(x64771,x64772),x64772),f250(x64771,x64772)),f775(f775(f167(x64771,x64772),x64773),x64774)),x64774) % 186.05/186.62 [6478]~E(f775(f181(f851(x64781)),x64783),f775(f181(f851(x64782)),x64784))+E(f775(f775(f143(f856(x64781,x64782),x64781),f240(x64781,x64782)),f775(f775(f167(x64781,x64782),x64783),x64784)),x64783) % 186.05/186.62 [6489]~P7(x64891)+E(f52(x64891,f775(f775(f83(x64891),x64892),f52(x64891,x64893,x64894)),x64894),f52(x64891,f775(f775(f83(x64891),x64892),x64893),x64894)) % 186.05/186.62 [6490]~P8(x64901)+E(f52(x64901,f775(f775(f3(x64901),x64902),f52(x64901,x64903,x64904)),x64904),f52(x64901,f775(f775(f3(x64901),x64902),x64903),x64904)) % 186.05/186.62 [6491]~P7(x64911)+E(f52(x64911,f775(f775(f82(x64911),x64912),f52(x64911,x64913,x64914)),x64914),f52(x64911,f775(f775(f82(x64911),x64912),x64913),x64914)) % 186.05/186.62 [6574]~P100(x65741)+E(f775(f775(f104(f857(x65741,a844)),f295(x65741,x65742,x65743)),f775(f293(x65741),x65744)),f295(x65741,x65742,f775(f775(f236(x65741),x65743),x65744))) % 186.05/186.62 [6575]~P100(x65751)+E(f775(f775(f104(f857(x65751,a844)),f295(x65751,x65752,x65753)),f775(f258(x65751),x65754)),f295(x65751,f775(f775(f179(x65751),x65752),x65754),x65753)) % 186.05/186.62 [6579]~E(f775(f181(f851(x65791)),x65793),f775(f181(f851(x65792)),x65794))+E(f775(f775(f167(x65791,x65792),f775(f142(x65791),x65793)),f775(f142(x65792),x65794)),f775(f142(f856(x65791,x65792)),f775(f775(f167(x65791,x65792),x65793),x65794))) % 186.05/186.62 [6588]E(x65881,f775(f775(f3(a850),f775(f181(f851(x65882)),x65883)),f80(a850)))+E(f116(x65882,f775(f775(f148(x65882,x65883),x65881),x65884)),f775(f775(f148(x65882,f116(x65882,x65883)),x65881),x65884)) % 186.05/186.62 [6605]~P1(f775(f127(x66052),x66054))+P1(f775(f127(f856(x66051,x66052)),f775(f775(f167(x66051,x66052),x66053),x66054))) % 186.05/186.62 [6606]~P1(f775(f127(x66061),x66063))+P1(f775(f127(f856(x66061,x66062)),f775(f775(f167(x66061,x66062),x66063),x66064))) % 186.05/186.62 [6704]E(x67041,f775(f775(f775(a189,x67042),x67043),f775(x67044,x67042)))+~P1(f775(f775(f187(f28(x67043,x67044)),x67042),x67041)) % 186.05/186.62 [6885]E(f775(f775(f43(a850),x68851),x68852),x68853)+~P1(f775(f55(x68851,x68852),f775(f775(f241(a850,a850),x68853),x68854))) % 186.05/186.62 [6911]E(f52(a850,x69111,x69112),x69113)+~P1(f775(f55(x69111,x69112),f775(f775(f241(a850,a850),x69114),x69113))) % 186.05/186.62 [6914]P1(f775(f127(x69141),x69142))+~P1(f775(f127(x69143),f775(f775(f143(x69141,x69143),x69144),x69142))) % 186.05/186.62 [6922]~P28(x69221,x69222,f775(f775(f302(f849(x69221)),x69223),x69224))+P28(x69221,x69222,f775(f775(f302(f849(x69221)),x69223),f180(f857(f849(x69221),a844)))) % 186.05/186.62 [6994]E(f151(x69941,x69942,f775(f775(f125(x69941),x69943),x69944)),f775(f775(f125(x69941),f151(x69941,x69942,x69943)),x69944))+~P1(f775(f775(f334(x69941),x69942),f775(f158(x69941),x69943))) % 186.05/186.62 [7090]~P8(x70901)+E(f52(x70901,f775(f775(f3(x70901),f52(x70901,x70902,x70903)),x70904),x70903),f52(x70901,f775(f775(f3(x70901),x70902),x70904),x70903)) % 186.05/186.62 [7091]~P7(x70911)+E(f52(x70911,f775(f775(f82(x70911),f52(x70911,x70912,x70913)),x70914),x70913),f52(x70911,f775(f775(f82(x70911),x70912),x70914),x70913)) % 186.05/186.62 [7092]~P7(x70921)+E(f52(x70921,f775(f775(f83(x70921),f52(x70921,x70922,x70923)),x70924),x70923),f52(x70921,f775(f775(f83(x70921),x70922),x70924),x70923)) % 186.05/186.62 [7298]~E(x72981,f775(f775(f140(x72982),x72983),x72984))+~P1(f775(f775(f232(a850),f775(f181(f851(x72982)),x72981)),f775(f181(f851(x72982)),x72984))) % 186.05/186.62 [7470]~E(f166(x74701,x74702,x74703),f166(x74701,x74702,x74704))+E(f775(f303(f856(x74701,x74702),x74701,f240(x74701,x74702)),f775(f158(f856(x74701,x74702)),x74703)),f775(f303(f856(x74701,x74702),x74701,f240(x74701,x74702)),f775(f158(f856(x74701,x74702)),x74704))) % 186.05/186.62 [7513]P29(x75131,x75132,x75133,f775(f158(x75131),x75134))+~P1(f775(f127(x75132),f775(f775(f143(x75131,x75132),x75133),x75134))) % 186.05/186.62 [7590]~P1(f775(f775(f232(f857(x75901,a844)),x75902),x75904))+P1(f775(f775(f232(f857(x75901,a844)),x75902),f775(f775(f302(x75901),x75903),x75904))) % 186.05/186.62 [7625]~P7(x76251)+E(f52(x76251,f775(f775(f82(x76251),f52(x76251,x76252,x76253)),f52(x76251,x76254,x76253)),x76253),f52(x76251,f775(f775(f82(x76251),x76252),x76254),x76253)) % 186.05/186.62 [7626]~P7(x76261)+E(f52(x76261,f775(f775(f83(x76261),f52(x76261,x76262,x76263)),f52(x76261,x76264,x76263)),x76263),f52(x76261,f775(f775(f83(x76261),x76262),x76264),x76263)) % 186.05/186.62 [7627]~P8(x76271)+E(f52(x76271,f775(f775(f3(x76271),f52(x76271,x76272,x76273)),f52(x76271,x76274,x76273)),x76273),f52(x76271,f775(f775(f3(x76271),x76272),x76274),x76273)) % 186.05/186.62 [7728]~E(f775(x77284,f652(x77284,x77283,x77281,x77282)),f239(f857(x77282,a844)))+E(f775(f775(f47(x77281,f857(x77282,a844)),x77283),x77284),f239(f857(x77282,a844))) % 186.05/186.62 [7729]~E(f775(x77294,f410(x77294,x77293,x77291,x77292)),f180(f857(x77292,a844)))+E(f775(f775(f46(x77291,f857(x77292,a844)),x77293),x77294),f180(f857(x77292,a844))) % 186.05/186.62 [7730]~E(f775(x77304,f411(x77304,x77303,x77302,x77301)),f180(f857(x77302,a844)))+E(f775(f775(f46(x77301,f857(x77302,a844)),x77303),x77304),f180(f857(x77302,a844))) % 186.05/186.62 [7731]~E(f775(x77314,f653(x77314,x77313,x77312,x77311)),f239(f857(x77312,a844)))+E(f775(f775(f47(x77311,f857(x77312,a844)),x77313),x77314),f239(f857(x77312,a844))) % 186.05/186.62 [8122]P1(f775(x81221,x81222))+~P1(f775(f775(f334(x81223),x81222),f775(f775(f104(f857(x81223,a844)),x81224),f775(f256(x81223),x81221)))) % 186.05/186.62 [8161]~P1(f775(f775(f232(f857(x81611,a844)),x81613),x81614))+P1(f775(f775(f232(f857(x81611,a844)),f775(f775(f302(x81611),x81612),x81613)),f775(f775(f302(x81611),x81612),x81614))) % 186.05/186.62 [8328]P1(f775(f775(f187(x83281),x83282),f435(x83283,x83282,x83284,x83281)))+~P1(f775(f775(f187(f36(x83281,x83284)),x83282),x83283)) % 186.05/186.62 [8329]P1(f775(f775(f187(x83291),x83292),f461(x83293,x83292,x83294,x83291)))+~P1(f775(f775(f187(f36(x83291,x83294)),x83292),x83293)) % 186.05/186.62 [8450]~P1(f775(f775(f233(a850),f775(x84504,x84502)),f775(x84504,x84503)))+P1(f775(f775(f334(f856(x84501,x84501)),f775(f775(f241(x84501,x84501),x84502),x84503)),f775(f775(f280(a850,x84501),a237),x84504))) % 186.05/186.62 [8597]P29(f851(x85971),f851(x85972),f775(f143(x85971,x85972),x85973),x85974)+~P29(x85971,x85972,x85973,f44(f857(x85971,a844),f775(f303(f851(x85971),f857(x85971,a844),f158(x85971)),x85974))) % 186.05/186.62 [8707]E(f775(f775(f47(x87071,f857(x87072,a844)),x87073),x87074),f239(f857(x87072,a844)))+P1(f775(f775(f334(x87071),f652(x87074,x87073,x87071,x87072)),x87073)) % 186.05/186.62 [8708]E(f775(f775(f46(x87081,f857(x87082,a844)),x87083),x87084),f180(f857(x87082,a844)))+P1(f775(f775(f334(x87081),f410(x87084,x87083,x87081,x87082)),x87083)) % 186.05/186.62 [8709]E(f775(f775(f46(x87091,f857(x87092,a844)),x87093),x87094),f180(f857(x87092,a844)))+P1(f775(f775(f334(x87091),f411(x87094,x87093,x87092,x87091)),x87093)) % 186.05/186.62 [8710]E(f775(f775(f47(x87101,f857(x87102,a844)),x87103),x87104),f239(f857(x87102,a844)))+P1(f775(f775(f334(x87101),f653(x87104,x87103,x87102,x87101)),x87103)) % 186.05/186.62 [8745]P1(f775(f775(f233(a850),f775(x87451,x87452)),f775(x87451,x87453)))+~P1(f775(f775(f334(f856(x87454,x87454)),f775(f775(f241(x87454,x87454),x87452),x87453)),f775(f775(f280(a850,x87454),a237),x87451))) % 186.05/186.62 [8794]P1(f775(f775(f187(x87941),f435(x87942,x87943,x87941,x87944)),x87942))+~P1(f775(f775(f187(f36(x87944,x87941)),x87943),x87942)) % 186.05/186.62 [8795]P1(f775(f775(f187(x87951),f461(x87952,x87953,x87951,x87954)),x87952))+~P1(f775(f775(f187(f36(x87954,x87951)),x87953),x87952)) % 186.05/186.62 [8906]P1(f775(f775(f334(x89061),f494(x89062,x89063,x89064,x89061)),x89063))+~P1(f775(f775(f334(f857(x89061,a844)),x89064),f775(f775(f61(x89061),x89063),x89062))) % 186.05/186.62 [8909]E(x89091,x89092)+~P1(f775(f775(f334(f856(x89093,x89093)),f775(f775(f241(x89093,x89093),x89091),x89092)),f775(f775(f173(f856(x89093,x89093),a844),f2(a850)),x89094))) % 186.05/186.62 [8981]E(f775(f277(x89811,x89811,x89812),f775(f775(f302(x89811),f494(x89812,x89813,x89814,x89811)),f180(f857(x89811,a844)))),x89814)+~P1(f775(f775(f334(f857(x89811,a844)),x89814),f775(f775(f61(x89811),x89813),x89812))) % 186.05/186.62 [8992]~P1(f775(f775(f334(f856(x89921,x89921)),f775(f775(f241(x89921,x89921),x89923),x89922)),f300(x89921,x89924)))+P1(f775(f775(f334(f856(x89921,x89921)),f775(f775(f241(x89921,x89921),x89922),x89923)),f300(x89921,f775(f278(x89921,x89921),x89924)))) % 186.05/186.62 [9005]~P7(x90051)+E(f775(f775(f82(x90051),f775(f775(f82(x90051),f775(f775(f83(x90051),x90052),f775(f775(f43(x90051),x90053),x90052))),f52(x90051,x90053,x90052))),x90054),f775(f775(f82(x90051),x90053),x90054)) % 186.05/186.62 [9012]~P1(f775(f775(f334(x90121),x90123),x90124))+P1(f775(f775(f334(f857(x90121,a844)),f775(f277(x90121,x90121,x90122),f775(f775(f302(x90121),x90123),f180(f857(x90121,a844))))),f775(f775(f61(x90121),x90124),x90122))) % 186.05/186.62 [9022]P1(f775(f775(f334(f856(x90221,x90221)),f775(f775(f241(x90221,x90221),x90222),x90223)),f300(x90221,x90224)))+~P1(f775(f775(f334(f856(x90221,x90221)),f775(f775(f241(x90221,x90221),x90223),x90222)),f300(x90221,f775(f278(x90221,x90221),x90224)))) % 186.05/186.62 [9105]E(f775(f775(f148(x91051,f775(f142(x91051),x91052)),f775(f775(f3(a850),f775(f775(f3(a850),f775(f181(f851(x91051)),x91052)),x91053)),f80(a850))),x91054),f775(f142(x91051),f775(f775(f148(x91051,x91052),x91053),x91054)))+~P1(f775(f775(f233(a850),x91053),f775(f181(f851(x91051)),x91052))) % 186.05/186.62 [9142]~P29(x91422,x91421,x91423,f239(f857(x91422,a844)))+P1(f775(f775(f232(f857(x91421,a844)),f775(f303(x91422,x91421,x91423),f775(f81(f857(x91422,a844)),x91424))),f775(f81(f857(x91421,a844)),f775(f303(x91422,x91421,x91423),x91424)))) % 186.05/186.62 [9150]~P9(x91501)+E(f775(f132(x91501,x91502,f775(f9(x91502,x91501,x91501),f775(f775(f10(x91501,f857(x91501,x91501),x91502),f103(x91501)),x91503)),f180(x91501)),x91504),f775(f775(f46(x91502,x91501),f775(f158(x91502),x91504)),x91503)) % 186.05/186.62 [9151]~P9(x91511)+E(f775(f132(x91511,x91512,f775(f9(x91512,x91511,x91511),f775(f775(f10(x91511,f857(x91511,x91511),x91512),f104(x91511)),x91513)),f239(x91511)),x91514),f775(f775(f47(x91512,x91511),f775(f158(x91512),x91514)),x91513)) % 186.05/186.62 [9217]~P1(f775(f775(f334(f856(f851(x92174),f851(x92174))),f775(f775(f241(f851(x92174),f851(x92174)),x92173),x92172)),f146(x92174,x92171)))+P1(f775(f775(f233(a850),f738(x92171,x92172,x92173,x92174)),f775(f181(f851(x92174)),x92173))) % 186.05/186.62 [9218]~P7(x92181)+E(f775(f775(f82(x92181),f775(f775(f82(x92181),f775(f775(f83(x92181),f775(f775(f43(x92181),x92182),x92183)),x92183)),f52(x92181,x92182,x92183))),x92184),f775(f775(f82(x92181),x92182),x92184)) % 186.05/186.62 [9247]~P1(f775(f775(f334(f856(f851(x92471),f851(x92471))),f775(f775(f241(f851(x92471),f851(x92471)),x92472),x92473)),f775(f278(f851(x92471),f851(x92471)),f146(x92471,x92474))))+P1(f775(f775(f334(f856(f851(x92471),f851(x92471))),f775(f775(f241(f851(x92471),f851(x92471)),x92472),x92473)),f146(x92471,f775(f278(x92471,x92471),x92474)))) % 186.05/186.62 [9248]P1(f775(f775(f334(f856(f851(x92481),f851(x92481))),f775(f775(f241(f851(x92481),f851(x92481)),x92482),x92483)),f775(f278(f851(x92481),f851(x92481)),f146(x92481,x92484))))+~P1(f775(f775(f334(f856(f851(x92481),f851(x92481))),f775(f775(f241(f851(x92481),f851(x92481)),x92482),x92483)),f146(x92481,f775(f278(x92481,x92481),x92484)))) % 186.05/186.62 [9285]~P1(f775(f775(f334(x92851),x92853),f775(f261(x92851,x92852),x92854)))+P1(f775(f775(f334(f856(x92851,x92852)),f775(f775(f241(x92851,x92852),x92853),f597(x92854,x92852,x92853,x92851))),x92854)) % 186.05/186.62 [9286]~P1(f775(f775(f334(x92861),x92863),f775(f261(x92861,x92862),x92864)))+P1(f775(f775(f334(f856(x92861,x92862)),f775(f775(f241(x92861,x92862),x92863),f598(x92864,x92862,x92863,x92861))),x92864)) % 186.05/186.62 [9412]~P1(f775(f63(f854(x94121)),f775(f303(x94122,f854(x94121),x94123),f239(f857(x94122,a844)))))+P1(f775(f63(f854(x94121)),f775(f303(x94122,f854(x94121),f170(x94122,x94121,x94123,f166(x94122,x94121,x94124))),f239(f857(x94122,a844))))) % 186.05/186.62 [9436]~P1(f775(f775(f334(f856(x94361,x94361)),f775(f775(f241(x94361,x94361),x94362),x94364)),f775(f775(f281(x94361,x94361,x94361),x94363),f300(x94361,x94363))))+P1(f775(f775(f334(f856(x94361,x94361)),f775(f775(f241(x94361,x94361),x94362),f655(x94363,x94364,x94362,x94361))),x94363)) % 186.05/186.62 [9594]~P1(f775(f775(f334(f856(x95942,x95941)),x95944),f775(f278(x95941,x95942),x95943)))+P1(f775(f775(f334(f856(x95941,x95942)),f775(f775(f241(x95941,x95942),f702(x95943,x95944,x95941,x95942)),f701(x95943,x95944,x95941,x95942))),x95943)) % 186.05/186.62 [9618]~P1(f775(f775(f334(f856(f851(x96181),f851(x96181))),f775(f775(f241(f851(x96181),f851(x96181)),x96184),x96183)),f146(x96181,x96182)))+P1(f775(f775(f334(f856(x96181,x96181)),f775(f775(f241(x96181,x96181),f743(x96182,x96183,x96184,x96181)),f744(x96182,x96183,x96184,x96181))),x96182)) % 186.05/186.62 [9694]~P1(f775(f775(f334(f856(f851(x96941),f851(x96941))),f775(f775(f241(f851(x96941),f851(x96941)),x96942),x96944)),f146(x96941,x96943)))+P1(f775(f775(f334(f856(x96941,x96941)),f775(f775(f241(x96941,x96941),f775(f775(f153(x96941),x96942),f738(x96943,x96944,x96942,x96941))),f739(x96943,x96944,x96942,x96941))),x96943)) % 186.05/186.62 [9715]~P1(f775(f63(x97152),x97154))+E(f775(f775(f775(f67(f857(x97151,a844),x97152,f103(f857(x97151,a844))),f775(f775(f9(x97152,f857(x97151,a844),f857(x97151,a844)),f775(f775(f10(x97151,f857(f857(x97151,a844),f857(x97151,a844)),x97152),f302(x97151)),x97153)),f180(f857(x97151,a844)))),f180(f857(x97151,a844))),x97154),f775(f303(x97152,x97151,x97153),x97154)) % 186.05/186.62 [9831]~P29(x98311,x98312,x98313,f239(f857(x98311,a844)))+P1(f775(f775(f232(f857(x98311,a844)),f775(f305(x98311,x98312,x98313),f775(f775(f302(x98312),x98314),f180(f857(x98312,a844))))),f775(f775(f302(x98311),f87(x98311,f775(f775(f9(x98311,x98312,a844),f775(f775(f10(x98312,f857(x98312,a844),x98311),a330),x98313)),x98314))),f180(f857(x98311,a844))))) % 186.05/186.62 [5493]~E(f775(f775(f125(x54931),x54932),x54934),x54933)+E(f775(f775(f159(x54931),f775(f181(f851(x54931)),x54932)),x54933),x54932) % 186.05/186.62 [5494]~E(f775(f775(f125(x54942),x54943),x54941),x54944)+E(x54941,f775(f775(f128(x54942),f775(f181(f851(x54942)),x54943)),x54944)) % 186.05/186.62 [5505]~E(x55054,f2(a850))+E(f775(f775(f153(x55051),f775(f775(f140(x55051),x55052),x55053)),x55054),x55052) % 186.05/186.62 [6037]~P85(x60371)+E(f775(f775(f242(x60371),f775(f775(f242(x60371),x60372),x60373)),x60374),f775(f775(f242(x60371),x60372),f775(f775(f83(a850),x60373),x60374))) % 186.05/186.62 [6038]~P75(x60381)+E(f775(f775(f242(x60381),f775(f775(f242(x60381),x60382),x60383)),x60384),f775(f775(f242(x60381),x60382),f775(f775(f83(a850),x60383),x60384))) % 186.05/186.62 [6054]E(x60541,f2(a850))+E(f775(f775(f153(x60542),f775(f775(f140(x60542),x60543),x60544)),x60541),f775(f775(f153(x60542),x60544),f775(f775(f3(a850),x60541),f80(a850)))) % 186.05/186.62 [6080]~P113(x60801)+E(f775(f775(f283(x60801),f775(f775(f83(x60801),x60802),x60803)),x60804),f775(f775(f83(x60801),x60802),f775(f775(f283(x60801),x60803),x60804))) % 186.05/186.62 [6081]~P5(x60811)+E(f775(f775(f82(x60811),f775(f775(f82(x60811),x60812),x60813)),x60814),f775(f775(f82(x60811),x60812),f775(f775(f82(x60811),x60813),x60814))) % 186.05/186.62 [6082]~P85(x60821)+E(f775(f775(f82(x60821),f775(f775(f82(x60821),x60822),x60823)),x60824),f775(f775(f82(x60821),x60822),f775(f775(f82(x60821),x60823),x60824))) % 186.05/186.62 [6083]~P85(x60831)+E(f775(f775(f83(x60831),f775(f775(f83(x60831),x60832),x60833)),x60834),f775(f775(f83(x60831),x60832),f775(f775(f83(x60831),x60833),x60834))) % 186.05/186.62 [6084]~P64(x60841)+E(f775(f775(f83(x60841),f775(f775(f83(x60841),x60842),x60843)),x60844),f775(f775(f83(x60841),x60842),f775(f775(f83(x60841),x60843),x60844))) % 186.05/186.62 [6087]~P100(x60871)+E(f775(f775(f236(x60871),f775(f775(f236(x60871),x60872),x60873)),x60874),f775(f775(f236(x60871),x60872),f775(f775(f236(x60871),x60873),x60874))) % 186.05/186.62 [6089]~P100(x60891)+E(f775(f775(f179(x60891),f775(f775(f179(x60891),x60892),x60893)),x60894),f775(f775(f179(x60891),x60892),f775(f775(f179(x60891),x60893),x60894))) % 186.05/186.62 [6091]~P92(x60911)+E(f775(f775(f103(x60911),f775(f775(f103(x60911),x60912),x60913)),x60914),f775(f775(f103(x60911),x60912),f775(f775(f103(x60911),x60913),x60914))) % 186.05/186.62 [6092]~P93(x60921)+E(f775(f775(f103(x60921),f775(f775(f103(x60921),x60922),x60923)),x60924),f775(f775(f103(x60921),x60922),f775(f775(f103(x60921),x60923),x60924))) % 186.05/186.62 [6093]~P93(x60931)+E(f775(f775(f104(x60931),f775(f775(f104(x60931),x60932),x60933)),x60934),f775(f775(f104(x60931),x60932),f775(f775(f104(x60931),x60933),x60934))) % 186.05/186.62 [6095]~P98(x60951)+E(f775(f775(f104(x60951),f775(f775(f104(x60951),x60952),x60953)),x60954),f775(f775(f104(x60951),x60952),f775(f775(f104(x60951),x60953),x60954))) % 186.05/186.62 [6106]~P7(x61061)+E(f52(x61061,f775(f775(f82(x61061),x61062),f775(f775(f83(x61061),x61063),x61064)),x61064),f52(x61061,x61062,x61064)) % 186.05/186.62 [6107]~P7(x61071)+E(f52(x61071,f775(f775(f82(x61071),x61072),f775(f775(f83(x61071),x61073),x61074)),x61073),f52(x61071,x61072,x61073)) % 186.05/186.62 [6245]E(f775(f775(f153(x62451),f775(f775(f159(x62451),x62452),x62453)),x62454),f775(f775(f153(x62451),x62453),x62454))+~P1(f775(f775(f233(a850),x62454),x62452)) % 186.05/186.62 [6431]~P85(x64311)+E(f775(f775(f82(x64311),f775(f775(f82(x64311),x64312),x64313)),x64314),f775(f775(f82(x64311),f775(f775(f82(x64311),x64312),x64314)),x64313)) % 186.05/186.62 [6432]~P85(x64321)+E(f775(f775(f83(x64321),f775(f775(f83(x64321),x64322),x64323)),x64324),f775(f775(f83(x64321),f775(f775(f83(x64321),x64322),x64324)),x64323)) % 186.05/186.62 [6494]~P2(x64942)+E(f775(f775(f8(x64941,x64942),f775(f18(x64942,x64941),x64943)),x64944),f775(f775(f83(x64942),f775(f102(x64942),f775(f42(x64941),x64944))),x64943)) % 186.05/186.62 [6673]E(f775(f775(f104(f857(x66731,a844)),f775(f775(f302(x66731),x66732),x66733)),x66734),f775(f775(f104(f857(x66731,a844)),x66733),x66734))+P1(f775(f775(f334(x66731),x66732),x66734)) % 186.05/186.62 [6748]~P74(x67481)+E(f775(f775(f236(x67481),f775(f775(f82(x67481),x67482),x67483)),f775(f775(f82(x67481),x67484),x67483)),f775(f775(f82(x67481),f775(f775(f236(x67481),x67482),x67484)),x67483)) % 186.05/186.62 [6749]~P74(x67491)+E(f775(f775(f179(x67491),f775(f775(f82(x67491),x67492),x67493)),f775(f775(f82(x67491),x67494),x67493)),f775(f775(f82(x67491),f775(f775(f179(x67491),x67492),x67494)),x67493)) % 186.05/186.62 [6751]~P109(x67511)+E(f775(f775(f82(x67511),f775(f775(f83(x67511),x67512),x67513)),f775(f775(f83(x67511),x67514),x67513)),f775(f775(f83(x67511),f775(f775(f82(x67511),x67512),x67514)),x67513)) % 186.05/186.62 [6752]~P77(x67521)+E(f775(f775(f236(x67521),f775(f775(f3(x67521),x67522),x67523)),f775(f775(f3(x67521),x67524),x67523)),f775(f775(f3(x67521),f775(f775(f236(x67521),x67522),x67524)),x67523)) % 186.05/186.62 [6753]~P77(x67531)+E(f775(f775(f179(x67531),f775(f775(f3(x67531),x67532),x67533)),f775(f775(f3(x67531),x67534),x67533)),f775(f775(f3(x67531),f775(f775(f179(x67531),x67532),x67534)),x67533)) % 186.05/186.62 [6754]~P85(x67541)+E(f775(f775(f83(x67541),f775(f775(f242(x67541),x67542),x67543)),f775(f775(f242(x67541),x67544),x67543)),f775(f775(f242(x67541),f775(f775(f83(x67541),x67542),x67544)),x67543)) % 186.05/186.62 [6755]~P70(x67551)+E(f775(f775(f83(x67551),f775(f775(f242(x67551),x67552),x67553)),f775(f775(f242(x67551),x67554),x67553)),f775(f775(f242(x67551),f775(f775(f83(x67551),x67552),x67554)),x67553)) % 186.05/186.62 [6756]~P60(x67561)+E(f775(f775(f283(x67561),f775(f775(f242(x67561),x67562),x67563)),f775(f775(f242(x67561),x67564),x67563)),f775(f775(f242(x67561),f775(f775(f283(x67561),x67562),x67564)),x67563)) % 186.05/186.62 [6757]~P113(x67571)+E(f775(f775(f82(x67571),f775(f775(f283(x67571),x67572),x67573)),f775(f775(f283(x67571),x67574),x67573)),f775(f775(f283(x67571),f775(f775(f82(x67571),x67572),x67574)),x67573)) % 186.05/186.62 [6758]~P113(x67581)+E(f775(f775(f3(x67581),f775(f775(f283(x67581),x67582),x67583)),f775(f775(f283(x67581),x67584),x67583)),f775(f775(f283(x67581),f775(f775(f3(x67581),x67582),x67584)),x67583)) % 186.05/186.62 [6759]~P100(x67591)+E(f775(f775(f179(x67591),f775(f775(f236(x67591),x67592),x67593)),f775(f775(f236(x67591),x67594),x67593)),f775(f775(f236(x67591),f775(f775(f179(x67591),x67592),x67594)),x67593)) % 186.05/186.62 [6760]~P100(x67601)+E(f775(f775(f236(x67601),f775(f775(f179(x67601),x67602),x67603)),f775(f775(f179(x67601),x67604),x67603)),f775(f775(f179(x67601),f775(f775(f236(x67601),x67602),x67604)),x67603)) % 186.05/186.62 [6761]~P97(x67611)+E(f775(f775(f104(x67611),f775(f775(f103(x67611),x67612),x67613)),f775(f775(f103(x67611),x67614),x67613)),f775(f775(f103(x67611),f775(f775(f104(x67611),x67612),x67614)),x67613)) % 186.05/186.62 [6762]~P97(x67621)+E(f775(f775(f103(x67621),f775(f775(f104(x67621),x67622),x67623)),f775(f775(f104(x67621),x67624),x67623)),f775(f775(f104(x67621),f775(f775(f103(x67621),x67622),x67624)),x67623)) % 186.05/186.62 [6763]~P85(x67631)+E(f775(f775(f82(x67631),f775(f775(f83(x67631),x67632),x67633)),f775(f775(f83(x67631),x67634),x67633)),f775(f775(f83(x67631),f775(f775(f82(x67631),x67632),x67634)),x67633)) % 186.05/186.62 [6798]E(f775(f775(f148(x67981,x67982),x67983),x67984),x67982)+~P1(f775(f775(f232(a850),f775(f181(f851(x67981)),x67982)),x67983)) % 186.05/186.62 [6825]~P1(f775(x68253,x68254))+P1(f775(f775(f775(f103(f857(x68251,a844)),x68252),x68253),x68254)) % 186.05/186.62 [6827]~P1(f775(x68272,x68274))+P1(f775(f775(f775(f103(f857(x68271,a844)),x68272),x68273),x68274)) % 186.05/186.62 [6849]E(f775(f775(f153(x68491),f775(f775(f125(x68491),x68492),x68493)),x68494),f775(f775(f153(x68491),x68492),x68494))+~P1(f775(f775(f233(a850),x68494),f775(f181(f851(x68491)),x68492))) % 186.05/186.62 [6859]E(f775(f775(f3(f857(x68591,a844)),f775(f775(f302(x68591),x68592),x68593)),x68594),f775(f775(f3(f857(x68591,a844)),x68593),x68594))+~P1(f775(f775(f334(x68591),x68592),x68594)) % 186.05/186.62 [6900]~E(f130(a850,f775(f294(a850,x69001),x69002)),f775(f775(f140(a850),x69004),x69003))+E(f130(a850,f775(f294(a850,f775(f775(f82(a850),x69001),f80(a850))),x69002)),x69003) % 186.05/186.62 [6969]E(x69691,f2(a850))+E(f775(f775(f140(x69692),x69693),f775(f775(f159(x69692),f775(f775(f3(a850),x69691),f80(a850))),x69694)),f775(f775(f159(x69692),x69691),f775(f775(f140(x69692),x69693),x69694))) % 186.05/186.62 [7073]E(f775(f775(f153(x70731),x70732),f775(f775(f3(a850),x70733),f775(f181(f851(x70731)),x70734))),f775(f775(f153(x70731),f775(f775(f125(x70731),x70734),x70732)),x70733))+P1(f775(f775(f233(a850),x70733),f775(f181(f851(x70731)),x70734))) % 186.05/186.62 [7101]E(f775(f775(f104(f857(x71011,a844)),x71012),f775(f775(f302(x71011),x71013),x71014)),f775(f775(f302(x71011),x71013),f775(f775(f104(f857(x71011,a844)),x71012),x71014)))+~P1(f775(f775(f334(x71011),x71013),x71012)) % 186.05/186.62 [7135]E(f775(f775(f153(x71351),f775(f775(f148(x71351,x71352),x71353),x71354)),x71353),x71354)+~P1(f775(f775(f233(a850),x71353),f775(f181(f851(x71351)),x71352))) % 186.05/186.62 [7156]E(x71561,f180(f857(x71562,a844)))+E(f775(f303(f856(x71563,x71562),x71563,f240(x71563,x71562)),f775(f775(f248(x71563,x71562),x71564),f775(f18(f857(x71562,a844),x71563),x71561))),x71564) % 186.05/186.62 [7157]E(x71571,f180(f857(x71572,a844)))+E(f775(f303(f856(x71572,x71573),x71573,f250(x71572,x71573)),f775(f775(f248(x71572,x71573),x71571),f775(f18(f857(x71573,a844),x71572),x71574))),x71574) % 186.05/186.62 [7241]E(f775(f775(f3(f857(x72411,a844)),f775(f775(f302(x72411),x72412),x72413)),x72414),f775(f775(f302(x72411),x72412),f775(f775(f3(f857(x72411,a844)),x72413),x72414)))+P1(f775(f775(f334(x72411),x72412),x72414)) % 186.05/186.62 [7282]~E(x72824,f180(f857(x72822,a844)))+E(f775(f303(f856(x72821,x72822),x72821,f240(x72821,x72822)),f775(f775(f248(x72821,x72822),x72823),f775(f18(f857(x72822,a844),x72821),x72824))),f180(f857(x72821,a844))) % 186.05/186.62 [7283]~E(x72833,f180(f857(x72831,a844)))+E(f775(f303(f856(x72831,x72832),x72832,f250(x72831,x72832)),f775(f775(f248(x72831,x72832),x72833),f775(f18(f857(x72832,a844),x72831),x72834))),f180(f857(x72832,a844))) % 186.05/186.62 [7342]~P1(f775(f775(f334(x73421),x73422),x73424))+P1(f775(f775(f334(x73421),x73422),f775(f775(f103(f857(x73421,a844)),x73423),x73424))) % 186.05/186.62 [7345]~P1(f775(f775(f334(x73451),x73452),x73453))+P1(f775(f775(f334(x73451),x73452),f775(f775(f103(f857(x73451,a844)),x73453),x73454))) % 186.05/186.62 [7367]E(f775(f775(f104(f857(x73671,a844)),f775(f775(f302(x73671),x73672),x73673)),x73674),f775(f775(f302(x73671),x73672),f775(f775(f104(f857(x73671,a844)),x73673),x73674)))+~P1(f775(f775(f334(x73671),x73672),x73674)) % 186.05/186.62 [7646]P1(f775(x76461,x76462))+~P1(f775(f775(f775(f104(f857(x76463,a844)),x76464),x76461),x76462)) % 186.05/186.62 [7647]P1(f775(x76471,x76472))+~P1(f775(f775(f775(f104(f857(x76473,a844)),x76471),x76474),x76472)) % 186.05/186.62 [7650]E(f775(f775(f8(x76501,a850),x76502),f775(f775(f3(f857(x76501,a844)),x76503),f775(f775(f302(x76501),x76504),f180(f857(x76501,a844))))),f775(f775(f8(x76501,a850),x76502),x76503))+P1(f775(f775(f334(x76501),x76504),x76503)) % 186.05/186.62 [7656]~P66(x76561)+E(f775(f155(x76561),f775(f775(f143(a850,x76561),x76562),f130(a850,f775(f294(a850,x76563),x76564)))),f775(f775(f8(a850,x76561),x76562),f775(f158(a850),f130(a850,f775(f294(a850,x76563),x76564))))) % 186.05/186.62 [7657]~P66(x76571)+E(f775(f775(f8(a850,x76571),x76572),f775(f158(a850),f130(a850,f775(f294(a850,x76573),x76574)))),f775(f155(x76571),f775(f775(f143(a850,x76571),x76572),f130(a850,f775(f294(a850,x76573),x76574))))) % 186.05/186.62 [7771]~E(x77713,x77714)+P1(f775(f64(x77711,x77712,f775(f775(f302(x77711),x77713),f180(f857(x77711,a844)))),x77714)) % 186.05/186.62 [7867]P1(f775(f775(f334(x78671),x78672),f775(f158(x78671),x78673)))+~P1(f775(f775(f334(x78671),x78672),f775(f158(x78671),f775(f775(f159(x78671),x78674),x78673)))) % 186.05/186.62 [7868]P1(f775(f775(f334(x78681),x78682),f775(f158(x78681),x78683)))+~P1(f775(f775(f334(x78681),x78682),f775(f158(x78681),f775(f775(f128(x78681),x78684),x78683)))) % 186.05/186.62 [7942]P1(f775(f775(f334(x79421),x79422),x79423))+~P1(f775(f775(f334(x79421),x79422),f775(f775(f3(f857(x79421,a844)),x79423),x79424))) % 186.05/186.62 [7944]P1(f775(f775(f334(x79441),x79442),x79443))+~P1(f775(f775(f334(x79441),x79442),f775(f775(f104(f857(x79441,a844)),x79444),x79443))) % 186.05/186.62 [7947]P1(f775(f775(f334(x79471),x79472),x79473))+~P1(f775(f775(f334(x79471),x79472),f775(f775(f104(f857(x79471,a844)),x79473),x79474))) % 186.05/186.62 [7964]E(f775(f775(f125(x79641),f775(f775(f159(x79641),x79642),x79643)),f775(f775(f140(x79641),x79644),f775(f775(f128(x79641),f775(a114,x79642)),x79643))),f775(f775(f148(x79641,x79643),x79642),x79644))+~P1(f775(f775(f233(a850),x79642),f775(f181(f851(x79641)),x79643))) % 186.05/186.62 [7987]P1(f775(f775(f334(x79871),x79872),x79873))+~P1(f775(f775(f232(f857(x79871,a844)),f775(f775(f302(x79871),x79872),x79874)),x79873)) % 186.05/186.62 [8017]~P1(f775(f775(f334(x80171),x80172),x80173))+~P1(f775(f775(f334(x80171),x80172),f775(f775(f3(f857(x80171,a844)),x80174),x80173))) % 186.05/186.62 [8050]~P1(f775(f775(f233(a850),x80504),f775(f181(f851(x80501)),x80503)))+P1(f775(f775(f334(x80501),x80502),f775(f158(x80501),f775(f775(f148(x80501,x80503),x80504),x80502)))) % 186.05/186.62 [8100]E(f775(f775(f153(x81001),f775(f775(f128(x81001),x81002),x81003)),x81004),f775(f775(f153(x81001),x81003),f775(f775(f82(a850),x81002),x81004)))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x81002),x81004)),f775(f181(f851(x81001)),x81003))) % 186.05/186.62 [8109]~P2(x81092)+E(f775(f775(f8(x81091,x81092),f775(f775(f10(a850,x81092,x81091),f102(x81092)),x81093)),x81094),f775(f102(x81092),f775(f775(f8(x81091,a850),x81093),x81094))) % 186.05/186.62 [8110]~P133(x81102)+E(f775(f775(f8(x81101,x81102),f775(f775(f10(a1,x81102,x81101),f105(x81102)),x81103)),x81104),f775(f105(x81102),f775(f775(f8(x81101,a1),x81103),x81104))) % 186.05/186.62 [8163]~P63(x81632)+E(f775(f775(f11(x81631,x81632),f775(f775(f10(x81632,x81632,x81631),f77(x81632)),x81633)),x81634),f775(f77(x81632),f775(f775(f11(x81631,x81632),x81633),x81634))) % 186.05/186.62 [8164]~P6(x81642)+E(f775(f775(f8(x81641,x81642),f775(f775(f10(x81642,x81642,x81641),f81(x81642)),x81643)),x81644),f775(f81(x81642),f775(f775(f8(x81641,x81642),x81643),x81644))) % 186.05/186.62 [8166]E(f775(f775(f8(x81661,a850),x81662),f775(f775(f3(f857(x81661,a844)),x81663),f775(f775(f302(x81661),x81664),f180(f857(x81661,a844))))),f775(f775(f3(a850),f775(f775(f8(x81661,a850),x81662),x81663)),f775(x81662,x81664)))+~P1(f775(f775(f334(x81661),x81664),x81663)) % 186.05/186.62 [8185]P1(f775(f775(f232(f857(x81851,a844)),x81852),x81853))+~P1(f775(f775(f232(f857(x81851,a844)),f775(f775(f302(x81851),x81854),x81852)),x81853)) % 186.05/186.62 [8393]P36(x83931,x83932)+~P36(x83931,f775(f775(f302(f856(x83931,x83931)),f775(f775(f241(x83931,x83931),x83933),x83934)),x83932)) % 186.05/186.62 [8394]P56(x83941,x83942)+~P56(x83941,f775(f775(f302(f856(x83941,x83941)),f775(f775(f241(x83941,x83941),x83943),x83944)),x83942)) % 186.05/186.62 [8402]~P100(x84021)+E(f775(f775(f138(x84021,x84021,f7(x84021)),x84022),f775(f775(f138(x84021,x84021,f7(x84021)),x84023),x84024)),f775(f775(f138(x84021,x84021,f7(x84021)),x84023),f775(f775(f138(x84021,x84021,f7(x84021)),x84022),x84024))) % 186.05/186.62 [8412]E(x84121,x84122)+~P1(f775(f64(x84123,x84124,f775(f775(f302(x84123),x84121),f180(f857(x84123,a844)))),x84122)) % 186.05/186.62 [8417]E(f775(f166(x84171,x84172,x84173),x84174),f183(x84172))+P1(f775(f775(f334(x84171),x84174),f775(f303(f856(x84171,x84172),x84171,f240(x84171,x84172)),f775(f158(f856(x84171,x84172)),x84173)))) % 186.05/186.62 [8423]E(f775(f775(f125(x84231),f775(f775(f159(x84231),x84232),x84233)),f775(f775(f159(x84231),x84234),f775(f775(f128(x84231),x84232),x84233))),f775(f775(f159(x84231),f775(f775(f82(a850),x84232),x84234)),x84233))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x84232),x84234)),f775(f181(f851(x84231)),x84233))) % 186.05/186.62 [8467]P1(f775(f63(x84671),x84672))+~E(x84672,f775(f303(a850,x84671,x84673),f775(f256(a850),f775(f775(f9(a850,a850,a844),f233(a850)),x84674)))) % 186.05/186.62 [8487]~P83(x84871)+E(f775(f132(x84871,x84871,f82(x84871),f775(f775(f82(x84871),x84872),x84873)),x84874),f775(f775(f82(x84871),x84872),f775(f132(x84871,x84871,f82(x84871),x84873),x84874))) % 186.05/186.62 [8519]P1(f775(f775(f232(f857(x85191,a844)),f775(f261(x85191,x85192),x85193)),f775(f261(x85191,x85192),x85194)))+~P1(f775(f775(f232(f857(f856(x85191,x85192),a844)),x85193),x85194)) % 186.05/186.62 [8530]~P1(f775(f775(f232(a850),x85302),x85304))+P1(f775(f775(f232(f857(x85301,a844)),f775(f158(x85301),f775(f775(f159(x85301),x85302),x85303))),f775(f158(x85301),f775(f775(f159(x85301),x85304),x85303)))) % 186.05/186.62 [8531]~P1(f775(f775(f232(a850),x85314),x85312))+P1(f775(f775(f232(f857(x85311,a844)),f775(f158(x85311),f775(f775(f128(x85311),x85312),x85313))),f775(f158(x85311),f775(f775(f128(x85311),x85314),x85313)))) % 186.05/186.62 [8574]~P1(f775(f63(x85741),f775(f775(f3(f857(x85741,a844)),x85742),x85744)))+P1(f775(f63(x85741),f775(f775(f3(f857(x85741,a844)),x85742),f775(f775(f302(x85741),x85743),x85744)))) % 186.05/186.62 [8608]P1(f775(f775(f334(f856(x86081,x86081)),x86082),f300(x86081,x86083)))+~P1(f775(f775(f334(f856(x86081,x86081)),x86082),f775(f775(f173(f856(x86081,x86081),a844),x86084),x86083))) % 186.05/186.62 [8683]~P1(f775(f63(x86831),f775(f775(f3(f857(x86831,a844)),x86832),f775(f775(f302(x86831),x86834),x86833))))+P1(f775(f63(x86831),f775(f775(f3(f857(x86831,a844)),x86832),x86833))) % 186.05/186.62 [8826]~E(f775(f166(x88261,x88262,x88263),x88264),f183(x88262))+~P1(f775(f775(f334(x88261),x88264),f775(f303(f856(x88261,x88262),x88261,f240(x88261,x88262)),f775(f158(f856(x88261,x88262)),x88263)))) % 186.05/186.62 [8863]~P100(x88631)+P1(f775(f775(f232(x88631),f775(f775(f179(x88631),x88632),f775(f775(f236(x88631),x88633),x88634))),f775(f775(f236(x88631),f775(f775(f179(x88631),x88632),x88633)),f775(f775(f179(x88631),x88632),x88634)))) % 186.05/186.62 [8864]~P93(x88641)+P1(f775(f775(f232(x88641),f775(f775(f103(x88641),x88642),f775(f775(f104(x88641),x88643),x88644))),f775(f775(f104(x88641),f775(f775(f103(x88641),x88642),x88643)),f775(f775(f103(x88641),x88642),x88644)))) % 186.05/186.62 [9008]E(x90081,x90082)+~P1(f775(f775(f334(f856(x90083,x90083)),f775(f775(f241(x90083,x90083),x90081),x90082)),f775(f158(f856(x90083,x90083)),f775(f775(f167(x90083,x90083),x90084),x90084)))) % 186.05/186.62 [9038]~P1(f775(f775(f334(f856(x90381,x90381)),f775(f775(f241(x90381,x90381),x90383),x90382)),f300(x90381,x90384)))+~P36(x90381,f775(f775(f302(f856(x90381,x90381)),f775(f775(f241(x90381,x90381),x90382),x90383)),x90384)) % 186.05/186.62 [9039]~P1(f775(f775(f334(f856(x90391,x90391)),f775(f775(f241(x90391,x90391),x90393),x90392)),f300(x90391,x90394)))+~P56(x90391,f775(f775(f302(f856(x90391,x90391)),f775(f775(f241(x90391,x90391),x90392),x90393)),x90394)) % 186.05/186.62 [9083]~P100(x90831)+P1(f775(f775(f232(x90831),f775(f775(f179(x90831),f775(f775(f236(x90831),x90832),x90833)),f775(f775(f236(x90831),x90832),x90834))),f775(f775(f236(x90831),x90832),f775(f775(f179(x90831),x90833),x90834)))) % 186.05/186.62 [9084]~P93(x90841)+P1(f775(f775(f232(x90841),f775(f775(f103(x90841),f775(f775(f104(x90841),x90842),x90843)),f775(f775(f104(x90841),x90842),x90844))),f775(f775(f104(x90841),x90842),f775(f775(f103(x90841),x90843),x90844)))) % 186.05/186.62 [9147]~E(f775(f303(x91472,x91471,x91473),f239(f857(x91472,a844))),f239(f857(x91471,a844)))+P1(f775(f775(f232(f857(x91471,a844)),f775(f81(f857(x91471,a844)),f775(f303(x91472,x91471,x91473),x91474))),f775(f303(x91472,x91471,x91473),f775(f81(f857(x91472,a844)),x91474)))) % 186.05/186.62 [9450]P1(f775(f775(f334(f856(x94501,x94501)),f775(f775(f241(x94501,x94501),x94502),x94503)),f775(f278(x94501,x94501),f775(f775(f281(x94501,x94501,x94501),x94504),f300(x94501,x94504)))))+~P1(f775(f775(f334(f856(x94501,x94501)),f775(f775(f241(x94501,x94501),x94502),x94503)),f775(f775(f281(x94501,x94501,x94501),f775(f278(x94501,x94501),x94504)),f300(x94501,f775(f278(x94501,x94501),x94504))))) % 186.05/186.62 [9451]~P1(f775(f775(f334(f856(x94511,x94511)),f775(f775(f241(x94511,x94511),x94512),x94513)),f775(f278(x94511,x94511),f775(f775(f281(x94511,x94511,x94511),x94514),f300(x94511,x94514)))))+P1(f775(f775(f334(f856(x94511,x94511)),f775(f775(f241(x94511,x94511),x94512),x94513)),f775(f775(f281(x94511,x94511,x94511),f775(f278(x94511,x94511),x94514)),f300(x94511,f775(f278(x94511,x94511),x94514))))) % 186.05/186.62 [9476]~P1(f775(f775(f334(x94762),x94764),f775(f259(x94761,x94762),x94763)))+P1(f775(f775(f334(f856(x94761,x94762)),f775(f775(f241(x94761,x94762),f594(x94763,x94761,x94764,x94762)),x94764)),x94763)) % 186.05/186.62 [9477]~P1(f775(f775(f334(x94772),x94774),f775(f259(x94771,x94772),x94773)))+P1(f775(f775(f334(f856(x94771,x94772)),f775(f775(f241(x94771,x94772),f595(x94773,x94771,x94774,x94772)),x94774)),x94773)) % 186.05/186.62 [9496]~P1(f775(f775(f334(x94961),x94964),f775(f775(f103(f857(x94961,a844)),x94962),x94963)))+P1(f775(f775(f775(f103(f857(x94961,a844)),f775(f775(f9(x94961,f857(x94961,a844),a844),f334(x94961)),x94962)),f775(f775(f9(x94961,f857(x94961,a844),a844),f334(x94961)),x94963)),x94964)) % 186.05/186.62 [9497]~P1(f775(f775(f334(x94971),x94974),f775(f775(f104(f857(x94971,a844)),x94972),x94973)))+P1(f775(f775(f775(f104(f857(x94971,a844)),f775(f775(f9(x94971,f857(x94971,a844),a844),f334(x94971)),x94972)),f775(f775(f9(x94971,f857(x94971,a844),a844),f334(x94971)),x94973)),x94974)) % 186.05/186.62 [9570]~P1(f775(f775(f334(f856(x95701,x95701)),f775(f775(f241(x95701,x95701),x95704),x95703)),f775(f775(f281(x95701,x95701,x95701),x95702),f300(x95701,x95702))))+P1(f775(f775(f334(f856(x95701,x95701)),f775(f775(f241(x95701,x95701),f656(x95702,x95703,x95704,x95701)),x95703)),x95702)) % 186.05/186.62 [9605]P1(f775(f775(f334(x96051),x96052),f775(f775(f103(f857(x96051,a844)),x96053),x96054)))+~P1(f775(f775(f775(f103(f857(x96051,a844)),f775(f775(f9(x96051,f857(x96051,a844),a844),f334(x96051)),x96053)),f775(f775(f9(x96051,f857(x96051,a844),a844),f334(x96051)),x96054)),x96052)) % 186.05/186.62 [9606]P1(f775(f775(f334(x96061),x96062),f775(f775(f104(f857(x96061,a844)),x96063),x96064)))+~P1(f775(f775(f775(f104(f857(x96061,a844)),f775(f775(f9(x96061,f857(x96061,a844),a844),f334(x96061)),x96063)),f775(f775(f9(x96061,f857(x96061,a844),a844),f334(x96061)),x96064)),x96062)) % 186.05/186.62 [9884]P34(x98841,f775(f775(f9(x98841,f857(f856(x98841,x98841),a844),f857(x98841,a844)),f775(f775(f10(f857(x98841,f857(f857(f856(x98841,x98841),a844),a844)),f857(f857(f856(x98841,x98841),a844),f857(x98841,a844)),x98841),f9(x98841,f857(f856(x98841,x98841),a844),a844)),f775(f775(f10(f857(x98841,f856(x98841,x98841)),f857(x98841,f857(f857(f856(x98841,x98841),a844),a844)),x98841),f775(f10(f856(x98841,x98841),f857(f857(f856(x98841,x98841),a844),a844),x98841),f334(f856(x98841,x98841)))),f241(x98841,x98841)))),x98842),x98843,x98844)+~P1(f775(f775(f334(f856(f851(x98841),f851(x98841))),f775(f775(f241(f851(x98841),f851(x98841)),x98843),x98844)),f147(x98841,x98842))) % 186.05/186.62 [9888]P57(x98881,f775(f775(f9(x98881,f857(f856(x98881,x98881),a844),f857(x98881,a844)),f775(f775(f10(f857(x98881,f857(f857(f856(x98881,x98881),a844),a844)),f857(f857(f856(x98881,x98881),a844),f857(x98881,a844)),x98881),f9(x98881,f857(f856(x98881,x98881),a844),a844)),f775(f775(f10(f857(x98881,f856(x98881,x98881)),f857(x98881,f857(f857(f856(x98881,x98881),a844),a844)),x98881),f775(f10(f856(x98881,x98881),f857(f857(f856(x98881,x98881),a844),a844),x98881),f334(f856(x98881,x98881)))),f241(x98881,x98881)))),x98882),x98883,x98884)+~P1(f775(f775(f334(f856(f857(x98881,a844),f857(x98881,a844))),f775(f775(f241(f857(x98881,a844),f857(x98881,a844)),x98883),x98884)),f324(x98881,x98882))) % 186.05/186.62 [9917]E(x99171,x99172)+~E(f775(f775(f9(x99173,f857(f856(x99173,x99174),a844),f857(x99174,a844)),f775(f775(f10(f857(x99174,f857(f857(f856(x99173,x99174),a844),a844)),f857(f857(f856(x99173,x99174),a844),f857(x99174,a844)),x99173),f9(x99174,f857(f856(x99173,x99174),a844),a844)),f775(f775(f10(f857(x99174,f856(x99173,x99174)),f857(x99174,f857(f857(f856(x99173,x99174),a844),a844)),x99173),f775(f10(f856(x99173,x99174),f857(f857(f856(x99173,x99174),a844),a844),x99174),f334(f856(x99173,x99174)))),f241(x99173,x99174)))),x99171),f775(f775(f9(x99173,f857(f856(x99173,x99174),a844),f857(x99174,a844)),f775(f775(f10(f857(x99174,f857(f857(f856(x99173,x99174),a844),a844)),f857(f857(f856(x99173,x99174),a844),f857(x99174,a844)),x99173),f9(x99174,f857(f856(x99173,x99174),a844),a844)),f775(f775(f10(f857(x99174,f856(x99173,x99174)),f857(x99174,f857(f857(f856(x99173,x99174),a844),a844)),x99173),f775(f10(f856(x99173,x99174),f857(f857(f856(x99173,x99174),a844),a844),x99174),f334(f856(x99173,x99174)))),f241(x99173,x99174)))),x99172)) % 186.05/186.62 [9920]~P34(x99201,f775(f775(f9(x99201,f857(f856(x99201,x99201),a844),f857(x99201,a844)),f775(f775(f10(f857(x99201,f857(f857(f856(x99201,x99201),a844),a844)),f857(f857(f856(x99201,x99201),a844),f857(x99201,a844)),x99201),f9(x99201,f857(f856(x99201,x99201),a844),a844)),f775(f775(f10(f857(x99201,f856(x99201,x99201)),f857(x99201,f857(f857(f856(x99201,x99201),a844),a844)),x99201),f775(f10(f856(x99201,x99201),f857(f857(f856(x99201,x99201),a844),a844),x99201),f334(f856(x99201,x99201)))),f241(x99201,x99201)))),x99204),x99202,x99203)+P1(f775(f775(f334(f856(f851(x99201),f851(x99201))),f775(f775(f241(f851(x99201),f851(x99201)),x99202),x99203)),f147(x99201,x99204))) % 186.05/186.62 [9921]~P57(x99211,f775(f775(f9(x99211,f857(f856(x99211,x99211),a844),f857(x99211,a844)),f775(f775(f10(f857(x99211,f857(f857(f856(x99211,x99211),a844),a844)),f857(f857(f856(x99211,x99211),a844),f857(x99211,a844)),x99211),f9(x99211,f857(f856(x99211,x99211),a844),a844)),f775(f775(f10(f857(x99211,f856(x99211,x99211)),f857(x99211,f857(f857(f856(x99211,x99211),a844),a844)),x99211),f775(f10(f856(x99211,x99211),f857(f857(f856(x99211,x99211),a844),a844),x99211),f334(f856(x99211,x99211)))),f241(x99211,x99211)))),x99214),x99212,x99213)+P1(f775(f775(f334(f856(f857(x99211,a844),f857(x99211,a844))),f775(f775(f241(f857(x99211,a844),f857(x99211,a844)),x99212),x99213)),f324(x99211,x99214))) % 186.05/186.62 [7415]~P88(x74151)+E(f775(f775(f82(x74151),f775(f106(x74151),x74152)),f775(f775(f82(x74151),f775(f106(x74151),x74153)),x74154)),f775(f775(f82(x74151),f775(f106(x74151),f775(f775(f82(a1),x74152),x74153))),x74154)) % 186.05/186.62 [7416]~P88(x74161)+E(f775(f775(f82(x74161),f775(f106(x74161),x74162)),f775(f775(f3(x74161),f775(f106(x74161),x74163)),x74164)),f775(f775(f3(x74161),f775(f106(x74161),f775(f775(f82(a1),x74162),x74163))),x74164)) % 186.05/186.62 [7417]~P88(x74171)+E(f775(f775(f83(x74171),f775(f106(x74171),x74172)),f775(f775(f83(x74171),f775(f106(x74171),x74173)),x74174)),f775(f775(f83(x74171),f775(f106(x74171),f775(f775(f83(a1),x74172),x74173))),x74174)) % 186.05/186.62 [7464]~P2(x74641)+E(f775(f155(x74641),f775(f775(f143(x74642,x74641),f775(f18(x74641,x74642),x74643)),x74644)),f775(f775(f83(x74641),f775(f102(x74641),f775(f181(f851(x74642)),x74644))),x74643)) % 186.05/186.62 [7700]E(f775(f265(x77001,f775(f775(f140(f856(a101,x77001)),x77002),x77003)),x77004),f775(f250(a101,x77001),x77002))+~P1(f775(f775(f233(a101),x77004),f775(f240(a101,x77001),x77002))) % 186.05/186.62 [7748]~P88(x77481)+E(f775(f775(f82(x77481),f775(f106(x77481),x77482)),f775(f775(f3(x77481),x77483),f775(f106(x77481),x77484))),f775(f775(f82(x77481),f775(f106(x77481),f775(f775(f82(a1),x77482),f775(f81(a1),x77484)))),x77483)) % 186.05/186.62 [7879]E(f775(f265(x78791,x78792),f775(f775(f3(a101),x78793),f775(f240(a101,x78791),x78794))),f775(f265(x78791,f775(f775(f140(f856(a101,x78791)),x78794),x78792)),x78793))+P1(f775(f775(f233(a101),x78793),f775(f240(a101,x78791),x78794))) % 186.05/186.62 [8310]~P1(f775(f775(f334(x83101),x83102),f775(f158(x83101),f116(x83101,x83104))))+P1(f775(f775(f334(x83101),x83102),f775(f158(x83101),f116(x83101,f775(f775(f125(x83101),x83103),x83104))))) % 186.05/186.62 [8311]~P1(f775(f775(f334(x83111),x83112),f775(f158(x83111),f116(x83111,x83113))))+P1(f775(f775(f334(x83111),x83112),f775(f158(x83111),f116(x83111,f775(f775(f125(x83111),x83113),x83114))))) % 186.05/186.62 [8334]E(f775(f775(f103(f857(x83341,a844)),f775(f775(f104(f857(x83341,a844)),x83342),x83343)),x83344),f775(f775(f104(f857(x83341,a844)),x83342),f775(f775(f103(f857(x83341,a844)),x83343),x83344)))+~P1(f775(f775(f232(f857(x83341,a844)),x83344),x83342)) % 186.05/186.62 [8621]~E(f775(f775(f103(f857(x86211,a844)),f775(f775(f104(f857(x86211,a844)),x86213),x86214)),x86212),f775(f775(f104(f857(x86211,a844)),x86213),f775(f775(f103(f857(x86211,a844)),x86214),x86212)))+P1(f775(f775(f232(f857(x86211,a844)),x86212),x86213)) % 186.05/186.62 [8870]~P1(f775(f775(f232(f857(x88701,a844)),x88702),f775(f775(f103(f857(x88701,a844)),x88703),x88704)))+P1(f775(f775(f232(f857(x88701,a844)),f775(f775(f3(f857(x88701,a844)),x88702),x88703)),x88704)) % 186.05/186.62 [8989]P1(f775(f775(f232(f857(x89891,a844)),x89892),f775(f775(f103(f857(x89891,a844)),x89893),x89894)))+~P1(f775(f775(f232(f857(x89891,a844)),f775(f775(f3(f857(x89891,a844)),x89892),x89893)),x89894)) % 186.05/186.62 [9065]~P79(x90651)+E(f775(f77(x90651),f775(f775(f8(x90652,x90651),f775(f775(f10(x90651,x90651,x90652),f77(x90651)),x90653)),x90654)),f775(f775(f8(x90652,x90651),f775(f775(f10(x90651,x90651,x90652),f77(x90651)),x90653)),x90654)) % 186.05/186.62 [9210]~P79(x92101)+P1(f775(f775(f232(x92101),f2(x92101)),f775(f775(f8(x92102,x92101),f775(f775(f10(x92101,x92101,x92102),f77(x92101)),x92103)),x92104))) % 186.05/186.62 [9213]~P6(x92131)+E(f775(f155(x92131),f775(f775(f143(x92132,x92131),f775(f75(x92131,x92131,x92132,f81(x92131)),x92133)),x92134)),f775(f81(x92131),f775(f155(x92131),f775(f775(f143(x92132,x92131),x92133),x92134)))) % 186.05/186.62 [9350]~P79(x93501)+P1(f775(f775(f232(x93501),f775(f77(x93501),f775(f775(f8(x93502,x93501),x93503),x93504))),f775(f775(f8(x93502,x93501),f775(f775(f10(x93501,x93501,x93502),f77(x93501)),x93503)),x93504))) % 186.05/186.62 [9378]~E(f775(f775(f82(a850),x93781),x93784),f775(f775(f82(a850),x93783),x93782))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x93781),x93782)),f775(f775(f241(a850,a850),x93783),x93784))),a111)) % 186.05/186.62 [9379]~P1(f775(f775(f233(a850),x93791),x93793))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x93791),x93792)),f775(f775(f241(a850,a850),x93793),x93794))),a40)) % 186.05/186.62 [9380]~P1(f775(f775(f233(a850),x93801),x93803))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x93801),x93802)),f775(f775(f241(a850,a850),x93803),x93804))),a72)) % 186.05/186.62 [9519]E(f775(f775(f82(a850),x95191),x95192),f775(f775(f82(a850),x95193),x95194))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x95191),x95194)),f775(f775(f241(a850,a850),x95193),x95192))),a111)) % 186.05/186.62 [9563]~P1(f775(f775(f334(x95632),x95634),f775(f775(f46(x95631,f857(x95632,a844)),f239(f857(x95631,a844))),x95633)))+P1(f775(f775(f775(f46(x95631,f857(x95632,a844)),f239(f857(x95631,a844))),f775(f775(f10(f857(x95632,a844),f857(x95632,a844),x95631),f775(f9(x95632,f857(x95632,a844),a844),f334(x95632))),x95633)),x95634)) % 186.05/186.62 [9564]~P1(f775(f775(f334(x95642),x95644),f775(f775(f47(x95641,f857(x95642,a844)),f239(f857(x95641,a844))),x95643)))+P1(f775(f775(f775(f47(x95641,f857(x95642,a844)),f239(f857(x95641,a844))),f775(f775(f10(f857(x95642,a844),f857(x95642,a844),x95641),f775(f9(x95642,f857(x95642,a844),a844),f334(x95642))),x95643)),x95644)) % 186.05/186.62 [9630]~P1(f775(f56(x96301,x96302),f775(f775(f241(a1,a1),x96304),x96303)))+P1(f775(f56(f775(f81(a1),x96301),x96302),f775(f775(f241(a1,a1),f775(f775(f775(f98(a1),f775(f775(a330,x96303),f2(a1))),f775(f81(a1),x96304)),f775(f775(f3(a1),f775(f81(a1),x96304)),f80(a1)))),f775(f775(f775(f98(a1),f775(f775(a330,x96303),f2(a1))),f2(a1)),f775(f775(f3(a1),x96302),x96303))))) % 186.05/186.62 [9639]P1(f775(f775(f334(x96391),x96392),f775(f775(f46(x96393,f857(x96391,a844)),f239(f857(x96393,a844))),x96394)))+~P1(f775(f775(f775(f46(x96393,f857(x96391,a844)),f239(f857(x96393,a844))),f775(f775(f10(f857(x96391,a844),f857(x96391,a844),x96393),f775(f9(x96391,f857(x96391,a844),a844),f334(x96391))),x96394)),x96392)) % 186.05/186.62 [9640]P1(f775(f775(f334(x96401),x96402),f775(f775(f47(x96403,f857(x96401,a844)),f239(f857(x96403,a844))),x96404)))+~P1(f775(f775(f775(f47(x96403,f857(x96401,a844)),f239(f857(x96403,a844))),f775(f775(f10(f857(x96401,a844),f857(x96401,a844),x96403),f775(f9(x96401,f857(x96401,a844),a844),f334(x96401))),x96404)),x96402)) % 186.05/186.62 [9651]E(f775(f775(f46(a850,f857(x96511,a844)),f239(f857(a850,a844))),x96512),f775(f775(f46(a850,f857(x96511,a844)),f239(f857(a850,a844))),x96513))+~E(f775(f775(f46(a850,f857(x96511,a844)),f775(f294(a850,f2(a850)),f398(x96512,x96514,x96513,x96511))),x96513),f775(f775(f46(a850,f857(x96511,a844)),f775(f294(a850,f2(a850)),f775(f775(f82(a850),f398(x96512,x96514,x96513,x96511)),x96514))),x96512)) % 186.05/186.62 [9981]~P1(f775(f775(f232(f857(f856(x99811,x99812),a844)),x99813),x99814))+P1(f775(f775(f232(f857(x99811,f857(x99812,a844))),f775(f775(f9(x99811,f857(f856(x99811,x99812),a844),f857(x99812,a844)),f775(f775(f10(f857(x99812,f857(f857(f856(x99811,x99812),a844),a844)),f857(f857(f856(x99811,x99812),a844),f857(x99812,a844)),x99811),f9(x99812,f857(f856(x99811,x99812),a844),a844)),f775(f775(f10(f857(x99812,f856(x99811,x99812)),f857(x99812,f857(f857(f856(x99811,x99812),a844),a844)),x99811),f775(f10(f856(x99811,x99812),f857(f857(f856(x99811,x99812),a844),a844),x99812),f334(f856(x99811,x99812)))),f241(x99811,x99812)))),x99813)),f775(f775(f9(x99811,f857(f856(x99811,x99812),a844),f857(x99812,a844)),f775(f775(f10(f857(x99812,f857(f857(f856(x99811,x99812),a844),a844)),f857(f857(f856(x99811,x99812),a844),f857(x99812,a844)),x99811),f9(x99812,f857(f856(x99811,x99812),a844),a844)),f775(f775(f10(f857(x99812,f856(x99811,x99812)),f857(x99812,f857(f857(f856(x99811,x99812),a844),a844)),x99811),f775(f10(f856(x99811,x99812),f857(f857(f856(x99811,x99812),a844),a844),x99812),f334(f856(x99811,x99812)))),f241(x99811,x99812)))),x99814))) % 186.05/186.62 [9997]P1(f775(f775(f232(f857(f856(x99971,x99972),a844)),x99973),x99974))+~P1(f775(f775(f232(f857(x99971,f857(x99972,a844))),f775(f775(f9(x99971,f857(f856(x99971,x99972),a844),f857(x99972,a844)),f775(f775(f10(f857(x99972,f857(f857(f856(x99971,x99972),a844),a844)),f857(f857(f856(x99971,x99972),a844),f857(x99972,a844)),x99971),f9(x99972,f857(f856(x99971,x99972),a844),a844)),f775(f775(f10(f857(x99972,f856(x99971,x99972)),f857(x99972,f857(f857(f856(x99971,x99972),a844),a844)),x99971),f775(f10(f856(x99971,x99972),f857(f857(f856(x99971,x99972),a844),a844),x99972),f334(f856(x99971,x99972)))),f241(x99971,x99972)))),x99973)),f775(f775(f9(x99971,f857(f856(x99971,x99972),a844),f857(x99972,a844)),f775(f775(f10(f857(x99972,f857(f857(f856(x99971,x99972),a844),a844)),f857(f857(f856(x99971,x99972),a844),f857(x99972,a844)),x99971),f9(x99972,f857(f856(x99971,x99972),a844),a844)),f775(f775(f10(f857(x99972,f856(x99971,x99972)),f857(x99972,f857(f857(f856(x99971,x99972),a844),a844)),x99971),f775(f10(f856(x99971,x99972),f857(f857(f856(x99971,x99972),a844),a844),x99972),f334(f856(x99971,x99972)))),f241(x99971,x99972)))),x99974))) % 186.05/186.62 [9110]~P1(f775(f775(f334(f856(x91101,x91101)),x91102),f300(x91101,x91104)))+P1(f775(f775(f334(f856(x91101,x91101)),x91102),f300(x91101,f775(f775(f103(f857(f856(x91101,x91101),a844)),x91103),x91104)))) % 186.05/186.62 [9111]~P1(f775(f775(f334(f856(x91111,x91111)),x91112),f300(x91111,x91113)))+P1(f775(f775(f334(f856(x91111,x91111)),x91112),f300(x91111,f775(f775(f103(f857(f856(x91111,x91111),a844)),x91113),x91114)))) % 186.05/186.62 [9442]~E(f775(f158(x94421),x94424),f169(x94421,x94422,x94423))+E(f166(x94421,x94422,f775(f775(f143(x94421,f856(x94421,x94422)),f775(f775(f20(x94421,x94422,f856(x94421,x94422)),f241(x94421,x94422)),f775(f775(f10(f854(x94422),x94422,x94421),f231(x94422)),x94423))),x94424)),x94423) % 186.05/186.62 [9733]~P1(f775(f775(f233(a850),f775(f775(f82(a850),x97331),x97334)),f775(f775(f82(a850),x97333),x97332)))+P1(f775(f775(f233(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x97331),x97332)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x97333),x97334)),f180(f857(f856(a850,a850),a844))))))) % 186.05/186.62 [9734]~P1(f775(f775(f232(a850),f775(f775(f82(a850),x97341),x97344)),f775(f775(f82(a850),x97343),x97342)))+P1(f775(f775(f232(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x97341),x97342)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x97343),x97344)),f180(f857(f856(a850,a850),a844))))))) % 186.05/186.62 [9822]P1(f775(f775(f233(a850),f775(f775(f82(a850),x98221),x98222)),f775(f775(f82(a850),x98223),x98224)))+~P1(f775(f775(f233(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x98221),x98224)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x98223),x98222)),f180(f857(f856(a850,a850),a844))))))) % 186.05/186.62 [9823]P1(f775(f775(f232(a850),f775(f775(f82(a850),x98231),x98232)),f775(f775(f82(a850),x98233),x98234)))+~P1(f775(f775(f232(a1),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x98231),x98234)),f180(f857(f856(a850,a850),a844)))))),f775(a91,f775(f277(f856(a850,a850),f856(a850,a850),a111),f775(f775(f302(f856(a850,a850)),f775(f775(f241(a850,a850),x98233),x98232)),f180(f857(f856(a850,a850),a844))))))) % 186.05/186.62 [9870]P1(f775(f775(f232(f857(x98701,a844)),f775(f775(f46(a850,f857(x98701,a844)),f239(f857(a850,a844))),x98702)),f775(f775(f46(a850,f857(x98701,a844)),f239(f857(a850,a844))),x98703)))+~P1(f775(f775(f232(f857(x98701,a844)),f775(f775(f46(a850,f857(x98701,a844)),f775(f294(a850,f2(a850)),f399(x98703,x98704,x98702,x98701))),x98702)),f775(f775(f46(a850,f857(x98701,a844)),f775(f294(a850,f2(a850)),f775(f775(f82(a850),f399(x98703,x98704,x98702,x98701)),x98704))),x98703))) % 186.05/186.62 [9923]P1(f775(f775(f232(a101),x99234),f2(a101)))+E(f775(f775(f253(f856(a101,a101),f856(x99231,f857(a853,a842)),f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101))),f775(x99232,x99233)),f775(f775(f10(f857(f857(a101,f857(a844,f854(f852(x99231)))),f857(f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101)))),f857(f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101))),f856(x99231,f857(a853,a842))),f775(f253(f856(a101,a101),f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101))),f272(x99231,x99232,f775(f775(f3(a101),x99234),f80(a101)),x99233))),f775(f775(f10(f857(f857(a101,f857(a844,f854(f852(x99231)))),f857(a101,f857(a844,f854(f852(x99231))))),f857(f857(a101,f857(a844,f854(f852(x99231)))),f857(f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101)))),f856(x99231,f857(a853,a842))),f775(f10(f857(a101,f857(a844,f854(f852(x99231)))),f857(f856(a101,a101),f856(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101))),f857(a101,f857(a844,f854(f852(x99231))))),f241(f857(a101,f857(a844,f854(f852(x99231)))),f856(a101,a101)))),f775(f775(f10(f857(a101,f857(a844,f854(f852(x99231)))),f857(f857(a101,f857(a844,f854(f852(x99231)))),f857(a101,f857(a844,f854(f852(x99231))))),f856(x99231,f857(a853,a842))),f51(x99231)),f775(f775(f10(x99231,f857(a101,f857(a844,f854(f852(x99231)))),f856(x99231,f857(a853,a842))),f49(x99231)),f240(x99231,f857(a853,a842))))))),f272(x99231,x99232,x99234,x99233)) % 186.05/186.62 [9972]~P1(f775(f775(f334(x99722),x99724),f775(f259(x99721,x99722),x99723)))+P1(f775(f247(x99721,x99722,f775(f775(f9(x99721,f857(f856(x99721,x99722),a844),f857(x99722,a844)),f775(f775(f10(f857(x99722,f857(f857(f856(x99721,x99722),a844),a844)),f857(f857(f856(x99721,x99722),a844),f857(x99722,a844)),x99721),f9(x99722,f857(f856(x99721,x99722),a844),a844)),f775(f775(f10(f857(x99722,f856(x99721,x99722)),f857(x99722,f857(f857(f856(x99721,x99722),a844),a844)),x99721),f775(f10(f856(x99721,x99722),f857(f857(f856(x99721,x99722),a844),a844),x99722),f334(f856(x99721,x99722)))),f241(x99721,x99722)))),x99723)),x99724)) % 186.05/186.62 [9973]~P1(f775(f775(f334(x99731),x99734),f775(f261(x99731,x99732),x99733)))+P1(f775(f246(x99731,x99732,f775(f775(f9(x99731,f857(f856(x99731,x99732),a844),f857(x99732,a844)),f775(f775(f10(f857(x99732,f857(f857(f856(x99731,x99732),a844),a844)),f857(f857(f856(x99731,x99732),a844),f857(x99732,a844)),x99731),f9(x99732,f857(f856(x99731,x99732),a844),a844)),f775(f775(f10(f857(x99732,f856(x99731,x99732)),f857(x99732,f857(f857(f856(x99731,x99732),a844),a844)),x99731),f775(f10(f856(x99731,x99732),f857(f857(f856(x99731,x99732),a844),a844),x99732),f334(f856(x99731,x99732)))),f241(x99731,x99732)))),x99733)),x99734)) % 186.05/186.62 [9984]P1(f775(f775(f334(x99841),x99842),f775(f259(x99843,x99841),x99844)))+~P1(f775(f247(x99843,x99841,f775(f775(f9(x99843,f857(f856(x99843,x99841),a844),f857(x99841,a844)),f775(f775(f10(f857(x99841,f857(f857(f856(x99843,x99841),a844),a844)),f857(f857(f856(x99843,x99841),a844),f857(x99841,a844)),x99843),f9(x99841,f857(f856(x99843,x99841),a844),a844)),f775(f775(f10(f857(x99841,f856(x99843,x99841)),f857(x99841,f857(f857(f856(x99843,x99841),a844),a844)),x99843),f775(f10(f856(x99843,x99841),f857(f857(f856(x99843,x99841),a844),a844),x99841),f334(f856(x99843,x99841)))),f241(x99843,x99841)))),x99844)),x99842)) % 186.05/186.62 [9985]P1(f775(f775(f334(x99851),x99852),f775(f261(x99851,x99853),x99854)))+~P1(f775(f246(x99851,x99853,f775(f775(f9(x99851,f857(f856(x99851,x99853),a844),f857(x99853,a844)),f775(f775(f10(f857(x99853,f857(f857(f856(x99851,x99853),a844),a844)),f857(f857(f856(x99851,x99853),a844),f857(x99853,a844)),x99851),f9(x99853,f857(f856(x99851,x99853),a844),a844)),f775(f775(f10(f857(x99853,f856(x99851,x99853)),f857(x99853,f857(f857(f856(x99851,x99853),a844),a844)),x99851),f775(f10(f856(x99851,x99853),f857(f857(f856(x99851,x99853),a844),a844),x99853),f334(f856(x99851,x99853)))),f241(x99851,x99853)))),x99854)),x99852)) % 186.05/186.62 [9747]~P85(x97471)+E(f775(f775(f83(x97471),f775(f775(f82(x97471),f80(x97471)),f80(x97471))),f775(f775(f8(a850,x97471),f775(f775(f10(x97471,x97471,a850),f775(f82(x97471),x97472)),f775(f775(f9(a850,x97471,x97471),f775(f775(f10(x97471,f857(x97471,x97471),a850),f83(x97471)),f102(x97471))),x97473))),f775(f257(a850),x97474))),f775(f775(f83(x97471),f775(f102(x97471),x97474)),f775(f775(f82(x97471),x97472),f775(f775(f82(x97471),x97472),f775(f775(f83(x97471),f775(f102(x97471),f775(f775(f3(a850),x97474),f80(a850)))),x97473))))) % 186.05/186.62 [9891]P1(f775(x98911,f591(x98912,x98913,x98914,x98911)))+P36(x98912,f775(f256(f856(x98912,x98912)),f775(f251(x98912,x98912,a844),f775(f775(f10(f857(x98912,a844),f857(x98912,a844),x98912),f775(f20(x98912,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98912),a331),x98911))),f775(f775(f9(x98912,f857(x98912,x98912),f857(x98912,a844)),f775(f775(f10(f857(x98912,a844),f857(f857(x98912,x98912),f857(x98912,a844)),x98912),f10(x98912,a844,x98912)),a330)),x98913))))) % 186.05/186.62 [9905]~P1(f775(f775(f233(a850),f775(x99054,f775(x99053,f591(x99051,x99053,x99054,x99052)))),f775(x99054,f591(x99051,x99053,x99054,x99052))))+P36(x99051,f775(f256(f856(x99051,x99051)),f775(f251(x99051,x99051,a844),f775(f775(f10(f857(x99051,a844),f857(x99051,a844),x99051),f775(f20(x99051,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99051),a331),x99052))),f775(f775(f9(x99051,f857(x99051,x99051),f857(x99051,a844)),f775(f775(f10(f857(x99051,a844),f857(f857(x99051,x99051),f857(x99051,a844)),x99051),f10(x99051,a844,x99051)),a330)),x99053))))) % 186.05/186.62 [10009]~P1(f775(f775(f334(f856(x100091,x100091)),f775(f775(f241(x100091,x100091),x100093),x100094)),f775(f775(f103(f857(f856(x100091,x100091),a844)),x100092),f300(x100091,f180(f857(f856(x100091,x100091),a844))))))+P1(f775(f775(f775(f775(f103(f857(x100091,f857(x100091,a844))),f775(f775(f9(x100091,f857(f856(x100091,x100091),a844),f857(x100091,a844)),f775(f775(f10(f857(x100091,f857(f857(f856(x100091,x100091),a844),a844)),f857(f857(f856(x100091,x100091),a844),f857(x100091,a844)),x100091),f9(x100091,f857(f856(x100091,x100091),a844),a844)),f775(f775(f10(f857(x100091,f856(x100091,x100091)),f857(x100091,f857(f857(f856(x100091,x100091),a844),a844)),x100091),f775(f10(f856(x100091,x100091),f857(f857(f856(x100091,x100091),a844),a844),x100091),f334(f856(x100091,x100091)))),f241(x100091,x100091)))),x100092)),a330),x100093),x100094)) % 186.05/186.62 [10017]P1(f775(f775(f334(f856(x100171,x100171)),f775(f775(f241(x100171,x100171),x100172),x100173)),f775(f775(f103(f857(f856(x100171,x100171),a844)),x100174),f300(x100171,f180(f857(f856(x100171,x100171),a844))))))+~P1(f775(f775(f775(f775(f103(f857(x100171,f857(x100171,a844))),f775(f775(f9(x100171,f857(f856(x100171,x100171),a844),f857(x100171,a844)),f775(f775(f10(f857(x100171,f857(f857(f856(x100171,x100171),a844),a844)),f857(f857(f856(x100171,x100171),a844),f857(x100171,a844)),x100171),f9(x100171,f857(f856(x100171,x100171),a844),a844)),f775(f775(f10(f857(x100171,f856(x100171,x100171)),f857(x100171,f857(f857(f856(x100171,x100171),a844),a844)),x100171),f775(f10(f856(x100171,x100171),f857(f857(f856(x100171,x100171),a844),a844),x100171),f334(f856(x100171,x100171)))),f241(x100171,x100171)))),x100174)),a330),x100172),x100173)) % 186.05/186.62 [9969]E(f775(f775(f140(f851(x99691)),f775(f775(f140(x99691),x99692),f775(f132(f851(x99691),f851(x99691),f125(x99691),f115(x99691)),f775(f775(f143(f851(x99691),f851(x99691)),f145(f851(x99691),x99691,f115(x99691),f775(f775(f10(f851(x99691),f857(f851(x99691),f851(x99691)),x99691),f18(f851(x99691),f851(x99691))),f775(f775(f9(x99691,f851(x99691),f851(x99691)),f140(x99691)),f115(x99691))))),x99693)))),f164(x99691,f775(f775(f140(f851(x99691)),x99694),f775(f132(f851(f851(x99691)),f851(f851(x99691)),f125(f851(x99691)),f115(f851(x99691))),f775(f775(f143(f851(x99691),f851(f851(x99691))),f145(f851(f851(x99691)),x99691,f115(f851(x99691)),f775(f18(f857(f851(x99691),f851(f851(x99691))),x99691),f775(f775(f9(f851(x99691),f851(f851(x99691)),f851(f851(x99691))),f140(f851(x99691))),f115(f851(x99691)))))),x99693))))),f164(x99691,f775(f775(f140(f851(x99691)),f775(f775(f140(x99691),x99692),x99694)),x99693)))+~P1(f775(f321(f851(f851(x99691)),f165(x99691)),f775(f775(f140(f851(x99691)),f775(f775(f140(x99691),x99692),x99694)),x99693))) % 186.05/186.62 [10008]~P1(f775(f63(x100082),f775(f256(x100082),x100084)))+P1(f775(f63(x100081),f775(f256(x100081),f775(f775(f10(f857(x100082,a844),a844,x100081),f89(x100082)),f775(f775(f9(x100081,f857(x100082,a844),f857(x100082,a844)),f775(f775(f10(f857(x100082,f857(a844,a844)),f857(f857(x100082,a844),f857(x100082,a844)),x100081),f20(x100082,a844,a844)),f775(f775(f10(f857(x100082,a844),f857(x100082,f857(a844,a844)),x100081),f775(f10(a844,f857(a844,a844),x100082),a331)),f775(f775(f9(x100081,f857(x100082,x100081),f857(x100082,a844)),f775(f775(f10(f857(x100081,a844),f857(f857(x100082,x100081),f857(x100082,a844)),x100081),f10(x100081,a844,x100082)),a330)),x100083)))),x100084))))) % 186.05/186.62 [7170]E(x71701,x71702)+~E(f316(x71703,x71704,x71705,x71701),f316(x71703,x71704,x71705,x71702)) % 186.05/186.62 [7171]E(x71711,x71712)+~E(f317(x71713,x71714,x71715,x71711),f317(x71713,x71714,x71715,x71712)) % 186.05/186.62 [8983]~P39(f36(x89831,x89835),x89832,x89833,x89834)+P39(x89831,x89832,x89833,f371(x89834,x89833,x89832,x89835,x89831)) % 186.05/186.62 [8984]~P39(f36(x89841,x89845),x89842,x89843,x89844)+P39(x89841,x89842,x89843,f383(x89844,x89843,x89842,x89845,x89841)) % 186.05/186.62 [8985]~P39(f36(x89855,x89851),x89854,x89853,x89852)+P39(x89851,f371(x89852,x89853,x89854,x89851,x89855),x89853,x89852) % 186.05/186.62 [8986]~P39(f36(x89865,x89861),x89864,x89863,x89862)+P39(x89861,f383(x89862,x89863,x89864,x89861,x89865),x89863,x89862) % 186.05/186.62 [5517]E(f775(f775(f302(x55171),x55172),f169(x55171,x55173,x55174)),f169(x55171,x55173,x55174))+~E(f775(x55174,x55172),f775(f227(x55173),x55175)) % 186.05/186.62 [5931]P1(f775(f247(x59311,x59312,x59313),x59314))+~P1(f775(f775(x59313,x59315),x59314)) % 186.05/186.62 [5933]P1(f775(f246(x59331,x59332,x59333),x59334))+~P1(f775(f775(x59333,x59334),x59335)) % 186.05/186.62 [5936]~E(f775(x59364,x59362),f775(f227(x59363),x59365))+P1(f775(f775(f334(x59361),x59362),f169(x59361,x59363,x59364))) % 186.05/186.62 [5937]~E(f775(x59374,x59375),f775(f227(x59371),x59372))+P1(f775(f775(f334(x59371),x59372),f171(x59373,x59371,x59374))) % 186.05/186.62 [6421]~E(x64215,f2(a101))+E(f775(f193(x64211,x64212,x64213,x64214),x64215),f117(x64212)) % 186.05/186.62 [6422]~E(x64225,f2(a101))+E(f775(f191(x64221,x64222,x64223,x64224),x64225),f124(x64222)) % 186.05/186.62 [6518]~P39(f28(x65183,x65184),x65182,x65185,x65181)+E(x65181,f775(f775(f775(a189,x65182),x65183),f775(x65184,x65182))) % 186.05/186.62 [6563]~E(x65633,f2(a101))+E(f775(f268(x65631,x65632,x65633,x65634),x65635),f775(f241(x65631,x65632),x65635)) % 186.05/186.62 [6643]~E(f775(x66434,x66435),f183(x66432))+E(f775(f229(f854(x66431),x66432,f183(x66431),x66433),f775(x66434,x66435)),f183(x66431)) % 186.05/186.62 [7293]E(f775(x72931,x72932),f183(x72933))+~E(f775(f170(x72934,x72933,x72935,x72931),x72932),f183(x72933)) % 186.05/186.62 [7294]E(f775(x72941,x72942),f183(x72943))+~E(f775(f170(x72944,x72943,x72941,x72945),x72942),f183(x72943)) % 186.05/186.62 [7334]E(f775(f170(x73341,x73342,x73343,x73344),x73345),f775(x73343,x73345))+P1(f775(f775(f334(x73341),x73345),f169(x73341,x73342,x73344))) % 186.05/186.62 [7335]E(f775(f170(x73351,x73352,x73353,x73354),x73355),f775(x73354,x73355))+P1(f775(f775(f334(x73351),x73355),f169(x73351,x73352,x73353))) % 186.05/186.62 [7661]~P24(x76614,x76611,x76612,x76615)+E(f775(f75(x76611,x76611,x76611,f775(x76612,x76613)),f775(x76612,x76613)),f775(x76612,x76613)) % 186.05/186.62 [7704]E(f775(f170(x77041,x77042,x77043,x77044),x77045),f775(x77044,x77045))+~P1(f775(f775(f334(x77041),x77045),f169(x77041,x77042,x77044))) % 186.05/186.62 [8051]~P20(x80515,x80511,x80512)+E(f775(f75(x80511,x80511,x80511,f775(x80512,x80513)),f775(x80512,x80514)),f775(f75(x80511,x80511,x80511,f775(x80512,x80514)),f775(x80512,x80513))) % 186.05/186.62 [8373]P1(f775(f775(f334(f856(x83731,x83731)),f775(f775(f241(x83731,x83731),x83732),x83733)),f327(x83731,x83734,x83735)))+~P1(f775(f775(f233(a850),f775(x83734,x83732)),f775(x83734,x83733))) % 186.05/186.62 [8473]~P1(f775(f775(f334(x84734),x84733),f282(x84734,x84731,x84732,x84735)))+P1(f775(f775(x84731,x84732),x84733)) % 186.05/186.62 [8474]~P1(f775(f775(f334(x84744),x84743),f291(x84744,x84741,x84742,x84745)))+P1(f775(f775(x84741,x84742),x84743)) % 186.05/186.62 [8475]~P1(f775(f775(f334(x84754),x84752),f282(x84754,x84751,x84755,x84753)))+P1(f775(f775(x84751,x84752),x84753)) % 186.05/186.62 [8476]~P1(f775(f775(f334(x84764),x84762),f291(x84764,x84761,x84765,x84763)))+P1(f775(f775(x84761,x84762),x84763)) % 186.05/186.62 [8598]~P55(x85982,x85981,x85985,x85983,x85984)+E(f775(f303(x85981,x85982,x85983),x85984),f239(f857(x85982,a844))) % 186.05/186.62 [9369]P1(f775(f775(f334(f856(f851(x93691),f851(x93691))),f775(f775(f241(f851(x93691),f851(x93691)),f775(f775(f140(x93691),x93692),x93693)),f775(f775(f140(x93691),x93692),x93694))),f146(x93691,x93695)))+~P1(f775(f775(f334(f856(f851(x93691),f851(x93691))),f775(f775(f241(f851(x93691),f851(x93691)),x93693),x93694)),f146(x93691,x93695))) % 186.05/186.62 [9370]P1(f775(f775(f334(f856(f851(x93701),f851(x93701))),f775(f775(f241(f851(x93701),f851(x93701)),f775(f775(f125(x93701),x93702),x93703)),f775(f775(f125(x93701),x93702),x93704))),f137(x93701,x93705)))+~P1(f775(f775(f334(f856(f851(x93701),f851(x93701))),f775(f775(f241(f851(x93701),f851(x93701)),x93703),x93704)),f137(x93701,x93705))) % 186.05/186.62 [9421]~E(f775(x94213,f396(x94212,x94211,x94214,x94215,x94213)),f775(f174(x94215,x94214,x94211),f396(x94212,x94211,x94214,x94215,x94213)))+E(f775(f775(x94211,x94212),f775(x94213,x94212)),f775(x94213,f775(a114,x94212))) % 186.05/186.62 [9546]E(f775(f775(f140(x95461),f718(x95462,x95463,x95464,x95465,x95461)),f721(x95462,x95463,x95464,x95465,x95461)),x95465)+~P1(f775(f775(f334(f856(f851(x95461),f851(x95461))),f775(f775(f241(f851(x95461),f851(x95461)),x95465),f775(f775(f140(x95461),x95464),x95463))),f147(x95461,x95462))) % 186.05/186.62 [9573]E(f775(f775(f140(x95731),f719(x95732,x95733,x95734,x95735,x95731)),f720(x95732,x95733,x95734,x95735,x95731)),x95733)+~P1(f775(f775(f334(f856(f851(x95731),f851(x95731))),f775(f775(f241(f851(x95731),f851(x95731)),f775(f775(f140(x95731),x95735),x95734)),x95733)),f147(x95731,x95732))) % 186.05/186.62 [9705]~P1(f775(f775(f334(f856(f851(x97051),f851(x97051))),f775(f775(f241(f851(x97051),f851(x97051)),f775(f775(f140(x97051),x97055),x97052)),x97054)),f147(x97051,x97053)))+P1(f775(f775(f334(f856(f851(x97051),f851(x97051))),f775(f775(f241(f851(x97051),f851(x97051)),x97052),f720(x97053,x97054,x97052,x97055,x97051))),f147(x97051,x97053))) % 186.05/186.62 [9790]~P1(f775(f775(f334(f856(f851(x97901),f851(x97901))),f775(f775(f241(f851(x97901),f851(x97901)),x97905),f775(f775(f140(x97901),x97904),x97903))),f147(x97901,x97902)))+P1(f775(f775(f334(f856(f851(x97901),f851(x97901))),f775(f775(f241(f851(x97901),f851(x97901)),f721(x97902,x97903,x97904,x97905,x97901)),x97903)),f147(x97901,x97902))) % 186.05/186.62 [9963]P1(f775(f775(f334(f856(x99631,x99631)),f775(f775(f241(x99631,x99631),f775(x99632,f775(f775(f82(a850),x99633),x99634))),f775(x99632,x99633))),f300(x99631,x99635)))+~P1(f775(f775(f334(f856(x99631,x99631)),f775(f775(f241(x99631,x99631),f775(x99632,f775(a114,f638(x99634,x99633,x99635,x99632,x99631)))),f775(x99632,f638(x99634,x99633,x99635,x99632,x99631)))),f300(x99631,x99635))) % 186.05/186.62 [9987]E(x99871,f2(a101))+E(f775(f229(f856(f851(x99872),x99873),f856(x99872,x99873),f775(f775(f241(f851(x99872),x99873),f115(x99872)),x99874),f775(f251(x99872,x99873,f856(f851(x99872),x99873)),f775(f775(f9(x99872,f857(x99873,f856(f851(x99872),x99873)),f857(x99873,f856(f851(x99872),x99873))),f775(f775(f10(f857(f856(f851(x99872),x99873),f856(f851(x99872),x99873)),f857(f857(x99873,f856(f851(x99872),x99873)),f857(x99873,f856(f851(x99872),x99873))),x99872),f10(f856(f851(x99872),x99873),f856(f851(x99872),x99873),x99873)),f775(f775(f10(f857(f851(x99872),f857(x99873,f856(f851(x99872),x99873))),f857(f856(f851(x99872),x99873),f856(f851(x99872),x99873)),x99872),f251(f851(x99872),x99873,f856(f851(x99872),x99873))),f775(f775(f10(f857(f851(x99872),f851(x99872)),f857(f851(x99872),f857(x99873,f856(f851(x99872),x99873))),x99872),f775(f10(f851(x99872),f857(x99873,f856(f851(x99872),x99873)),f851(x99872)),f241(f851(x99872),x99873))),f140(x99872))))),f119(x99873,x99872,x99875,f775(f775(f3(a101),x99871),f80(a101)))))),f775(x99875,x99874)),f775(f119(x99873,x99872,x99875,x99871),x99874)) % 186.05/186.62 [5120]E(x51201,x51202)+~E(f775(f775(f140(x51203),x51204),x51201),f775(f775(f140(x51203),x51205),x51202)) % 186.05/186.62 [5121]E(x51211,x51212)+~E(f775(f775(f140(x51213),x51211),x51214),f775(f775(f140(x51213),x51212),x51215)) % 186.05/186.62 [5315]~E(f775(f775(f128(x53151),x53153),x53152),f775(f775(f140(x53151),x53154),x53155))+E(f775(f775(f153(x53151),x53152),x53153),x53154) % 186.05/186.62 [5448]~P19(x54484,x54485,x54481)+E(f775(f775(x54481,x54482),f775(f775(x54481,x54482),x54483)),f775(f775(x54481,x54482),x54483)) % 186.05/186.62 [6064]~P100(x60642)+~E(f775(f775(f138(x60641,x60642,x60643),x60644),x60645),f115(x60641)) % 186.05/186.62 [6463]E(x64631,x64632)+~E(f775(f775(f125(x64633),x64634),f775(f775(f140(x64633),x64631),f115(x64633))),f775(f775(f125(x64633),x64635),f775(f775(f140(x64633),x64632),f115(x64633)))) % 186.05/186.62 [6464]E(x64641,x64642)+~E(f775(f775(f125(x64643),x64641),f775(f775(f140(x64643),x64644),f115(x64643))),f775(f775(f125(x64643),x64642),f775(f775(f140(x64643),x64645),f115(x64643)))) % 186.05/186.62 [6726]E(f775(f172(x67261,x67262,x67263,x67264),x67265),f183(x67262))+P1(f775(f775(f334(x67261),x67265),x67264)) % 186.05/186.62 [6796]E(f775(f775(f302(x67961),f775(x67962,x67963)),f775(f303(x67964,x67961,x67962),x67965)),f775(f303(x67964,x67961,x67962),x67965))+~P1(f775(f775(f334(x67964),x67963),x67965)) % 186.05/186.62 [6805]~P1(f775(x68054,f775(x68053,x68055)))+P1(f775(f775(f305(x68051,x68052,x68053),x68054),x68055)) % 186.05/186.62 [6810]~E(x68104,f2(a101))+E(f775(f119(x68101,x68102,x68103,x68104),x68105),f775(f775(f241(f851(x68102),x68101),f115(x68102)),x68105)) % 186.05/186.62 [6904]~E(f775(f303(x69041,x69042,x69043),x69044),x69045)+E(f775(f303(f857(x69041,a844),f857(x69042,a844),f303(x69041,x69042,x69043)),f775(f301(x69041),x69044)),f775(f301(x69042),x69045)) % 186.05/186.62 [6935]E(f775(f172(x69351,x69352,x69353,x69354),x69355),f775(x69353,x69355))+~P1(f775(f775(f334(x69351),x69355),x69354)) % 186.05/186.62 [7250]P29(x72501,x72502,x72503,x72504)+~P29(x72501,x72502,x72503,f775(f775(f302(x72501),x72505),x72504)) % 186.05/186.62 [7321]P1(f775(x73211,x73212))+~P1(f775(f775(f94(x73213,x73214,x73211),x73215),x73212)) % 186.05/186.62 [7372]~P1(f775(f775(f334(x73724),x73723),x73725))+P1(f775(f775(f334(x73721),f775(x73722,x73723)),f775(f303(x73724,x73721,x73722),x73725))) % 186.05/186.62 [7424]P1(f775(x74241,f775(x74242,x74243)))+~P1(f775(f775(f305(x74244,x74245,x74242),x74241),x74243)) % 186.05/186.62 [7425]P1(f775(f775(x74251,x74252),x74253))+~P1(f775(f775(f94(x74254,x74251,x74255),x74252),x74253)) % 186.05/186.62 [7494]~P1(f775(f775(f334(x74943),f775(x74944,x74942)),x74945))+P1(f775(f775(f334(x74941),x74942),f775(f305(x74941,x74943,x74944),x74945))) % 186.05/186.62 [7893]~P1(f775(f775(f334(x78935),x78933),f775(f305(x78935,x78931,x78932),x78934)))+P1(f775(f775(f334(x78931),f775(x78932,x78933)),x78934)) % 186.05/186.62 [8111]~E(x81113,f775(f775(f775(f74(x81111,f854(x81112)),f775(f18(f854(x81112),x81111),f183(x81112))),x81114),f775(f227(x81112),x81115)))+E(f169(x81111,x81112,x81113),f775(f775(f302(x81111),x81114),f180(f857(x81111,a844)))) % 186.05/186.62 [8207]E(f775(x82071,f416(x82072,x82071,x82073,x82074)),x82074)+~P1(f775(f775(f334(x82075),x82074),f775(f303(x82073,x82075,x82071),x82072))) % 186.05/186.62 [8459]P1(f775(f775(f334(f858(x84591,x84592)),f775(f313(x84592,x84591),x84593)),f314(x84591,x84592,x84594,x84595)))+~P1(f775(f775(f334(x84592),x84593),x84595)) % 186.05/186.62 [8460]P1(f775(f775(f334(f858(x84601,x84602)),f775(f304(x84601,x84602),x84603)),f314(x84601,x84602,x84604,x84605)))+~P1(f775(f775(f334(x84601),x84603),x84604)) % 186.05/186.62 [8517]~E(x85172,f775(f775(f140(x85171),x85174),x85175))+P1(f775(f775(f334(f856(f851(x85171),f851(x85171))),f775(f775(f241(f851(x85171),f851(x85171)),f115(x85171)),x85172)),f137(x85171,x85173))) % 186.05/186.62 [8568]P1(f775(f775(f232(f857(x85681,a844)),f775(f775(f47(x85682,f857(x85681,a844)),x85683),x85684)),f775(x85684,x85685)))+~P1(f775(f775(f334(x85682),x85685),x85683)) % 186.05/186.62 [8614]~P55(x86141,x86142,x86143,x86145,x86144)+E(f775(f303(x86141,x86142,x86143),f239(f857(x86141,a844))),x86144) % 186.05/186.62 [8803]E(f775(f775(f775(f74(x88031,f854(x88032)),f172(x88031,x88032,x88033,x88034)),x88035),f183(x88032)),f172(x88031,x88032,x88033,x88034))+P1(f775(f775(f334(x88031),x88035),x88034)) % 186.05/186.62 [8806]E(f775(x88061,f703(x88062,x88063,x88061,x88064,x88065)),x88062)+~E(f775(f775(f196(x88065,x88064),x88061),x88063),f775(f227(x88064),x88062)) % 186.05/186.62 [8809]E(f775(f227(x88091),f703(x88092,x88093,x88094,x88095,x88091)),x88093)+~E(f775(f775(f196(x88091,x88095),x88094),x88093),f775(f227(x88095),x88092)) % 186.05/186.62 [8893]E(f775(f181(f851(x88931)),x88932),x88933)+~P1(f775(f775(f334(f856(f851(x88931),f851(x88931))),f775(f775(f241(f851(x88931),f851(x88931)),x88934),x88932)),f775(f133(x88931,x88935),x88933))) % 186.05/186.62 [8894]E(f775(f181(f851(x88941)),x88942),x88943)+~P1(f775(f775(f334(f856(f851(x88941),f851(x88941))),f775(f775(f241(f851(x88941),f851(x88941)),x88942),x88944)),f775(f133(x88941,x88945),x88943))) % 186.05/186.62 [8955]P1(f775(f775(f334(x89551),f416(x89552,x89553,x89551,x89554)),x89552))+~P1(f775(f775(f334(x89555),x89554),f775(f303(x89551,x89555,x89553),x89552))) % 186.05/186.62 [9108]E(f775(f303(x91081,x91082,x91083),f362(x91084,x91083,x91081,x91085,x91082)),x91085)+~P1(f775(f775(f232(f857(x91082,a844)),x91085),f775(f303(x91081,x91082,x91083),x91084))) % 186.05/186.62 [9341]E(f775(x93411,f536(x93412,x93411,x93413,x93414,x93415)),f775(f227(x93415),x93414))+~P1(f775(f775(f334(x93415),x93414),f171(x93413,x93415,f172(x93413,x93415,x93411,x93412)))) % 186.05/186.62 [9385]P1(f775(f775(f334(f856(f851(x93851),f851(x93851))),f775(f775(f241(f851(x93851),f851(x93851)),f775(f775(f140(x93851),x93852),x93853)),f775(f775(f140(x93851),x93852),x93854))),f300(f851(x93851),f146(x93851,x93855))))+~P1(f775(f775(f334(f856(f851(x93851),f851(x93851))),f775(f775(f241(f851(x93851),f851(x93851)),x93853),x93854)),f300(f851(x93851),f146(x93851,x93855)))) % 186.05/186.62 [9414]~E(f775(x94143,f704(x94145,x94144,x94143,x94142,x94141)),f775(x94145,f704(x94145,x94144,x94143,x94142,x94141)))+E(f775(f775(f143(x94141,x94142),x94143),x94144),f775(f775(f143(x94141,x94142),x94145),x94144)) % 186.05/186.62 [9492]E(f775(f775(f143(x94921,x94922),x94923),x94924),f775(f775(f143(x94921,x94922),x94925),x94924))+P1(f775(f775(f334(x94921),f704(x94923,x94924,x94925,x94922,x94921)),f775(f158(x94921),x94924))) % 186.05/186.62 [9520]~P1(f775(f775(f334(x95205),x95204),f775(f277(x95201,x95205,x95203),x95202)))+P1(f775(f775(f334(x95201),f488(x95202,x95203,x95201,x95204,x95205)),x95202)) % 186.05/186.62 [9521]~P1(f775(f775(f334(x95215),x95214),f775(f277(x95211,x95215,x95213),x95212)))+P1(f775(f775(f334(x95211),f534(x95212,x95213,x95211,x95214,x95215)),x95212)) % 186.05/186.62 [9544]~P1(f775(f775(f232(f857(x95445,a844)),x95444),f775(f303(x95441,x95445,x95443),x95442)))+P1(f775(f775(f232(f857(x95441,a844)),f362(x95442,x95443,x95441,x95444,x95445)),x95442)) % 186.05/186.62 [9588]~P1(f775(f775(f334(x95885),x95884),f171(x95881,x95885,f172(x95881,x95885,x95883,x95882))))+P1(f775(f775(f334(x95881),f536(x95882,x95883,x95881,x95884,x95885)),x95882)) % 186.05/186.62 [5329]~E(f775(x53293,x53294),x53295)+E(f775(f775(f775(f74(x53291,x53292),x53293),x53294),x53295),x53293) % 186.05/186.62 [5778]E(f775(x57781,x57782),x57783)+~E(f775(f775(f775(f74(x57784,x57785),x57781),x57782),x57783),x57781) % 186.05/186.62 [5867]E(x58671,x58672)+~E(f775(f250(x58673,x58674),f775(f775(f241(x58673,x58674),x58675),x58671)),x58672) % 186.05/186.62 [5868]E(x58681,x58682)+~E(f775(f240(x58683,x58684),f775(f775(f241(x58683,x58684),x58681),x58685)),x58682) % 186.05/186.62 [6551]E(f775(f303(x65511,x65512,f775(f18(x65512,x65511),x65513)),x65514),f775(f775(f302(x65512),x65513),f180(f857(x65512,a844))))+~P1(f775(f775(f334(x65511),x65515),x65514)) % 186.05/186.62 [6625]E(f775(f775(f103(f857(x66251,a844)),f775(f158(x66251),x66252)),f775(f158(x66251),x66253)),f775(f158(x66251),x66254))+~E(f156(x66251,x66255,x66254),f775(f775(f241(f851(x66251),f851(x66251)),x66252),x66253)) % 186.05/186.62 [6732]~P100(x67322)+E(f775(f181(f851(x67321)),f775(f775(f138(x67321,x67322,x67323),x67324),x67325)),f775(a114,f775(f181(f851(x67321)),x67325))) % 186.05/186.62 [6747]~P100(x67472)+E(f775(f158(x67471),f775(f775(f138(x67471,x67472,x67473),x67474),x67475)),f775(f775(f302(x67471),x67474),f775(f158(x67471),x67475))) % 186.05/186.62 [7025]~P85(x70251)+E(f775(f775(f82(x70251),f775(f775(f82(x70251),x70252),x70253)),f775(f775(f82(x70251),x70254),x70255)),f775(f775(f82(x70251),f775(f775(f82(x70251),x70252),x70254)),f775(f775(f82(x70251),x70253),x70255))) % 186.05/186.62 [7026]~P85(x70261)+E(f775(f775(f83(x70261),f775(f775(f83(x70261),x70262),x70263)),f775(f775(f83(x70261),x70264),x70265)),f775(f775(f83(x70261),f775(f775(f83(x70261),x70262),x70264)),f775(f775(f83(x70261),x70263),x70265))) % 186.05/186.62 [7027]~P60(x70271)+E(f775(f775(f283(x70271),f775(f775(f83(x70271),x70272),x70273)),f775(f775(f83(x70271),x70274),x70275)),f775(f775(f83(x70271),f775(f775(f283(x70271),x70272),x70274)),f775(f775(f283(x70271),x70273),x70275))) % 186.05/186.62 [7041]~P100(x70411)+E(f295(x70411,f775(f775(f179(x70411),x70412),x70413),f775(f775(f236(x70411),x70414),x70415)),f775(f775(f104(f857(x70411,a844)),f295(x70411,x70412,x70414)),f295(x70411,x70413,x70415))) % 186.05/186.62 [7042]~P100(x70421)+E(f297(x70421,f775(f775(f179(x70421),x70422),x70423),f775(f775(f236(x70421),x70424),x70425)),f775(f775(f104(f857(x70421,a844)),f297(x70421,x70422,x70424)),f297(x70421,x70423,x70425))) % 186.05/186.62 [7043]~P100(x70431)+E(f298(x70431,f775(f775(f179(x70431),x70432),x70433),f775(f775(f236(x70431),x70434),x70435)),f775(f775(f104(f857(x70431,a844)),f298(x70431,x70432,x70434)),f298(x70431,x70433,x70435))) % 186.05/186.62 [7044]~P100(x70441)+E(f775(f775(f104(f857(x70441,a844)),f775(f294(x70441,x70442),x70443)),f775(f294(x70441,x70444),x70445)),f775(f294(x70441,f775(f775(f179(x70441),x70442),x70444)),f775(f775(f236(x70441),x70443),x70445))) % 186.05/186.62 [7162]~P1(f775(x71621,f824(x71623,x71622,x71621)))+P1(f775(x71621,f775(f775(f241(x71622,x71623),x71624),x71625))) % 186.05/186.62 [7262]~E(f775(x72623,x72624),f183(x72622))+E(f171(x72621,x72622,f775(f775(f775(f74(x72621,f854(x72622)),x72623),x72624),f775(f227(x72622),x72625))),f775(f775(f302(x72622),x72625),f171(x72621,x72622,x72623))) % 186.05/186.62 [7285]~E(x72852,f775(x72854,x72855))+P1(f775(f775(f334(x72851),x72852),f775(f303(x72853,x72851,x72854),f239(f857(x72853,a844))))) % 186.05/186.62 [7346]~E(f775(x73463,x73464),f183(x73462))+E(f775(f775(f3(f857(x73461,a844)),f169(x73461,x73462,x73463)),f775(f775(f302(x73461),x73464),x73465)),f775(f775(f3(f857(x73461,a844)),f169(x73461,x73462,x73463)),x73465)) % 186.05/186.62 [7368]~P19(x73683,x73682,x73684)+P19(x73681,x73682,f775(f775(f10(x73683,f857(x73682,x73682),x73681),x73684),x73685)) % 186.05/186.62 [7369]~P20(x73693,x73692,x73694)+P20(x73691,x73692,f775(f775(f10(x73693,f857(x73692,x73692),x73691),x73694),x73695)) % 186.05/186.62 [7510]~P29(x75101,x75102,x75103,x75104)+P29(x75101,x75102,x75103,f775(f775(f3(f857(x75101,a844)),x75104),x75105)) % 186.05/186.62 [7670]~P1(f775(f775(x76703,x76704),x76705))+P1(f775(f775(f251(x76701,x76702,a844),x76703),f775(f775(f241(x76701,x76702),x76704),x76705))) % 186.05/186.62 [7804]P29(x78041,x78042,x78043,x78044)+~P29(x78041,x78042,x78043,f775(f775(f103(f857(x78041,a844)),x78045),x78044)) % 186.05/186.62 [7805]P29(x78051,x78052,x78053,x78054)+~P29(x78051,x78052,x78053,f775(f775(f103(f857(x78051,a844)),x78054),x78055)) % 186.05/186.62 [8010]~P31(x80101,f775(a114,x80102),f775(f775(f775(f93(x80101),x80103),f775(a27,x80104)),x80105))+P31(x80101,x80102,f775(f775(f775(f93(x80101),x80103),f775(f231(a845),f775(a30,x80104))),x80105)) % 186.05/186.62 [8138]P31(x81381,f775(a114,x81382),f775(f775(f775(f93(x81381),x81383),f775(a27,x81384)),x81385))+~P31(x81381,x81382,f775(f775(f775(f93(x81381),x81383),f775(f231(a845),f775(a30,x81384))),x81385)) % 186.05/186.62 [8167]~P19(x81672,x81671,x81673)+E(f775(f132(x81671,x81672,f775(f9(x81672,x81671,x81671),x81673),x81674),x81675),f775(f775(f66(x81672,x81671,x81673),x81674),f775(f158(x81672),x81675))) % 186.05/186.62 [8217]P1(f775(f775(x82171,x82172),x82173))+~P1(f775(f775(f251(x82174,x82175,a844),x82171),f775(f775(f241(x82174,x82175),x82172),x82173))) % 186.05/186.62 [8288]P39(x82884,f798(x82885,x82884,x82883,x82882),x82882,f813(x82885,x82884,x82883,x82882))+P31(x82881,x82882,f775(f775(f775(f93(x82881),x82883),x82884),x82885)) % 186.05/186.62 [8304]~E(f775(f166(x83041,x83042,x83045),x83043),f775(f227(x83042),x83044))+P1(f775(f775(f334(f856(x83041,x83042)),f775(f775(f241(x83041,x83042),x83043),x83044)),f775(f158(f856(x83041,x83042)),x83045))) % 186.05/186.62 [8667]P1(f775(f775(f232(f857(x86671,a844)),f775(f303(x86672,x86671,x86673),x86674)),f775(f303(x86672,x86671,x86673),x86675)))+~P1(f775(f775(f232(f857(x86672,a844)),x86674),x86675)) % 186.05/186.62 [8668]P1(f775(f775(f232(f857(x86681,a844)),f775(f305(x86681,x86682,x86683),x86684)),f775(f305(x86681,x86682,x86683),x86685)))+~P1(f775(f775(f232(f857(x86682,a844)),x86684),x86685)) % 186.05/186.62 [8739]E(x87391,f2(a101))+E(f775(f775(f253(x87392,x87393,x87392,f856(x87393,x87392)),f775(x87394,x87395)),f268(x87393,x87392,f775(f775(f3(a101),x87391),f80(a101)),x87394)),f775(f268(x87393,x87392,x87391,x87394),x87395)) % 186.05/186.62 [8825]P1(f775(f775(f249(x88251,x88252,a844,x88253),x88254),x88255))+~P1(f775(x88253,f775(f775(f241(x88251,x88252),x88254),x88255))) % 186.05/186.62 [9026]P31(x90261,x90262,f775(f775(f775(f93(x90261),x90263),x90264),x90265))+P1(f775(f775(x90263,f783(x90265,x90264,x90263,x90262)),f798(x90265,x90264,x90263,x90262))) % 186.05/186.62 [9087]~P1(f775(f775(f249(x90872,x90873,a844,x90871),x90874),x90875))+P1(f775(x90871,f775(f775(f241(x90872,x90873),x90874),x90875))) % 186.05/186.62 [9196]E(f775(f227(x91961),f715(x91962,x91963,x91964,x91961,x91965)),f775(f166(x91965,x91961,x91962),x91964))+~P1(f775(f775(f334(f856(x91965,x91961)),f775(f775(f241(x91965,x91961),x91964),x91963)),f775(f158(f856(x91965,x91961)),x91962))) % 186.05/186.62 [9239]P31(x92391,x92392,f775(f775(f775(f93(x92391),x92393),x92394),x92395))+~P1(f775(f775(x92395,f783(x92395,x92394,x92393,x92392)),f813(x92395,x92394,x92393,x92392))) % 186.05/186.62 [9306]~P28(x93061,x93062,f775(f775(f302(f849(x93061)),f775(f775(f775(f93(x93061),x93063),f775(f231(a845),f775(a30,x93064))),x93065)),f180(f857(f849(x93061),a844))))+P28(x93061,x93062,f775(f775(f302(f849(x93061)),f775(f775(f775(f93(x93061),x93063),f775(a27,x93064)),x93065)),f180(f857(f849(x93061),a844)))) % 186.05/186.62 [9333]~P1(f775(f63(x93333),f775(f303(x93332,x93333,x93335),f239(f857(x93332,a844)))))+P1(f775(f63(x93331),f775(f303(x93332,x93331,f775(f775(f10(x93333,x93331,x93332),x93334),x93335)),f239(f857(x93332,a844))))) % 186.05/186.62 [9355]P1(f775(f775(f232(f857(f857(x93551,a844),a844)),f775(f303(f857(x93552,a844),f857(x93551,a844),f303(x93552,x93551,x93553)),f775(f301(x93552),x93554))),f775(f301(x93551),x93555)))+~P1(f775(f775(f232(f857(x93551,a844)),f775(f303(x93552,x93551,x93553),x93554)),x93555)) % 186.05/186.62 [9365]~P1(f775(f63(f854(x93651)),f775(f303(x93652,f854(x93651),x93653),f239(f857(x93652,a844)))))+P1(f775(f63(f854(x93651)),f775(f303(x93652,f854(x93651),f775(f775(f775(f74(x93652,f854(x93651)),x93653),x93654),f775(f227(x93651),x93655))),f239(f857(x93652,a844))))) % 186.05/186.62 [9424]E(x94241,x94242)+~P1(f775(f68(x94243,x94244,x94245,x94241,f180(f857(x94243,a844))),x94242)) % 186.05/186.62 [9437]E(f775(f775(f241(x94371,x94372),f569(x94373,x94374,x94375,x94372,x94371)),f570(x94373,x94374,x94375,x94372,x94371)),x94375)+~P1(f775(f775(f334(f856(x94371,x94372)),x94375),f775(f775(f248(x94371,x94372),x94374),x94373))) % 186.05/186.62 [9525]P1(f775(f775(f334(x95251),f569(x95252,x95253,x95254,x95255,x95251)),x95253))+~P1(f775(f775(f334(f856(x95251,x95255)),x95254),f775(f775(f248(x95251,x95255),x95253),x95252))) % 186.05/186.62 [9621]P28(x96215,x96214,f775(f775(f302(f849(x96215)),f775(f775(f775(f93(x96215),x96211),x96213),x96212)),f180(f857(f849(x96215),a844))))+P1(f775(f775(x96211,f484(x96212,x96213,x96214,x96215,x96211)),f485(x96212,x96213,x96214,x96215,x96211))) % 186.05/186.62 [9663]P1(f775(f775(f334(x96631),f570(x96632,x96633,x96634,x96631,x96635)),f775(x96632,f569(x96632,x96633,x96634,x96631,x96635))))+~P1(f775(f775(f334(f856(x96635,x96631)),x96634),f775(f775(f248(x96635,x96631),x96633),x96632))) % 186.05/186.62 [9682]P1(f775(f775(f334(f856(x96821,x96821)),f775(f775(f241(x96821,x96821),x96822),f659(x96823,x96824,x96825,x96822,x96821))),x96823))+~P1(f775(f775(f334(f856(x96821,x96821)),f775(f775(f241(x96821,x96821),x96822),x96825)),f775(f775(f173(f856(x96821,x96821),a844),f775(a114,x96824)),x96823))) % 186.05/186.62 [9683]P1(f775(f775(f334(f856(x96831,x96831)),f775(f775(f241(x96831,x96831),x96832),f661(x96833,x96834,x96835,x96832,x96831))),x96833))+~P1(f775(f775(f334(f856(x96831,x96831)),f775(f775(f241(x96831,x96831),x96832),x96835)),f775(f775(f173(f856(x96831,x96831),a844),f775(a114,x96834)),x96833))) % 186.05/186.62 [9701]~P1(f775(f775(f334(f856(f851(x97011),f851(x97011))),f775(f775(f241(f851(x97011),f851(x97011)),f775(f775(f140(x97011),x97012),x97015)),x97014)),f147(x97011,x97013)))+P1(f775(f775(f334(f856(x97011,x97011)),f775(f775(f241(x97011,x97011),x97012),f719(x97013,x97014,x97015,x97012,x97011))),x97013)) % 186.05/186.62 [9703]~P28(x97031,x97032,f775(f775(f302(f849(x97031)),f775(f775(f775(f93(x97031),f94(x97031,x97033,x97034)),x97035),x97033)),f180(f857(f849(x97031),a844))))+P28(x97031,x97032,f775(f775(f302(f849(x97031)),f775(f775(f775(f93(x97031),x97033),f35(x97034,x97035)),f94(x97031,x97033,f775(f75(a844,a844,a847,a328),x97034)))),f180(f857(f849(x97031),a844)))) % 186.05/186.62 [9988]P28(x99881,x99882,f775(f775(f302(f849(x99881)),f775(f775(f775(f93(x99881),x99883),x99884),x99885)),f180(f857(f849(x99881),a844))))+~P28(x99881,x99882,f775(f775(f302(f849(x99881)),f775(f775(f775(f93(x99881),f775(f18(f857(a847,a844),x99881),f775(f775(f9(a847,a847,a844),a330),f485(x99885,x99884,x99882,x99881,x99883)))),x99884),f775(f18(f857(a847,a844),x99881),f775(x99885,f484(x99885,x99884,x99882,x99881,x99883))))),f180(f857(f849(x99881),a844)))) % 186.05/186.62 [6215]P1(f775(x62152,x62154))+E(f162(x62151,x62152,f775(f775(f125(x62151),x62153),f775(f775(f140(x62151),x62154),x62155))),f162(x62151,x62152,x62153)) % 186.05/186.62 [6265]~P71(x62652)+E(f775(f775(f775(f3(f857(x62651,x62652)),x62653),x62654),x62655),f775(f775(f3(x62652),f775(x62653,x62655)),f775(x62654,x62655))) % 186.05/186.62 [6267]~P93(x62672)+E(f775(f775(f775(f103(f857(x62671,x62672)),x62673),x62674),x62675),f775(f775(f103(x62672),f775(x62673,x62675)),f775(x62674,x62675))) % 186.05/186.62 [6269]~P93(x62692)+E(f775(f775(f775(f104(f857(x62691,x62692)),x62693),x62694),x62695),f775(f775(f104(x62692),f775(x62693,x62695)),f775(x62694,x62695))) % 186.05/186.62 [6291]E(x62911,x62912)+E(f775(f775(f153(x62913),f775(f775(f148(x62913,x62914),x62911),x62915)),x62912),f775(f775(f153(x62913),x62914),x62912)) % 186.05/186.62 [6568]~E(x65684,f180(f857(x65683,a844)))+E(f775(f775(f3(f857(x65681,a844)),x65682),f775(f775(f46(x65683,f857(x65681,a844)),x65684),x65685)),x65682) % 186.05/186.62 [6569]~E(x65694,f180(f857(x65693,a844)))+E(f775(f775(f103(f857(x65691,a844)),x65692),f775(f775(f46(x65693,f857(x65691,a844)),x65694),x65695)),x65692) % 186.05/186.62 [6570]~E(x65704,f180(f857(x65703,a844)))+E(f775(f775(f104(f857(x65701,a844)),x65702),f775(f775(f47(x65703,f857(x65701,a844)),x65704),x65705)),x65702) % 186.05/186.62 [6584]~E(x65844,f180(f857(x65843,a844)))+E(f775(f775(f302(x65841),x65842),f775(f775(f46(x65843,f857(x65841,a844)),x65844),x65845)),f775(f775(f302(x65841),x65842),f180(f857(x65841,a844)))) % 186.05/186.62 [7413]E(f775(f775(f153(x74131),f775(f775(f143(x74132,x74131),x74133),x74134)),x74135),f775(x74133,f775(f775(f153(x74132),x74134),x74135)))+~P1(f775(f775(f233(a850),x74135),f775(f181(f851(x74132)),x74134))) % 186.05/186.62 [7482]E(f775(f775(f103(f857(x74821,a844)),f775(x74822,x74823)),f775(f775(f46(x74824,f857(x74821,a844)),x74825),x74822)),f775(f775(f46(x74824,f857(x74821,a844)),x74825),x74822))+~P1(f775(f775(f334(x74824),x74823),x74825)) % 186.05/186.62 [7483]E(f775(f775(f104(f857(x74831,a844)),f775(x74832,x74833)),f775(f775(f47(x74834,f857(x74831,a844)),x74835),x74832)),f775(f775(f47(x74834,f857(x74831,a844)),x74835),x74832))+~P1(f775(f775(f334(x74834),x74833),x74835)) % 186.05/186.62 [8086]~E(x80863,f180(f857(x80861,a844)))+E(f775(f775(f46(x80861,f857(x80862,a844)),x80863),f775(f775(f10(f857(x80862,a844),f857(x80862,a844),x80861),f775(f302(x80862),x80864)),x80865)),f180(f857(x80862,a844))) % 186.05/186.62 [8092]~P1(f775(f775(f334(x80924),x80923),x80925))+P1(f775(f775(f232(f857(x80921,a844)),f775(x80922,x80923)),f775(f775(f46(x80924,f857(x80921,a844)),x80925),x80922))) % 186.05/186.62 [8216]~E(f775(x82164,x82162),x82165)+P1(f775(f775(f334(x82161),x82162),f775(f305(x82161,x82163,x82164),f775(f775(f302(x82163),x82165),f180(f857(x82163,a844)))))) % 186.05/186.62 [8262]~P53(x82621,x82622,f775(f278(x82622,x82621),x82623))+E(f775(f775(f104(f857(x82621,a844)),f775(f277(x82622,x82621,x82623),x82624)),f775(f277(x82622,x82621,x82623),x82625)),f775(f277(x82622,x82621,x82623),f775(f775(f104(f857(x82622,a844)),x82624),x82625))) % 186.05/186.62 [8287]E(x82871,f2(a101))+E(f118(x82872,x82873,f775(x82874,f775(f775(f3(a101),x82871),f80(a101))),f775(f775(f9(x82872,a101,f852(x82873)),x82875),x82871)),f775(f193(x82872,x82873,x82874,x82875),x82871)) % 186.05/186.62 [8383]E(x83831,f180(f857(x83832,a844)))+E(f775(f775(f46(x83832,f857(x83833,a844)),x83831),f775(f775(f10(f857(x83833,a844),f857(x83833,a844),x83832),f775(f302(x83833),x83834)),x83835)),f775(f775(f302(x83833),x83834),f775(f775(f46(x83832,f857(x83833,a844)),x83831),x83835))) % 186.05/186.62 [8437]~P29(x84372,x84371,x84373,f239(f857(x84372,a844)))+E(f775(f775(f3(f857(x84371,a844)),f775(f303(x84372,x84371,x84373),x84374)),f775(f303(x84372,x84371,x84373),x84375)),f775(f303(x84372,x84371,x84373),f775(f775(f3(f857(x84372,a844)),x84374),x84375))) % 186.05/186.62 [8438]~P29(x84382,x84381,x84383,f239(f857(x84382,a844)))+E(f775(f775(f104(f857(x84381,a844)),f775(f303(x84382,x84381,x84383),x84384)),f775(f303(x84382,x84381,x84383),x84385)),f775(f303(x84382,x84381,x84383),f775(f775(f104(f857(x84382,a844)),x84384),x84385))) % 186.05/186.62 [8505]~P1(f775(f775(f69(x85051,x85052,x85055),x85053),x85054))+P1(f775(f775(f334(f856(x85051,x85052)),f775(f775(f241(x85051,x85052),x85053),x85054)),x85055)) % 186.05/186.62 [8533]P1(f775(f775(f334(x85331),x85332),f775(f259(x85333,x85331),x85334)))+~P1(f775(f775(f334(f856(x85333,x85331)),f775(f775(f241(x85333,x85331),x85335),x85332)),x85334)) % 186.05/186.62 [8535]P1(f775(f775(f334(x85351),x85352),f775(f261(x85351,x85353),x85354)))+~P1(f775(f775(f334(f856(x85351,x85353)),f775(f775(f241(x85351,x85353),x85352),x85355)),x85354)) % 186.05/186.62 [8656]P1(f775(f775(f69(x86561,x86562,x86563),x86564),x86565))+~P1(f775(f775(f334(f856(x86561,x86562)),f775(f775(f241(x86561,x86562),x86564),x86565)),x86563)) % 186.05/186.62 [8689]E(f775(x86891,x86892),x86893)+~P1(f775(f775(f334(x86894),x86892),f775(f305(x86894,x86895,x86891),f775(f775(f302(x86895),x86893),f180(f857(x86895,a844)))))) % 186.05/186.62 [8890]P1(f775(f775(f334(f856(x88901,x88902)),f775(f775(f241(x88901,x88902),x88903),x88904)),f775(f278(x88902,x88901),x88905)))+~P1(f775(f775(f334(f856(x88902,x88901)),f775(f775(f241(x88902,x88901),x88904),x88903)),x88905)) % 186.05/186.62 [8908]~P1(f775(f775(x89081,x89085),x89084))+P1(f775(f775(x89081,f775(f250(x89082,x89083),f775(f775(f241(x89082,x89083),x89084),x89085))),f775(f240(x89082,x89083),f775(f775(f241(x89082,x89083),x89084),x89085)))) % 186.05/186.62 [8935]~P1(f775(f775(f334(f856(x89352,x89351)),f775(f775(f241(x89352,x89351),x89354),x89353)),f775(f278(x89351,x89352),x89355)))+P1(f775(f775(f334(f856(x89351,x89352)),f775(f775(f241(x89351,x89352),x89353),x89354)),x89355)) % 186.05/186.62 [8963]~P1(f775(f775(f334(f856(x89633,x89631)),f775(f775(f241(x89633,x89631),x89635),x89632)),x89634))+P1(f775(f775(f334(x89631),x89632),f775(f277(x89633,x89631,x89634),f775(f775(f302(x89633),x89635),f180(f857(x89633,a844)))))) % 186.05/186.62 [9010]P1(f775(f775(f334(f856(x90101,x90102)),f775(f775(f241(x90101,x90102),x90103),x90104)),x90105))+~P1(f775(f775(f334(x90102),x90104),f775(f277(x90101,x90102,x90105),f775(f775(f302(x90101),x90103),f180(f857(x90101,a844)))))) % 186.05/186.62 [9029]E(f775(f775(f775(f74(x90291,f854(x90292)),f172(x90291,x90292,x90293,x90294)),x90295),f183(x90292)),f172(x90291,x90292,x90293,f775(f775(f3(f857(x90291,a844)),x90294),f775(f775(f302(x90291),x90295),f180(f857(x90291,a844))))))+~P1(f775(f775(f334(x90291),x90295),x90294)) % 186.05/186.62 [9093]~P66(x90931)+E(f775(f775(f8(a850,x90931),x90932),f295(a850,f775(f775(f82(a850),x90933),x90934),f775(f775(f82(a850),x90935),x90934))),f775(f775(f8(a850,x90931),f775(f775(f10(a850,x90931,a850),x90932),f775(f775(f9(a850,a850,a850),f82(a850)),x90934))),f295(a850,x90933,x90935))) % 186.05/186.62 [9112]~P66(x91121)+E(f775(f775(f8(a850,x91121),x91122),f775(f294(a850,f775(f775(f82(a850),x91123),x91124)),f775(f775(f82(a850),x91125),x91124))),f775(f775(f8(a850,x91121),f775(f775(f10(a850,x91121,a850),x91122),f775(f775(f9(a850,a850,a850),f82(a850)),x91124))),f775(f294(a850,x91123),x91125))) % 186.05/186.62 [9321]P1(f775(f775(f334(f856(f851(x93211),f851(x93211))),f775(f775(f241(f851(x93211),f851(x93211)),f775(f775(f140(x93211),x93212),x93213)),f775(f775(f140(x93211),x93214),x93213))),f146(x93211,x93215)))+~P1(f775(f775(f334(f856(x93211,x93211)),f775(f775(f241(x93211,x93211),x93212),x93214)),x93215)) % 186.05/186.62 [9422]P28(x94221,x94222,f775(f775(f302(f849(x94221)),f775(f775(f775(f93(x94221),x94223),f775(a27,x94224)),x94225)),f180(f857(f849(x94221),a844))))+~P28(x94221,f775(f775(f302(f849(x94221)),f775(f775(f775(f93(x94221),x94223),f775(a27,x94224)),x94225)),x94222),f775(f775(f302(f849(x94221)),f775(f775(f775(f93(x94221),x94223),f775(f231(a845),f775(a30,x94224))),x94225)),f180(f857(f849(x94221),a844)))) % 186.05/186.62 [9433]E(f775(f775(f302(x94331),f540(x94332,x94333,x94334,x94335,x94331)),f545(x94332,x94333,x94334,x94335,x94331)),f775(f775(f302(x94331),x94334),x94333))+~P1(f775(f64(x94331,x94335,f775(f775(f302(x94331),x94334),x94333)),x94332)) % 186.05/186.62 [9434]E(f775(f775(f302(x94341),f546(x94342,x94343,x94344,x94345,x94341)),f551(x94342,x94343,x94344,x94345,x94341)),f775(f775(f302(x94341),x94344),x94343))+~P1(f775(f64(x94341,x94345,f775(f775(f302(x94341),x94344),x94343)),x94342)) % 186.05/186.62 [9511]P1(f775(f775(f334(x95111),f667(x95112,x95113,x95114,x95115,x95111)),x95114))+P1(f775(f775(f775(f47(x95111,f857(x95115,a844)),x95114),x95113),x95112)) % 186.05/186.62 [9516]P1(f775(f775(f334(x95161),f666(x95162,x95163,x95161,x95164,x95165)),x95163))+P1(f775(f775(f334(x95165),x95164),f775(f775(f47(x95161,f857(x95165,a844)),x95163),x95162))) % 186.05/186.62 [9524]P1(f775(f775(f334(x95241),f668(x95242,x95243,x95241,x95244,x95245)),x95243))+P1(f775(f775(f232(f857(x95245,a844)),x95244),f775(f775(f47(x95241,f857(x95245,a844)),x95243),x95242))) % 186.05/186.62 [9526]P1(f775(f775(x95261,f386(x95262,x95261,x95263,x95264,x95265)),x95262))+~P1(f775(f775(f775(f46(x95265,f857(x95264,a844)),x95263),x95261),x95262)) % 186.05/186.62 [9528]P1(f775(f775(f334(x95281),f386(x95282,x95283,x95284,x95285,x95281)),x95284))+~P1(f775(f775(f775(f46(x95281,f857(x95285,a844)),x95284),x95283),x95282)) % 186.05/186.62 [9538]P1(f775(f775(f334(x95381),f417(x95382,x95383,x95381,x95384,x95385)),x95383))+~P1(f775(f775(f334(x95385),x95384),f775(f775(f46(x95381,f857(x95385,a844)),x95383),x95382))) % 186.05/186.62 [9543]P1(f775(f775(f334(x95431),x95432),f775(x95433,f417(x95433,x95434,x95435,x95432,x95431))))+~P1(f775(f775(f334(x95431),x95432),f775(f775(f46(x95435,f857(x95431,a844)),x95434),x95433))) % 186.05/186.62 [9625]~P1(f775(f775(x96254,f667(x96255,x96254,x96253,x96252,x96251)),x96255))+P1(f775(f775(f775(f47(x96251,f857(x96252,a844)),x96253),x96254),x96255)) % 186.05/186.62 [9628]~P1(f775(f775(f334(x96281),x96282),f775(x96285,f666(x96285,x96284,x96283,x96282,x96281))))+P1(f775(f775(f334(x96281),x96282),f775(f775(f47(x96283,f857(x96281,a844)),x96284),x96285))) % 186.05/186.62 [9631]~P1(f775(f775(f232(f857(x96311,a844)),x96312),f775(x96315,f668(x96315,x96314,x96313,x96312,x96311))))+P1(f775(f775(f232(f857(x96311,a844)),x96312),f775(f775(f47(x96313,f857(x96311,a844)),x96314),x96315))) % 186.05/186.62 [9686]~P1(f775(f775(f334(x96861),f540(x96865,x96864,x96863,x96862,x96861)),f545(x96865,x96864,x96863,x96862,x96861)))+~P1(f775(f64(x96861,x96862,f775(f775(f302(x96861),x96863),x96864)),x96865)) % 186.05/186.62 [9687]~P1(f775(f775(f334(x96871),f546(x96875,x96874,x96873,x96872,x96871)),f551(x96875,x96874,x96873,x96872,x96871)))+~P1(f775(f64(x96871,x96872,f775(f775(f302(x96871),x96873),x96874)),x96875)) % 186.05/186.62 [9688]~P1(f775(f775(f334(f856(x96881,x96881)),f775(f775(f241(x96881,x96881),x96882),x96885)),f775(f775(f173(f856(x96881,x96881),a844),f775(a114,x96884)),x96883)))+P1(f775(f775(f334(f856(x96881,x96881)),f775(f775(f241(x96881,x96881),x96882),f660(x96883,x96884,x96885,x96882,x96881))),f775(f775(f173(f856(x96881,x96881),a844),x96884),x96883))) % 186.05/186.62 [9695]P1(f775(f68(x96951,x96951,x96952,f540(x96953,x96954,x96955,x96952,x96951),f545(x96953,x96954,x96955,x96952,x96951)),x96953))+~P1(f775(f64(x96951,x96952,f775(f775(f302(x96951),x96955),x96954)),x96953)) % 186.05/186.62 [9696]P1(f775(f68(x96961,x96961,x96962,f546(x96963,x96964,x96965,x96962,x96961),f551(x96963,x96964,x96965,x96962,x96961)),x96963))+~P1(f775(f64(x96961,x96962,f775(f775(f302(x96961),x96965),x96964)),x96963)) % 186.05/186.62 [9707]~P100(x97071)+P18(x97071,f775(f775(f143(x97072,x97071),x97073),f775(f126(x97072,f775(f775(f9(x97072,x97071,a844),f775(f775(f10(x97071,f857(x97071,a844),x97072),a330),x97073)),f775(x97074,x97075))),x97075))) % 186.05/186.62 [9762]~P1(f775(f775(f334(x97622),x97625),f775(f277(x97621,x97622,x97624),x97623)))+P1(f775(f775(f334(f856(x97621,x97622)),f775(f775(f241(x97621,x97622),f488(x97623,x97624,x97621,x97625,x97622)),x97625)),x97624)) % 186.05/186.62 [9763]~P1(f775(f775(f334(x97632),x97635),f775(f277(x97631,x97632,x97634),x97633)))+P1(f775(f775(f334(f856(x97631,x97632)),f775(f775(f241(x97631,x97632),f534(x97633,x97634,x97631,x97635,x97632)),x97635)),x97634)) % 186.05/186.62 [9783]~P1(f775(f775(f334(f856(x97831,x97831)),f775(f775(f241(x97831,x97831),x97835),x97834)),f775(f775(f173(f856(x97831,x97831),a844),f775(a114,x97833)),x97832)))+P1(f775(f775(f334(f856(x97831,x97831)),f775(f775(f241(x97831,x97831),f660(x97832,x97833,x97834,x97835,x97831)),x97834)),x97832)) % 186.05/186.62 [9786]~P1(f775(f775(f334(f856(x97861,x97861)),f775(f775(f241(x97861,x97861),x97865),x97864)),f775(f775(f173(f856(x97861,x97861),a844),f775(a114,x97863)),x97862)))+P1(f775(f775(f334(f856(x97861,x97861)),f775(f775(f241(x97861,x97861),f659(x97862,x97863,x97864,x97865,x97861)),x97864)),f775(f775(f173(f856(x97861,x97861),a844),x97863),x97862))) % 186.05/186.62 [9787]~P1(f775(f775(f334(f856(x97871,x97871)),f775(f775(f241(x97871,x97871),x97875),x97874)),f775(f775(f173(f856(x97871,x97871),a844),f775(a114,x97873)),x97872)))+P1(f775(f775(f334(f856(x97871,x97871)),f775(f775(f241(x97871,x97871),f661(x97872,x97873,x97874,x97875,x97871)),x97874)),f775(f775(f173(f856(x97871,x97871),a844),x97873),x97872))) % 186.05/186.62 [9788]~P1(f775(f775(f334(f856(f851(x97881),f851(x97881))),f775(f775(f241(f851(x97881),f851(x97881)),x97885),f775(f775(f140(x97881),x97884),x97883))),f147(x97881,x97882)))+P1(f775(f775(f334(f856(x97881,x97881)),f775(f775(f241(x97881,x97881),f718(x97882,x97883,x97884,x97885,x97881)),x97884)),x97882)) % 186.05/186.62 [6984]E(x69841,f183(x69842))+E(f169(x69843,x69842,f775(f775(f775(f74(x69843,f854(x69842)),x69844),x69845),x69841)),f775(f775(f302(x69843),x69845),f169(x69843,x69842,x69844))) % 186.05/186.62 [7503]~E(x75033,f180(f857(x75032,a844)))+E(f775(f775(f103(f857(x75031,a844)),f775(f775(f46(x75032,f857(x75031,a844)),x75033),x75034)),x75035),x75035) % 186.05/186.62 [7504]~E(x75043,f180(f857(x75042,a844)))+E(f775(f775(f104(f857(x75041,a844)),f775(f775(f47(x75042,f857(x75041,a844)),x75043),x75044)),x75045),x75045) % 186.05/186.62 [7866]~E(x78665,f183(x78662))+E(f169(x78661,x78662,f775(f775(f775(f74(x78661,f854(x78662)),x78663),x78664),x78665)),f775(f775(f3(f857(x78661,a844)),f169(x78661,x78662,x78663)),f775(f775(f302(x78661),x78664),f180(f857(x78661,a844))))) % 186.05/186.62 [7936]~E(x79363,f180(f857(x79362,a844)))+E(f775(f775(f3(f857(x79361,a844)),f775(f775(f47(x79362,f857(x79361,a844)),x79363),x79364)),x79365),f775(f775(f3(f857(x79361,a844)),f239(f857(x79361,a844))),x79365)) % 186.05/186.62 [8064]E(f775(f775(f148(x80641,f775(f775(f125(x80641),x80642),x80643)),x80644),x80645),f775(f775(f125(x80641),f775(f775(f148(x80641,x80642),x80644),x80645)),x80643))+~P1(f775(f775(f233(a850),x80644),f775(f181(f851(x80641)),x80642))) % 186.05/186.62 [8194]P1(f775(f775(f334(x81941),x81945),f775(f158(x81941),x81943)))+E(f775(f166(x81941,x81942,f775(f775(f167(x81941,x81942),x81943),f775(f775(f143(x81941,x81942),x81944),x81943))),x81945),f183(x81942)) % 186.05/186.62 [8302]~P1(f775(f775(f334(x83021),x83025),f775(f158(x83021),x83023)))+E(f775(f166(x83021,x83022,f775(f775(f167(x83021,x83022),x83023),f775(f775(f143(x83021,x83022),x83024),x83023))),x83025),f775(f227(x83022),f775(x83024,x83025))) % 186.05/186.62 [8333]E(f775(f775(f153(x83331),f775(f775(f143(a850,x83331),x83332),f130(a850,f775(f294(a850,x83333),x83334)))),x83335),f775(x83332,f775(f775(f82(a850),x83333),x83335)))+~P1(f775(f775(f233(a850),x83335),f775(f775(f3(a850),x83334),x83333))) % 186.05/186.62 [8346]E(x83461,f2(a101))+E(f121(x83462,x83463,f775(x83464,f775(f775(f3(a101),x83461),f80(a101))),f775(f775(f9(x83462,a101,f852(f854(x83463))),x83465),x83461)),f775(f191(x83462,x83463,x83464,x83465),x83461)) % 186.05/186.62 [8370]~E(x83703,f180(f857(x83701,a844)))+E(f775(f775(f46(x83701,f857(x83702,a844)),x83703),f775(f775(f10(f857(x83702,a844),f857(x83702,a844),x83701),f775(f103(f857(x83702,a844)),x83704)),x83705)),f180(f857(x83702,a844))) % 186.05/186.62 [8371]~E(x83713,f180(f857(x83711,a844)))+E(f775(f775(f47(x83711,f857(x83712,a844)),x83713),f775(f775(f10(f857(x83712,a844),f857(x83712,a844),x83711),f775(f3(f857(x83712,a844)),x83714)),x83715)),f239(f857(x83712,a844))) % 186.05/186.62 [8372]~E(x83723,f180(f857(x83721,a844)))+E(f775(f775(f47(x83721,f857(x83722,a844)),x83723),f775(f775(f10(f857(x83722,a844),f857(x83722,a844),x83721),f775(f104(f857(x83722,a844)),x83724)),x83725)),f239(f857(x83722,a844))) % 186.05/186.62 [8377]~P136(x83772)+E(f775(f775(f8(x83771,x83772),f775(f775(f10(x83772,x83772,x83771),f775(f83(x83772),x83773)),x83774)),x83775),f775(f775(f83(x83772),x83773),f775(f775(f8(x83771,x83772),x83774),x83775))) % 186.05/186.62 [8641]E(x86411,f180(f857(x86412,a844)))+E(f775(f775(f46(x86412,f857(x86413,a844)),x86411),f775(f775(f10(f857(x86413,a844),f857(x86413,a844),x86412),f775(f103(f857(x86413,a844)),x86414)),x86415)),f775(f775(f103(f857(x86413,a844)),x86414),f775(f775(f46(x86412,f857(x86413,a844)),x86411),x86415))) % 186.05/186.62 [8642]E(x86421,f180(f857(x86422,a844)))+E(f775(f775(f47(x86422,f857(x86423,a844)),x86421),f775(f775(f10(f857(x86423,a844),f857(x86423,a844),x86422),f775(f3(f857(x86423,a844)),x86424)),x86425)),f775(f775(f3(f857(x86423,a844)),x86424),f775(f775(f46(x86422,f857(x86423,a844)),x86421),x86425))) % 186.05/186.62 [8643]E(x86431,f180(f857(x86432,a844)))+E(f775(f775(f47(x86432,f857(x86433,a844)),x86431),f775(f775(f10(f857(x86433,a844),f857(x86433,a844),x86432),f775(f104(f857(x86433,a844)),x86434)),x86435)),f775(f775(f104(f857(x86433,a844)),x86434),f775(f775(f47(x86432,f857(x86433,a844)),x86431),x86435))) % 186.05/186.62 [9062]~P29(x90622,x90621,x90623,f775(f775(f103(f857(x90622,a844)),x90624),x90625))+E(f775(f775(f104(f857(x90621,a844)),f775(f303(x90622,x90621,x90623),f775(f775(f3(f857(x90622,a844)),x90624),x90625))),f775(f303(x90622,x90621,x90623),f775(f775(f3(f857(x90622,a844)),x90625),x90624))),f180(f857(x90621,a844))) % 186.05/186.62 [9317]~P1(f775(f775(f232(f857(x93173,a844)),f775(f277(x93171,x93173,x93174),x93172)),x93175))+P1(f775(f775(f232(f857(x93171,a844)),x93172),f775(f81(f857(x93171,a844)),f775(f277(x93173,x93171,f775(f278(x93171,x93173),x93174)),f775(f81(f857(x93173,a844)),x93175))))) % 186.05/186.62 [9340]~P29(x93401,x93402,x93403,f775(f775(f302(x93401),x93404),x93405))+~P1(f775(f775(f334(x93402),f775(x93403,x93404)),f775(f303(x93401,x93402,x93403),f775(f775(f3(f857(x93401,a844)),x93405),f775(f775(f302(x93401),x93404),f180(f857(x93401,a844))))))) % 186.05/186.62 [9389]P1(f775(f775(f232(f857(x93891,a844)),f775(f277(x93892,x93891,x93893),x93894)),x93895))+~P1(f775(f775(f232(f857(x93892,a844)),x93894),f775(f81(f857(x93892,a844)),f775(f277(x93891,x93892,f775(f278(x93892,x93891),x93893)),f775(f81(f857(x93891,a844)),x93895))))) % 186.05/186.62 [9462]~P79(x94621)+P1(f775(f775(f232(x94621),f775(f77(x94621),f775(f775(f3(x94621),f775(f775(f82(x94621),x94622),x94623)),f775(f775(f82(x94621),x94624),x94625)))),f775(f775(f82(x94621),f775(f77(x94621),f775(f775(f3(x94621),x94622),x94624))),f775(f77(x94621),f775(f775(f3(x94621),x94623),x94625))))) % 186.05/186.62 [9555]P1(f775(f775(f334(x95551),f392(x95552,x95553,x95554,x95551,x95555)),x95554))+P1(f775(f775(f232(f857(x95555,a844)),f775(f775(f46(x95551,f857(x95555,a844)),x95554),x95553)),x95552)) % 186.05/186.62 [9727]~P1(f775(f775(f232(f857(x97271,a844)),f775(x97274,f392(x97275,x97274,x97273,x97272,x97271))),x97275))+P1(f775(f775(f232(f857(x97271,a844)),f775(f775(f46(x97272,f857(x97271,a844)),x97273),x97274)),x97275)) % 186.05/186.62 [8486]E(f775(f775(f125(x84861),x84862),f775(f775(f148(x84861,x84863),f775(f775(f3(a850),x84864),f775(f181(f851(x84861)),x84862))),x84865)),f775(f775(f148(x84861,f775(f775(f125(x84861),x84862),x84863)),x84864),x84865))+P1(f775(f775(f233(a850),x84864),f775(f181(f851(x84861)),x84862))) % 186.05/186.62 [8511]~P135(x85111)+E(f775(f775(f82(x85111),f775(f775(f83(x85111),x85112),x85113)),f775(f775(f82(x85111),f775(f775(f83(x85111),x85114),x85113)),x85115)),f775(f775(f82(x85111),f775(f775(f83(x85111),f775(f775(f82(x85111),x85112),x85114)),x85113)),x85115)) % 186.05/186.62 [9019]~P136(x90191)+E(f775(f155(x90191),f775(f775(f143(x90192,x90191),f775(f775(f10(x90191,x90191,x90192),f775(f83(x90191),x90193)),x90194)),x90195)),f775(f775(f83(x90191),x90193),f775(f155(x90191),f775(f775(f143(x90192,x90191),x90194),x90195)))) % 186.05/186.62 [9396]~P136(x93962)+E(f775(f775(f8(x93961,x93962),f775(f775(f9(x93961,x93962,x93962),f775(f775(f10(x93962,f857(x93962,x93962),x93961),f83(x93962)),x93963)),x93964)),x93965),f775(f775(f83(x93962),f775(f775(f8(x93961,x93962),x93963),x93965)),x93964)) % 186.05/186.62 [9397]~P61(x93972)+E(f775(f775(f8(x93971,x93972),f775(f775(f9(x93971,x93972,x93972),f775(f775(f10(x93972,f857(x93972,x93972),x93971),f283(x93972)),x93973)),x93974)),x93975),f775(f775(f283(x93972),f775(f775(f8(x93971,x93972),x93973),x93975)),x93974)) % 186.05/186.62 [9404]~P66(x94042)+E(f775(f775(f8(x94041,x94042),f775(f775(f20(x94041,x94042,x94042),f775(f775(f10(x94042,f857(x94042,x94042),x94041),f82(x94042)),x94043)),x94044)),x94045),f775(f775(f82(x94042),f775(f775(f8(x94041,x94042),x94043),x94045)),f775(f775(f8(x94041,x94042),x94044),x94045))) % 186.05/186.62 [9405]~P6(x94052)+E(f775(f775(f8(x94051,x94052),f775(f775(f20(x94051,x94052,x94052),f775(f775(f10(x94052,f857(x94052,x94052),x94051),f3(x94052)),x94053)),x94054)),x94055),f775(f775(f3(x94052),f775(f775(f8(x94051,x94052),x94053),x94055)),f775(f775(f8(x94051,x94052),x94054),x94055))) % 186.05/186.62 [9406]~P70(x94062)+E(f775(f775(f11(x94061,x94062),f775(f775(f20(x94061,x94062,x94062),f775(f775(f10(x94062,f857(x94062,x94062),x94061),f83(x94062)),x94063)),x94064)),x94065),f775(f775(f83(x94062),f775(f775(f11(x94061,x94062),x94063),x94065)),f775(f775(f11(x94061,x94062),x94064),x94065))) % 186.05/186.62 [9445]~E(x94453,f180(f857(x94451,a844)))+E(f775(f775(f46(x94451,f857(x94452,a844)),x94453),f775(f775(f9(x94451,f857(x94452,a844),f857(x94452,a844)),f775(f775(f10(f857(x94452,a844),f857(f857(x94452,a844),f857(x94452,a844)),x94451),f103(f857(x94452,a844))),x94454)),x94455)),f180(f857(x94452,a844))) % 186.05/186.62 [9446]~E(x94463,f180(f857(x94461,a844)))+E(f775(f775(f47(x94461,f857(x94462,a844)),x94463),f775(f775(f9(x94461,f857(x94462,a844),f857(x94462,a844)),f775(f775(f10(f857(x94462,a844),f857(f857(x94462,a844),f857(x94462,a844)),x94461),f3(f857(x94462,a844))),x94464)),x94465)),f239(f857(x94462,a844))) % 186.05/186.62 [9447]~E(x94473,f180(f857(x94471,a844)))+E(f775(f775(f47(x94471,f857(x94472,a844)),x94473),f775(f775(f9(x94471,f857(x94472,a844),f857(x94472,a844)),f775(f775(f10(f857(x94472,a844),f857(f857(x94472,a844),f857(x94472,a844)),x94471),f104(f857(x94472,a844))),x94474)),x94475)),f239(f857(x94472,a844))) % 186.05/186.62 [9472]E(x94721,f180(f857(x94722,a844)))+E(f775(f775(f46(x94722,f857(x94723,a844)),x94721),f775(f775(f9(x94722,f857(x94723,a844),f857(x94723,a844)),f775(f775(f10(f857(x94723,a844),f857(f857(x94723,a844),f857(x94723,a844)),x94722),f103(f857(x94723,a844))),x94724)),x94725)),f775(f775(f103(f857(x94723,a844)),f775(f775(f46(x94722,f857(x94723,a844)),x94721),x94724)),x94725)) % 186.05/186.62 [9473]E(x94731,f180(f857(x94732,a844)))+E(f775(f775(f47(x94732,f857(x94733,a844)),x94731),f775(f775(f9(x94732,f857(x94733,a844),f857(x94733,a844)),f775(f775(f10(f857(x94733,a844),f857(f857(x94733,a844),f857(x94733,a844)),x94732),f3(f857(x94733,a844))),x94734)),x94735)),f775(f775(f3(f857(x94733,a844)),f775(f775(f47(x94732,f857(x94733,a844)),x94731),x94734)),x94735)) % 186.05/186.62 [9474]E(x94741,f180(f857(x94742,a844)))+E(f775(f775(f47(x94742,f857(x94743,a844)),x94741),f775(f775(f9(x94742,f857(x94743,a844),f857(x94743,a844)),f775(f775(f10(f857(x94743,a844),f857(f857(x94743,a844),f857(x94743,a844)),x94742),f104(f857(x94743,a844))),x94744)),x94745)),f775(f775(f104(f857(x94743,a844)),f775(f775(f47(x94742,f857(x94743,a844)),x94741),x94744)),x94745)) % 186.05/186.62 [9066]~P1(f775(f775(f232(a850),x90661),x90664))+E(f775(f775(f3(a850),f775(f775(f82(a850),f775(f775(f83(a850),x90661),x90662)),x90663)),f775(f775(f82(a850),f775(f775(f83(a850),x90664),x90662)),x90665)),f775(f775(f3(a850),x90663),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x90664),x90661)),x90662)),x90665))) % 186.05/186.62 [9608]~P136(x96081)+E(f775(f155(x96081),f775(f775(f143(x96082,x96081),f775(f775(f9(x96082,x96081,x96081),f775(f775(f10(x96081,f857(x96081,x96081),x96082),f83(x96081)),x96083)),x96084)),x96085)),f775(f775(f83(x96081),f775(f155(x96081),f775(f775(f143(x96082,x96081),x96083),x96085))),x96084)) % 186.05/186.62 [9614]~P66(x96141)+E(f775(f155(x96141),f775(f775(f143(x96142,x96141),f775(f775(f20(x96142,x96141,x96141),f775(f775(f10(x96141,f857(x96141,x96141),x96142),f82(x96141)),x96143)),x96144)),x96145)),f775(f775(f82(x96141),f775(f155(x96141),f775(f775(f143(x96142,x96141),x96143),x96145))),f775(f155(x96141),f775(f775(f143(x96142,x96141),x96144),x96145)))) % 186.05/186.62 [9615]~P6(x96151)+E(f775(f155(x96151),f775(f775(f143(x96152,x96151),f775(f775(f20(x96152,x96151,x96151),f775(f775(f10(x96151,f857(x96151,x96151),x96152),f3(x96151)),x96153)),x96154)),x96155)),f775(f775(f3(x96151),f775(f155(x96151),f775(f775(f143(x96152,x96151),x96153),x96155))),f775(f155(x96151),f775(f775(f143(x96152,x96151),x96154),x96155)))) % 186.05/186.62 [9284]~P1(f775(f775(f232(a850),x92844),x92841))+E(f775(f775(f3(a850),f775(f775(f82(a850),f775(f775(f83(a850),x92841),x92842)),x92843)),f775(f775(f82(a850),f775(f775(f83(a850),x92844),x92842)),x92845)),f775(f775(f3(a850),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x92841),x92844)),x92842)),x92843)),x92845)) % 186.05/186.62 [10012]P28(x100121,x100122,f775(f303(a846,f849(x100121),f775(f775(f20(a846,f857(x100121,f857(a847,a844)),f849(x100121)),f775(f775(f20(a846,a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),f775(f775(f10(f857(x100121,f857(a847,a844)),f857(a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),a846),f93(x100121)),x100123)),a27)),x100124)),x100125))+~P28(x100121,f775(f775(f103(f857(f849(x100121),a844)),x100122),f775(f303(a846,f849(x100121),f775(f775(f20(a846,f857(x100121,f857(a847,a844)),f849(x100121)),f775(f775(f20(a846,a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),f775(f775(f10(f857(x100121,f857(a847,a844)),f857(a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),a846),f93(x100121)),x100123)),a27)),x100124)),x100125)),f775(f303(a846,f849(x100121),f775(f775(f20(a846,f857(x100121,f857(a847,a844)),f849(x100121)),f775(f775(f20(a846,a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),f775(f775(f10(f857(x100121,f857(a847,a844)),f857(a845,f857(f857(x100121,f857(a847,a844)),f849(x100121))),a846),f93(x100121)),x100123)),f775(f775(f10(f854(a845),a845,a846),f231(a845)),a30))),x100124)),x100125)) % 186.05/186.62 [5145]E(x51451,x51452)+~E(f33(x51453,x51454,x51451),f33(x51455,x51456,x51452)) % 186.05/186.62 [5146]E(x51461,x51462)+~E(f33(x51463,x51461,x51464),f33(x51465,x51462,x51466)) % 186.05/186.62 [5147]E(x51471,x51472)+~E(f33(x51471,x51473,x51474),f33(x51472,x51475,x51476)) % 186.05/186.62 [5148]E(x51481,x51482)+~E(f32(x51483,x51484,x51481),f32(x51485,x51486,x51482)) % 186.05/186.62 [5149]E(x51491,x51492)+~E(f32(x51493,x51491,x51494),f32(x51495,x51492,x51496)) % 186.05/186.62 [5150]E(x51501,x51502)+~E(f32(x51501,x51503,x51504),f32(x51502,x51505,x51506)) % 186.05/186.62 [5151]E(x51511,x51512)+~E(f31(x51513,x51514,x51511),f31(x51515,x51516,x51512)) % 186.05/186.62 [5152]E(x51521,x51522)+~E(f31(x51523,x51521,x51524),f31(x51525,x51522,x51526)) % 186.05/186.62 [5153]E(x51531,x51532)+~E(f31(x51531,x51533,x51534),f31(x51532,x51535,x51536)) % 186.05/186.62 [7172]E(x71721,x71722)+~E(f215(x71723,x71724,x71725,x71721),f215(x71723,x71724,x71726,x71722)) % 186.05/186.62 [7173]E(x71731,x71732)+~E(f215(x71733,x71734,x71731,x71735),f215(x71733,x71734,x71732,x71736)) % 186.05/186.62 [6615]E(f775(f170(x66151,x66152,x66153,x66154),x66155),f775(f227(x66152),x66156))+~E(f775(x66154,x66155),f775(f227(x66152),x66156)) % 186.05/186.62 [6767]E(f775(f229(f854(x67671),x67672,f183(x67671),x67673),f775(x67674,x67675)),f775(x67673,x67676))+~E(f775(x67674,x67675),f775(f227(x67672),x67676)) % 186.05/186.62 [8313]~P23(x83135,x83131,x83132,x83136)+E(f775(f75(x83131,x83131,x83131,f775(x83132,x83133)),f775(x83132,x83134)),f775(f75(x83131,x83131,x83131,f775(x83132,x83134)),f775(x83132,x83133))) % 186.05/186.62 [8546]~P55(x85464,x85465,x85462,x85461,x85466)+E(f775(x85461,f775(x85462,x85463)),x85463) % 186.05/186.62 [8687]P29(x86871,x86872,x86873,x86874)+~P29(x86871,x86875,f775(f75(x86872,x86875,x86871,x86876),x86873),x86874) % 186.05/186.62 [8764]~P29(x87644,x87642,f775(f75(x87641,x87642,x87644,x87643),x87645),x87646)+P29(x87641,x87642,x87643,f775(f303(x87644,x87641,x87645),x87646)) % 186.05/186.62 [9407]P1(f775(f63(x94071),x94072))+~P1(f775(f68(x94071,x94073,x94074,x94075,x94072),x94076)) % 186.05/186.62 [9417]~P1(f775(f775(f334(x94174),x94173),f292(x94174,x94175,x94171,x94172,x94176)))+P1(f775(f775(x94171,x94172),x94173)) % 186.05/186.62 [9418]~P1(f775(f775(f334(x94184),x94183),f289(x94184,x94181,x94185,x94182,x94186)))+P1(f775(f775(x94181,x94182),x94183)) % 186.05/186.62 [9419]~P1(f775(f775(f334(x94194),x94192),f292(x94194,x94191,x94195,x94196,x94193)))+P1(f775(f775(x94191,x94192),x94193)) % 186.05/186.62 [9420]~P1(f775(f775(f334(x94204),x94202),f289(x94204,x94205,x94201,x94206,x94203)))+P1(f775(f775(x94201,x94202),x94203)) % 186.05/186.62 [5632]E(x56321,x56322)+~E(f775(f775(f241(x56323,x56324),x56325),x56321),f775(f775(f241(x56323,x56324),x56326),x56322)) % 186.05/186.62 [5634]E(x56341,x56342)+~E(f775(f775(f241(x56343,x56344),x56341),x56345),f775(f775(f241(x56343,x56344),x56342),x56346)) % 186.05/186.62 [5773]~P20(x57735,x57736,x57731)+E(f775(f775(x57731,x57732),f775(f775(x57731,x57733),x57734)),f775(f775(x57731,x57733),f775(f775(x57731,x57732),x57734))) % 186.05/186.62 [7243]~P34(x72434,x72431,f775(f775(f140(x72434),x72432),x72435),f775(f775(f140(x72434),x72433),x72436))+P1(f775(f775(x72431,x72432),x72433)) % 186.05/186.62 [7622]P34(x76221,x76222,x76223,x76224)+~P34(x76221,x76222,f775(f775(f140(x76221),x76225),x76223),f775(f775(f140(x76221),x76226),x76224)) % 186.05/186.62 [8632]~P55(x86325,x86321,x86322,x86326,x86324)+P1(f775(f775(f334(x86321),f775(x86322,x86323)),x86324)) % 186.05/186.62 [8786]E(f775(f78(x87861,x87862,x87863,x87864,x87865),x87866),f775(x87863,x87866))+P1(f775(f775(f334(x87861),x87866),x87865)) % 186.05/186.62 [8804]~E(x88043,f775(f775(f140(x88041),x88045),x88046))+P1(f775(f775(f334(f856(f851(x88041),f851(x88041))),f775(f775(f241(f851(x88041),f851(x88041)),x88042),f775(f775(f125(x88041),x88042),x88043))),f137(x88041,x88044))) % 186.05/186.62 [8808]E(f775(f78(x88081,x88082,x88083,x88084,x88085),x88086),f775(x88084,x88086))+~P1(f775(f775(f334(x88081),x88086),x88085)) % 186.05/186.62 [9484]~P27(x94844,x94842,x94845,x94843,x94846,x94841)+E(f775(x94841,f180(f857(x94842,a844))),x94843) % 186.05/186.62 [9689]~E(f775(x96894,f775(f240(x96891,x96893),x96895)),f775(x96896,f775(f240(x96891,x96893),x96895)))+E(f775(f252(x96891,x96892,x96893,x96893,x96894,f39(x96893)),x96895),f775(f252(x96891,x96892,x96893,x96893,x96896,f39(x96893)),x96895)) % 186.05/186.62 [9690]~E(f775(x96904,f775(f250(x96901,x96902),x96905)),f775(x96906,f775(f250(x96901,x96902),x96905)))+E(f775(f252(x96901,x96901,x96902,x96903,f39(x96901),x96904),x96905),f775(f252(x96901,x96901,x96902,x96903,f39(x96901),x96906),x96905)) % 186.05/186.62 [9750]~E(f775(f252(x97502,x97506,x97503,x97503,x97501,f39(x97503)),x97504),f775(f252(x97502,x97506,x97503,x97503,x97505,f39(x97503)),x97504))+E(f775(x97501,f775(f240(x97502,x97503),x97504)),f775(x97505,f775(f240(x97502,x97503),x97504))) % 186.05/186.62 [9751]~E(f775(f252(x97512,x97512,x97513,x97516,f39(x97512),x97511),x97514),f775(f252(x97512,x97512,x97513,x97516,f39(x97512),x97515),x97514))+E(f775(x97511,f775(f250(x97512,x97513),x97514)),f775(x97515,f775(f250(x97512,x97513),x97514))) % 186.05/186.62 [8721]P1(f775(f775(f334(x87211),x87212),x87213))+~P1(f775(f775(f334(f856(x87211,x87214)),f775(f775(f241(x87211,x87214),x87212),x87215)),f775(f775(f248(x87211,x87214),x87213),x87216))) % 186.05/186.62 [8736]P1(f775(f775(f334(x87361),x87362),f775(x87363,x87364)))+~P1(f775(f775(f334(f856(x87365,x87361)),f775(f775(f241(x87365,x87361),x87364),x87362)),f775(f775(f248(x87365,x87361),x87366),x87363))) % 186.05/186.62 [9042]P1(f775(f775(f334(x90421),x90424),f169(x90421,x90422,x90426)))+E(f170(x90421,x90422,f775(f775(f775(f74(x90421,f854(x90422)),x90423),x90424),f775(f227(x90422),x90425)),x90426),f775(f775(f775(f74(x90421,f854(x90422)),f170(x90421,x90422,x90423,x90426)),x90424),f775(f227(x90422),x90425))) % 186.05/186.62 [9133]P1(f775(f775(f334(f856(x91331,x91331)),f775(f775(f241(x91331,x91331),f775(x91332,x91333)),f775(x91332,x91334))),x91335))+~P1(f775(f775(f334(f856(x91336,x91336)),f775(f775(f241(x91336,x91336),x91333),x91334)),f775(f775(f280(x91331,x91336),x91335),x91332))) % 186.05/186.62 [9145]~P1(f775(f775(f334(f856(x91454,x91454)),f775(f775(f241(x91454,x91454),f775(x91456,x91452)),f775(x91456,x91453))),x91455))+P1(f775(f775(f334(f856(x91451,x91451)),f775(f775(f241(x91451,x91451),x91452),x91453)),f775(f775(f280(x91454,x91451),x91455),x91456))) % 186.05/186.62 [9753]E(f775(f775(f241(x97531,x97532),f706(x97533,x97534,x97535,x97536,x97532,x97531)),f709(x97533,x97534,x97535,x97536,x97532,x97531)),x97536)+~P1(f775(f775(f334(f856(x97531,x97532)),x97536),f775(f775(f281(x97531,x97535,x97532),x97534),x97533))) % 186.05/186.62 [9961]~P1(f775(f775(f334(f856(x99611,x99616)),x99615),f775(f775(f281(x99611,x99612,x99616),x99614),x99613)))+P1(f775(f775(f334(f856(x99611,x99612)),f775(f775(f241(x99611,x99612),f706(x99613,x99614,x99612,x99615,x99616,x99611)),f710(x99613,x99614,x99612,x99615,x99616,x99611))),x99614)) % 186.05/186.62 [9962]~P1(f775(f775(f334(f856(x99626,x99622)),x99625),f775(f775(f281(x99626,x99621,x99622),x99624),x99623)))+P1(f775(f775(f334(f856(x99621,x99622)),f775(f775(f241(x99621,x99622),f710(x99623,x99624,x99621,x99625,x99622,x99626)),f709(x99623,x99624,x99621,x99625,x99622,x99626))),x99623)) % 186.05/186.62 [6051]~E(x60516,x60514)+E(f775(f775(f775(f775(f74(x60511,x60512),x60513),x60514),x60515),x60516),x60515) % 186.05/186.62 [6100]E(x61001,x61002)+E(f775(f775(f775(f775(f74(x61003,x61004),x61005),x61002),x61006),x61001),f775(x61005,x61001)) % 186.05/186.62 [7688]~P9(x76882)+E(f775(f775(f46(x76881,x76882),x76883),f775(f775(f9(x76881,x76884,x76882),x76885),x76886)),f775(f775(f775(f46(x76881,f857(x76884,x76882)),x76883),x76885),x76886)) % 186.05/186.62 [7689]~P9(x76892)+E(f775(f775(f47(x76891,x76892),x76893),f775(f775(f9(x76891,x76894,x76892),x76895),x76896)),f775(f775(f775(f47(x76891,f857(x76894,x76892)),x76893),x76895),x76896)) % 186.05/186.62 [8468]E(f775(f775(f46(x84681,f857(x84682,a844)),x84683),f775(f775(f10(f857(x84682,a844),f857(x84682,a844),x84681),f775(f302(x84682),x84684)),x84685)),f775(f775(f302(x84682),x84684),f775(f775(f46(x84681,f857(x84682,a844)),x84683),x84685)))+~P1(f775(f775(f334(x84681),x84686),x84683)) % 186.05/186.62 [8848]~P9(x88482)+E(f775(f775(f46(x88481,x88482),x88483),f775(f775(f10(f857(x88484,x88482),x88482,x88481),f775(f46(x88484,x88482),x88485)),f775(f9(x88484,x88481,x88482),x88486))),f775(f775(f46(x88484,x88482),x88485),f775(f775(f10(f857(x88481,x88482),x88482,x88484),f775(f46(x88481,x88482),x88483)),x88486))) % 186.05/186.62 [8849]~P9(x88492)+E(f775(f775(f47(x88491,x88492),x88493),f775(f775(f10(f857(x88494,x88492),x88492,x88491),f775(f47(x88494,x88492),x88495)),f775(f9(x88494,x88491,x88492),x88496))),f775(f775(f47(x88494,x88492),x88495),f775(f775(f10(f857(x88491,x88492),x88492,x88494),f775(f47(x88491,x88492),x88493)),x88496))) % 186.05/186.62 [9050]P1(f775(f775(f334(x90501),x90502),f775(f158(x90501),x90503)))+~P1(f775(f775(f334(f856(x90504,x90501)),f775(f775(f241(x90504,x90501),x90505),x90502)),f775(f158(f856(x90504,x90501)),f775(f775(f167(x90504,x90501),x90506),x90503)))) % 186.05/186.62 [9051]P1(f775(f775(f334(x90511),x90512),f775(f158(x90511),x90513)))+~P1(f775(f775(f334(f856(x90511,x90514)),f775(f775(f241(x90511,x90514),x90512),x90515)),f775(f158(f856(x90511,x90514)),f775(f775(f167(x90511,x90514),x90513),x90516)))) % 186.05/186.62 [9143]P1(f775(f775(f232(f857(x91431,a844)),f775(f277(x91432,x91431,x91433),x91434)),x91435))+~P1(f775(f775(f232(f857(f856(x91432,x91431),a844)),x91433),f775(f775(f248(x91432,x91431),x91436),f775(f18(f857(x91431,a844),x91432),x91435)))) % 186.05/186.62 [9320]P1(f775(f775(f334(f856(f851(x93201),f851(x93201))),f775(f775(f241(f851(x93201),f851(x93201)),f775(f775(f140(x93201),x93202),x93203)),f775(f775(f140(x93201),x93204),x93205))),f137(x93201,x93206)))+~P1(f775(f775(f334(f856(x93201,x93201)),f775(f775(f241(x93201,x93201),x93202),x93204)),x93206)) % 186.05/186.62 [9749]E(f775(f775(f241(x97491,x97492),f613(x97493,x97494,x97495,x97492,x97491,x97496)),f616(x97493,x97494,x97495,x97492,x97491,x97496)),x97496)+P1(f775(f775(f334(x97495),x97494),f775(f775(f251(x97491,x97492,f857(x97495,a844)),x97493),x97496))) % 186.05/186.62 [9754]E(f775(f775(f241(x97541,x97542),f614(x97543,x97544,x97542,x97541,x97545,x97546)),f615(x97543,x97544,x97542,x97541,x97545,x97546)),x97543)+~P1(f775(f775(f334(x97546),x97545),f775(f775(f251(x97541,x97542,f857(x97546,a844)),x97544),x97543))) % 186.05/186.62 [9916]P1(f775(f775(f334(x99161),x99162),f775(f775(x99163,f614(x99164,x99163,x99165,x99166,x99162,x99161)),f615(x99164,x99163,x99165,x99166,x99162,x99161))))+~P1(f775(f775(f334(x99161),x99162),f775(f775(f251(x99166,x99165,f857(x99161,a844)),x99163),x99164))) % 186.05/186.62 [9940]~P1(f775(f775(f334(x99401),x99402),f775(f775(x99405,f613(x99405,x99402,x99401,x99404,x99403,x99406)),f616(x99405,x99402,x99401,x99404,x99403,x99406))))+P1(f775(f775(f334(x99401),x99402),f775(f775(f251(x99403,x99404,f857(x99401,a844)),x99405),x99406))) % 186.05/186.62 [7813]P1(f775(f775(f334(x78131),x78134),x78136))+E(f172(x78131,x78132,f775(f775(f775(f74(x78131,f854(x78132)),x78133),x78134),x78135),x78136),f172(x78131,x78132,x78133,x78136)) % 186.05/186.62 [7888]P1(f775(f775(f334(x78881),x78884),x78886))+E(f775(f303(x78881,x78882,f775(f775(f775(f74(x78881,x78882),x78883),x78884),x78885)),x78886),f775(f303(x78881,x78882,x78883),x78886)) % 186.05/186.62 [7916]P1(f775(f775(f334(x79161),x79164),f775(f158(x79161),x79166)))+E(f775(f775(f143(x79161,x79162),f775(f775(f775(f74(x79161,x79162),x79163),x79164),x79165)),x79166),f775(f775(f143(x79161,x79162),x79163),x79166)) % 186.05/186.62 [8363]E(x83631,x83632)+E(f775(f775(f148(x83633,f775(f775(f148(x83633,x83634),x83631),x83635)),x83632),x83636),f775(f775(f148(x83633,f775(f775(f148(x83633,x83634),x83632),x83636)),x83631),x83635)) % 186.05/186.62 [8854]~P1(f775(f775(f334(x88543),x88546),x88545))+E(f775(f775(f302(x88541),x88542),f775(f303(x88543,x88541,x88544),f775(f775(f3(f857(x88543,a844)),x88545),f775(f775(f302(x88543),x88546),f180(f857(x88543,a844)))))),f775(f303(x88543,x88541,f775(f775(f775(f74(x88543,x88541),x88544),x88546),x88542)),x88545)) % 186.05/186.62 [8682]~E(x86823,x86826)+E(f775(f166(x86821,x86822,f775(f775(f140(f856(x86821,x86822)),f775(f775(f241(x86821,x86822),x86823),x86824)),x86825)),x86826),f775(f227(x86822),x86824)) % 186.05/186.62 [8723]E(x87231,x87232)+E(f775(f166(x87233,x87234,f775(f775(f140(f856(x87233,x87234)),f775(f775(f241(x87233,x87234),x87231),x87235)),x87236)),x87232),f775(f166(x87233,x87234,x87236),x87232)) % 186.05/186.62 [8929]~P1(f775(f775(x89294,x89295),x89296))+P1(f775(f775(f775(f775(f103(f857(x89291,f857(x89292,a844))),x89293),x89294),x89295),x89296)) % 186.05/186.62 [8931]~P1(f775(f775(x89313,x89315),x89316))+P1(f775(f775(f775(f775(f103(f857(x89311,f857(x89312,a844))),x89313),x89314),x89315),x89316)) % 186.05/186.62 [8947]P1(f775(f775(f334(x89471),x89476),f775(f158(x89471),x89474)))+E(f775(f170(x89471,x89472,x89473,f166(x89471,x89472,f775(f142(f856(x89471,x89472)),f775(f775(f167(x89471,x89472),x89474),x89475)))),x89476),f775(x89473,x89476)) % 186.05/186.62 [9096]~E(f775(f181(f851(x90961)),x90964),f775(f181(f851(x90962)),x90965))+E(f170(x90961,x90962,x90963,f166(x90961,x90962,f775(f142(f856(x90961,x90962)),f775(f775(f167(x90961,x90962),x90964),f775(f775(f125(x90962),x90965),x90966))))),f170(x90961,x90962,x90963,f166(x90961,x90962,f775(f142(f856(x90961,x90962)),f775(f775(f167(x90961,x90962),x90964),x90965))))) % 186.05/186.62 [9183]P1(f775(f775(x91831,x91832),x91833))+~P1(f775(f775(f775(f775(f104(f857(x91834,f857(x91835,a844))),x91836),x91831),x91832),x91833)) % 186.05/186.62 [9184]P1(f775(f775(x91841,x91842),x91843))+~P1(f775(f775(f775(f775(f104(f857(x91844,f857(x91845,a844))),x91841),x91846),x91842),x91843)) % 186.05/186.62 [9597]~P66(x95972)+E(f775(f775(f8(x95971,x95972),f775(f775(f9(x95971,f857(x95973,a844),x95972),f775(f775(f10(f857(x95973,x95972),f857(f857(x95973,a844),x95972),x95971),f8(x95973,x95972)),x95974)),x95975)),x95976),f775(f775(f8(f856(x95971,x95973),x95972),f775(f251(x95971,x95973,x95972),x95974)),f775(f775(f248(x95971,x95973),x95976),f775(f18(f857(x95973,a844),x95971),x95975)))) % 186.05/186.62 [9598]~P70(x95982)+E(f775(f775(f11(x95981,x95982),f775(f775(f9(x95981,f857(x95983,a844),x95982),f775(f775(f10(f857(x95983,x95982),f857(f857(x95983,a844),x95982),x95981),f11(x95983,x95982)),x95984)),x95985)),x95986),f775(f775(f11(f856(x95981,x95983),x95982),f775(f251(x95981,x95983,x95982),x95984)),f775(f775(f248(x95981,x95983),x95986),f775(f18(f857(x95983,a844),x95981),x95985)))) % 186.05/186.62 [9716]~P66(x97162)+E(f775(f775(f8(x97161,x97162),f775(f775(f9(x97161,f857(x97163,a844),x97162),f775(f775(f10(f857(x97163,x97162),f857(f857(x97163,a844),x97162),x97161),f8(x97163,x97162)),f775(f9(x97163,x97161,x97162),x97164))),x97165)),x97166),f775(f775(f8(x97163,x97162),f775(f775(f9(x97163,f857(x97161,a844),x97162),f775(f775(f10(f857(x97161,x97162),f857(f857(x97161,a844),x97162),x97163),f8(x97161,x97162)),x97164)),x97166)),x97165)) % 186.05/186.62 [9185]~E(f775(f181(f851(x91851)),x91854),f775(f181(f851(x91852)),x91856))+E(f170(x91851,x91852,x91853,f166(x91851,x91852,f775(f142(f856(x91851,x91852)),f775(f775(f167(x91851,x91852),f775(f775(f125(x91851),x91854),x91855)),x91856)))),f170(x91851,x91852,x91853,f166(x91851,x91852,f775(f142(f856(x91851,x91852)),f775(f775(f167(x91851,x91852),x91854),x91856))))) % 186.05/186.62 [9449]~P1(f775(f775(f334(x94491),x94495),x94494))+E(f775(f775(f775(f74(x94491,f854(x94492)),f172(x94491,x94492,x94493,f775(f775(f3(f857(x94491,a844)),x94494),f775(f775(f302(x94491),x94495),f180(f857(x94491,a844)))))),x94495),x94496),f172(x94491,x94492,f775(f775(f775(f74(x94491,f854(x94492)),x94493),x94495),x94496),x94494)) % 186.05/186.62 [9656]E(f170(x96561,x96562,x96563,f166(x96561,x96562,f775(f142(f856(x96561,x96562)),f775(f775(f167(x96561,x96562),f775(f775(f125(x96561),x96564),f775(f775(f140(x96561),x96565),f115(x96561)))),x96566)))),f775(f775(f775(f74(x96561,f854(x96562)),f170(x96561,x96562,x96563,f166(x96561,x96562,f775(f142(f856(x96561,x96562)),f775(f775(f167(x96561,x96562),x96564),x96566))))),x96565),f775(f227(x96562),f775(f775(f153(x96562),x96566),f775(f181(f851(x96561)),x96564)))))+~P1(f775(f775(f233(a850),f775(f181(f851(x96561)),x96564)),f775(f181(f851(x96562)),x96566))) % 186.05/186.62 [10015]~P1(f775(f775(f334(f856(x100151,x100152)),f775(f775(f241(x100151,x100152),x100155),x100156)),f775(f775(f103(f857(f856(x100151,x100152),a844)),x100153),x100154)))+P1(f775(f775(f775(f775(f103(f857(x100151,f857(x100152,a844))),f775(f775(f9(x100151,f857(f856(x100151,x100152),a844),f857(x100152,a844)),f775(f775(f10(f857(x100152,f857(f857(f856(x100151,x100152),a844),a844)),f857(f857(f856(x100151,x100152),a844),f857(x100152,a844)),x100151),f9(x100152,f857(f856(x100151,x100152),a844),a844)),f775(f775(f10(f857(x100152,f856(x100151,x100152)),f857(x100152,f857(f857(f856(x100151,x100152),a844),a844)),x100151),f775(f10(f856(x100151,x100152),f857(f857(f856(x100151,x100152),a844),a844),x100152),f334(f856(x100151,x100152)))),f241(x100151,x100152)))),x100153)),f775(f775(f9(x100151,f857(f856(x100151,x100152),a844),f857(x100152,a844)),f775(f775(f10(f857(x100152,f857(f857(f856(x100151,x100152),a844),a844)),f857(f857(f856(x100151,x100152),a844),f857(x100152,a844)),x100151),f9(x100152,f857(f856(x100151,x100152),a844),a844)),f775(f775(f10(f857(x100152,f856(x100151,x100152)),f857(x100152,f857(f857(f856(x100151,x100152),a844),a844)),x100151),f775(f10(f856(x100151,x100152),f857(f857(f856(x100151,x100152),a844),a844),x100152),f334(f856(x100151,x100152)))),f241(x100151,x100152)))),x100154)),x100155),x100156)) % 186.05/186.62 [10016]~P1(f775(f775(f334(f856(x100161,x100162)),f775(f775(f241(x100161,x100162),x100165),x100166)),f775(f775(f104(f857(f856(x100161,x100162),a844)),x100163),x100164)))+P1(f775(f775(f775(f775(f104(f857(x100161,f857(x100162,a844))),f775(f775(f9(x100161,f857(f856(x100161,x100162),a844),f857(x100162,a844)),f775(f775(f10(f857(x100162,f857(f857(f856(x100161,x100162),a844),a844)),f857(f857(f856(x100161,x100162),a844),f857(x100162,a844)),x100161),f9(x100162,f857(f856(x100161,x100162),a844),a844)),f775(f775(f10(f857(x100162,f856(x100161,x100162)),f857(x100162,f857(f857(f856(x100161,x100162),a844),a844)),x100161),f775(f10(f856(x100161,x100162),f857(f857(f856(x100161,x100162),a844),a844),x100162),f334(f856(x100161,x100162)))),f241(x100161,x100162)))),x100163)),f775(f775(f9(x100161,f857(f856(x100161,x100162),a844),f857(x100162,a844)),f775(f775(f10(f857(x100162,f857(f857(f856(x100161,x100162),a844),a844)),f857(f857(f856(x100161,x100162),a844),f857(x100162,a844)),x100161),f9(x100162,f857(f856(x100161,x100162),a844),a844)),f775(f775(f10(f857(x100162,f856(x100161,x100162)),f857(x100162,f857(f857(f856(x100161,x100162),a844),a844)),x100161),f775(f10(f856(x100161,x100162),f857(f857(f856(x100161,x100162),a844),a844),x100162),f334(f856(x100161,x100162)))),f241(x100161,x100162)))),x100164)),x100165),x100166)) % 186.05/186.62 [10020]P1(f775(f775(f334(f856(x100201,x100202)),f775(f775(f241(x100201,x100202),x100203),x100204)),f775(f775(f103(f857(f856(x100201,x100202),a844)),x100205),x100206)))+~P1(f775(f775(f775(f775(f103(f857(x100201,f857(x100202,a844))),f775(f775(f9(x100201,f857(f856(x100201,x100202),a844),f857(x100202,a844)),f775(f775(f10(f857(x100202,f857(f857(f856(x100201,x100202),a844),a844)),f857(f857(f856(x100201,x100202),a844),f857(x100202,a844)),x100201),f9(x100202,f857(f856(x100201,x100202),a844),a844)),f775(f775(f10(f857(x100202,f856(x100201,x100202)),f857(x100202,f857(f857(f856(x100201,x100202),a844),a844)),x100201),f775(f10(f856(x100201,x100202),f857(f857(f856(x100201,x100202),a844),a844),x100202),f334(f856(x100201,x100202)))),f241(x100201,x100202)))),x100205)),f775(f775(f9(x100201,f857(f856(x100201,x100202),a844),f857(x100202,a844)),f775(f775(f10(f857(x100202,f857(f857(f856(x100201,x100202),a844),a844)),f857(f857(f856(x100201,x100202),a844),f857(x100202,a844)),x100201),f9(x100202,f857(f856(x100201,x100202),a844),a844)),f775(f775(f10(f857(x100202,f856(x100201,x100202)),f857(x100202,f857(f857(f856(x100201,x100202),a844),a844)),x100201),f775(f10(f856(x100201,x100202),f857(f857(f856(x100201,x100202),a844),a844),x100202),f334(f856(x100201,x100202)))),f241(x100201,x100202)))),x100206)),x100203),x100204)) % 186.05/186.62 [10021]P1(f775(f775(f334(f856(x100211,x100212)),f775(f775(f241(x100211,x100212),x100213),x100214)),f775(f775(f104(f857(f856(x100211,x100212),a844)),x100215),x100216)))+~P1(f775(f775(f775(f775(f104(f857(x100211,f857(x100212,a844))),f775(f775(f9(x100211,f857(f856(x100211,x100212),a844),f857(x100212,a844)),f775(f775(f10(f857(x100212,f857(f857(f856(x100211,x100212),a844),a844)),f857(f857(f856(x100211,x100212),a844),f857(x100212,a844)),x100211),f9(x100212,f857(f856(x100211,x100212),a844),a844)),f775(f775(f10(f857(x100212,f856(x100211,x100212)),f857(x100212,f857(f857(f856(x100211,x100212),a844),a844)),x100211),f775(f10(f856(x100211,x100212),f857(f857(f856(x100211,x100212),a844),a844),x100212),f334(f856(x100211,x100212)))),f241(x100211,x100212)))),x100215)),f775(f775(f9(x100211,f857(f856(x100211,x100212),a844),f857(x100212,a844)),f775(f775(f10(f857(x100212,f857(f857(f856(x100211,x100212),a844),a844)),f857(f857(f856(x100211,x100212),a844),f857(x100212,a844)),x100211),f9(x100212,f857(f856(x100211,x100212),a844),a844)),f775(f775(f10(f857(x100212,f856(x100211,x100212)),f857(x100212,f857(f857(f856(x100211,x100212),a844),a844)),x100211),f775(f10(f856(x100211,x100212),f857(f857(f856(x100211,x100212),a844),a844),x100212),f334(f856(x100211,x100212)))),f241(x100211,x100212)))),x100216)),x100213),x100214)) % 186.05/186.62 [10010]~P1(f775(f775(f334(f856(x100102,x100103)),f775(f775(f241(x100102,x100103),x100105),x100106)),f775(f775(f46(x100101,f857(f856(x100102,x100103),a844)),f239(f857(x100101,a844))),x100104)))+P1(f775(f775(f775(f775(f46(x100101,f857(x100102,f857(x100103,a844))),f239(f857(x100101,a844))),f775(f775(f10(f857(f856(x100102,x100103),a844),f857(x100102,f857(x100103,a844)),x100101),f775(f9(x100102,f857(f856(x100102,x100103),a844),f857(x100103,a844)),f775(f775(f10(f857(x100103,f857(f857(f856(x100102,x100103),a844),a844)),f857(f857(f856(x100102,x100103),a844),f857(x100103,a844)),x100102),f9(x100103,f857(f856(x100102,x100103),a844),a844)),f775(f775(f10(f857(x100103,f856(x100102,x100103)),f857(x100103,f857(f857(f856(x100102,x100103),a844),a844)),x100102),f775(f10(f856(x100102,x100103),f857(f857(f856(x100102,x100103),a844),a844),x100103),f334(f856(x100102,x100103)))),f241(x100102,x100103))))),x100104)),x100105),x100106)) % 186.05/186.62 [10011]~P1(f775(f775(f334(f856(x100112,x100113)),f775(f775(f241(x100112,x100113),x100115),x100116)),f775(f775(f47(x100111,f857(f856(x100112,x100113),a844)),f239(f857(x100111,a844))),x100114)))+P1(f775(f775(f775(f775(f47(x100111,f857(x100112,f857(x100113,a844))),f239(f857(x100111,a844))),f775(f775(f10(f857(f856(x100112,x100113),a844),f857(x100112,f857(x100113,a844)),x100111),f775(f9(x100112,f857(f856(x100112,x100113),a844),f857(x100113,a844)),f775(f775(f10(f857(x100113,f857(f857(f856(x100112,x100113),a844),a844)),f857(f857(f856(x100112,x100113),a844),f857(x100113,a844)),x100112),f9(x100113,f857(f856(x100112,x100113),a844),a844)),f775(f775(f10(f857(x100113,f856(x100112,x100113)),f857(x100113,f857(f857(f856(x100112,x100113),a844),a844)),x100112),f775(f10(f856(x100112,x100113),f857(f857(f856(x100112,x100113),a844),a844),x100113),f334(f856(x100112,x100113)))),f241(x100112,x100113))))),x100114)),x100115),x100116)) % 186.05/186.62 [10018]P1(f775(f775(f334(f856(x100181,x100182)),f775(f775(f241(x100181,x100182),x100183),x100184)),f775(f775(f46(x100185,f857(f856(x100181,x100182),a844)),f239(f857(x100185,a844))),x100186)))+~P1(f775(f775(f775(f775(f46(x100185,f857(x100181,f857(x100182,a844))),f239(f857(x100185,a844))),f775(f775(f10(f857(f856(x100181,x100182),a844),f857(x100181,f857(x100182,a844)),x100185),f775(f9(x100181,f857(f856(x100181,x100182),a844),f857(x100182,a844)),f775(f775(f10(f857(x100182,f857(f857(f856(x100181,x100182),a844),a844)),f857(f857(f856(x100181,x100182),a844),f857(x100182,a844)),x100181),f9(x100182,f857(f856(x100181,x100182),a844),a844)),f775(f775(f10(f857(x100182,f856(x100181,x100182)),f857(x100182,f857(f857(f856(x100181,x100182),a844),a844)),x100181),f775(f10(f856(x100181,x100182),f857(f857(f856(x100181,x100182),a844),a844),x100182),f334(f856(x100181,x100182)))),f241(x100181,x100182))))),x100186)),x100183),x100184)) % 186.05/186.62 [10019]P1(f775(f775(f334(f856(x100191,x100192)),f775(f775(f241(x100191,x100192),x100193),x100194)),f775(f775(f47(x100195,f857(f856(x100191,x100192),a844)),f239(f857(x100195,a844))),x100196)))+~P1(f775(f775(f775(f775(f47(x100195,f857(x100191,f857(x100192,a844))),f239(f857(x100195,a844))),f775(f775(f10(f857(f856(x100191,x100192),a844),f857(x100191,f857(x100192,a844)),x100195),f775(f9(x100191,f857(f856(x100191,x100192),a844),f857(x100192,a844)),f775(f775(f10(f857(x100192,f857(f857(f856(x100191,x100192),a844),a844)),f857(f857(f856(x100191,x100192),a844),f857(x100192,a844)),x100191),f9(x100192,f857(f856(x100191,x100192),a844),a844)),f775(f775(f10(f857(x100192,f856(x100191,x100192)),f857(x100192,f857(f857(f856(x100191,x100192),a844),a844)),x100191),f775(f10(f856(x100191,x100192),f857(f857(f856(x100191,x100192),a844),a844),x100192),f334(f856(x100191,x100192)))),f241(x100191,x100192))))),x100196)),x100193),x100194)) % 186.05/186.62 [9118]E(x91181,x91182)+~E(f319(x91183,x91184,x91185,x91186,x91181),f319(x91183,x91184,x91185,x91187,x91182)) % 186.05/186.62 [9119]E(x91191,x91192)+~E(f319(x91193,x91194,x91195,x91191,x91196),f319(x91193,x91194,x91195,x91192,x91197)) % 186.05/186.62 [7361]E(f775(x73611,f775(x73612,x73613)),f775(x73614,x73613))+~E(f775(f75(x73615,x73616,x73617,x73611),x73612),x73614) % 186.05/186.62 [9483]~P26(x94833,x94834,x94831,x94835,x94836,x94837)+E(f775(f775(x94831,x94832),x94832),x94832) % 186.05/186.62 [9809]~P51(x98095,x98096,x98097,x98091,x98094,x98092,x98093)+P1(f775(f775(x98091,x98092),f588(x98093,x98092,x98094,x98091))) % 186.05/186.62 [9834]~E(f775(f229(f854(x98347),x98341,f183(x98347),x98345),f775(x98344,x98343)),f775(f227(x98347),x98342))+E(f775(f227(x98341),f713(x98342,x98343,x98344,x98345,x98346,x98347,x98341)),f775(x98344,x98343)) % 186.05/186.62 [9835]~E(f775(f229(f854(x98356),x98357,f183(x98356),x98351),f775(x98354,x98353)),f775(f227(x98356),x98352))+E(f775(x98351,f713(x98352,x98353,x98354,x98351,x98355,x98356,x98357)),f775(f227(x98356),x98352)) % 186.05/186.62 [5869]~E(f775(f775(f143(x58691,x58695),x58696),x58692),f775(f775(f143(x58693,x58695),x58697),x58694))+E(f775(f181(f851(x58691)),x58692),f775(f181(f851(x58693)),x58694)) % 186.05/186.62 [7437]E(x74371,x74372)+~E(f775(f775(f775(f74(x74373,f854(x74374)),x74375),x74376),f775(f227(x74374),x74371)),f775(f775(f775(f74(x74373,f854(x74374)),x74377),x74376),f775(f227(x74374),x74372))) % 186.05/186.62 [8398]E(f775(x83981,f775(x83982,x83983)),f775(x83984,x83983))+~E(f775(f75(x83985,x83986,x83987,x83981),x83982),f775(f75(x83986,x83986,x83987,f39(x83986)),x83984)) % 186.05/186.62 [9814]~P51(x98145,x98146,x98147,x98144,x98141,x98143,x98142)+P1(f775(f775(x98141,f588(x98142,x98143,x98141,x98144)),x98142)) % 186.05/186.62 [5916]E(x59161,x59162)+~E(f775(f775(f775(f93(x59163),x59164),x59165),x59161),f775(f775(f775(f93(x59163),x59166),x59167),x59162)) % 186.05/186.62 [5917]E(x59171,x59172)+~E(f775(f775(f775(f93(x59173),x59174),x59171),x59175),f775(f775(f775(f93(x59173),x59176),x59172),x59177)) % 186.05/186.62 [5918]E(x59181,x59182)+~E(f775(f775(f775(f93(x59183),x59181),x59184),x59185),f775(f775(f775(f93(x59183),x59182),x59186),x59187)) % 186.05/186.62 [8811]~P24(x88116,x88111,x88113,x88117)+E(f775(f75(x88111,x88111,x88112,f775(x88113,x88114)),f775(f75(x88111,x88111,x88112,f775(x88113,x88114)),x88115)),f775(f75(x88111,x88111,x88112,f775(x88113,x88114)),x88115)) % 186.05/186.62 [8810]~P1(f775(f775(f334(x88101),x88102),f775(f775(x88105,x88106),x88107)))+P1(f775(f775(f334(x88101),x88102),f775(f775(f251(x88103,x88104,f857(x88101,a844)),x88105),f775(f775(f241(x88103,x88104),x88106),x88107)))) % 186.05/186.62 [9077]P1(f775(f775(f775(x90771,x90772),x90773),x90774))+~P1(f775(f775(f775(f251(x90775,x90776,f857(x90777,a844)),x90771),f775(f775(f241(x90775,x90776),x90772),x90773)),x90774)) % 186.05/186.62 [9197]P1(f775(f775(f334(x91971),f775(f775(x91972,x91973),x91974)),f775(f303(f856(x91975,x91976),x91971,f775(f251(x91975,x91976,x91971),x91972)),x91977)))+~P1(f775(f775(f334(f856(x91975,x91976)),f775(f775(f241(x91975,x91976),x91973),x91974)),x91977)) % 186.05/186.62 [9522]P1(f775(f775(f334(f856(f851(x95221),f851(x95221))),f775(f775(f241(f851(x95221),f851(x95221)),f775(f775(f125(x95221),x95222),f775(f775(f140(x95221),x95223),x95224))),f775(f775(f125(x95221),x95222),f775(f775(f140(x95221),x95225),x95226)))),f137(x95221,x95227)))+~P1(f775(f775(f334(f856(x95221,x95221)),f775(f775(f241(x95221,x95221),x95223),x95225)),x95227)) % 186.05/186.62 [9939]P51(x99391,x99392,x99393,f775(f775(f9(x99391,f857(f856(x99391,x99392),a844),f857(x99392,a844)),f775(f775(f10(f857(x99392,f857(f857(f856(x99391,x99392),a844),a844)),f857(f857(f856(x99391,x99392),a844),f857(x99392,a844)),x99391),f9(x99392,f857(f856(x99391,x99392),a844),a844)),f775(f775(f10(f857(x99392,f856(x99391,x99392)),f857(x99392,f857(f857(f856(x99391,x99392),a844),a844)),x99391),f775(f10(f856(x99391,x99392),f857(f857(f856(x99391,x99392),a844),a844),x99392),f334(f856(x99391,x99392)))),f241(x99391,x99392)))),x99394),f775(f775(f9(x99392,f857(f856(x99392,x99393),a844),f857(x99393,a844)),f775(f775(f10(f857(x99393,f857(f857(f856(x99392,x99393),a844),a844)),f857(f857(f856(x99392,x99393),a844),f857(x99393,a844)),x99392),f9(x99393,f857(f856(x99392,x99393),a844),a844)),f775(f775(f10(f857(x99393,f856(x99392,x99393)),f857(x99393,f857(f857(f856(x99392,x99393),a844),a844)),x99392),f775(f10(f856(x99392,x99393),f857(f857(f856(x99392,x99393),a844),a844),x99393),f334(f856(x99392,x99393)))),f241(x99392,x99393)))),x99395),x99396,x99397)+~P1(f775(f775(f334(f856(x99391,x99393)),f775(f775(f241(x99391,x99393),x99396),x99397)),f775(f775(f281(x99391,x99392,x99393),x99394),x99395))) % 186.05/186.62 [9968]~P51(x99681,x99685,x99682,f775(f775(f9(x99681,f857(f856(x99681,x99685),a844),f857(x99685,a844)),f775(f775(f10(f857(x99685,f857(f857(f856(x99681,x99685),a844),a844)),f857(f857(f856(x99681,x99685),a844),f857(x99685,a844)),x99681),f9(x99685,f857(f856(x99681,x99685),a844),a844)),f775(f775(f10(f857(x99685,f856(x99681,x99685)),f857(x99685,f857(f857(f856(x99681,x99685),a844),a844)),x99681),f775(f10(f856(x99681,x99685),f857(f857(f856(x99681,x99685),a844),a844),x99685),f334(f856(x99681,x99685)))),f241(x99681,x99685)))),x99686),f775(f775(f9(x99685,f857(f856(x99685,x99682),a844),f857(x99682,a844)),f775(f775(f10(f857(x99682,f857(f857(f856(x99685,x99682),a844),a844)),f857(f857(f856(x99685,x99682),a844),f857(x99682,a844)),x99685),f9(x99682,f857(f856(x99685,x99682),a844),a844)),f775(f775(f10(f857(x99682,f856(x99685,x99682)),f857(x99682,f857(f857(f856(x99685,x99682),a844),a844)),x99685),f775(f10(f856(x99685,x99682),f857(f857(f856(x99685,x99682),a844),a844),x99682),f334(f856(x99685,x99682)))),f241(x99685,x99682)))),x99687),x99683,x99684)+P1(f775(f775(f334(f856(x99681,x99682)),f775(f775(f241(x99681,x99682),x99683),x99684)),f775(f775(f281(x99681,x99685,x99682),x99686),x99687))) % 186.05/186.62 [9586]P1(f775(f775(f334(x95861),x95864),f775(f158(x95861),x95866)))+E(f170(x95861,x95862,f775(f775(f775(f74(x95861,f854(x95862)),x95863),x95864),f775(f227(x95862),x95865)),f166(x95861,x95862,f775(f142(f856(x95861,x95862)),f775(f775(f167(x95861,x95862),x95866),x95867)))),f775(f775(f775(f74(x95861,f854(x95862)),f170(x95861,x95862,x95863,f166(x95861,x95862,f775(f142(f856(x95861,x95862)),f775(f775(f167(x95861,x95862),x95866),x95867))))),x95864),f775(f227(x95862),x95865))) % 186.05/186.62 [9072]E(x90721,x90722)+E(f775(f775(f775(f74(x90723,x90724),f775(f775(f775(f74(x90723,x90724),x90725),x90721),x90726)),x90722),x90727),f775(f775(f775(f74(x90723,x90724),f775(f775(f775(f74(x90723,x90724),x90725),x90722),x90727)),x90721),x90726)) % 186.05/186.62 [9324]E(f170(x93241,x93242,f775(f775(f775(f74(x93241,f854(x93242)),x93243),x93244),f775(f227(x93242),x93245)),f166(x93241,x93242,f775(f142(f856(x93241,x93242)),f775(f775(f167(x93241,x93242),x93246),x93247)))),f170(x93241,x93242,x93243,f166(x93241,x93242,f775(f142(f856(x93241,x93242)),f775(f775(f167(x93241,x93242),x93246),x93247)))))+~P1(f775(f775(f334(x93241),x93244),f775(f158(x93241),f775(f775(f159(x93241),f775(f181(f851(x93242)),x93247)),x93246)))) % 186.05/186.62 [9604]E(f170(x96041,x96042,f775(f775(f775(f74(x96041,f854(x96042)),x96043),x96044),f775(f227(x96042),x96045)),f166(x96041,x96042,f775(f142(f856(x96041,x96042)),f775(f775(f167(x96041,x96042),x96046),x96047)))),f775(f775(f775(f74(x96041,f854(x96042)),f170(x96041,x96042,x96043,f166(x96041,x96042,f775(f142(f856(x96041,x96042)),f775(f775(f167(x96041,x96042),x96046),x96047))))),x96044),f775(f227(x96042),x96045)))+P1(f775(f775(f334(x96041),x96044),f775(f158(x96041),f775(f775(f159(x96041),f775(f181(f851(x96042)),x96047)),x96046)))) % 186.05/186.62 [9950]P1(f775(f775(f334(x99501),f669(x99502,x99503,x99504,x99505,x99506,x99507,x99501)),x99505))+P1(f775(f775(f775(f775(f47(x99501,f857(x99507,f857(x99506,a844))),x99505),x99504),x99503),x99502)) % 186.05/186.62 [9951]P1(f775(f775(f334(x99511),f430(x99512,x99513,x99514,x99515,x99516,x99517,x99511)),x99515))+~P1(f775(f775(f775(f775(f46(x99511,f857(x99517,f857(x99516,a844))),x99515),x99514),x99513),x99512)) % 186.05/186.62 [9978]P1(f775(f775(f775(x99781,f430(x99782,x99783,x99781,x99784,x99785,x99786,x99787)),x99783),x99782))+~P1(f775(f775(f775(f775(f46(x99787,f857(x99786,f857(x99785,a844))),x99784),x99781),x99783),x99782)) % 186.05/186.62 [9995]~P1(f775(f775(f775(x99955,f669(x99957,x99956,x99955,x99954,x99953,x99952,x99951)),x99956),x99957))+P1(f775(f775(f775(f775(f47(x99951,f857(x99952,f857(x99953,a844))),x99954),x99955),x99956),x99957)) % 186.05/186.62 [9960]~P136(x99602)+E(f775(f775(f8(x99601,x99602),f775(f775(f9(x99601,f857(x99603,a844),x99602),f775(f775(f10(f857(x99603,x99602),f857(f857(x99603,a844),x99602),x99601),f8(x99603,x99602)),f775(f775(f9(x99601,f857(x99603,x99602),f857(x99603,x99602)),f775(f775(f10(f857(x99602,x99602),f857(f857(x99603,x99602),f857(x99603,x99602)),x99601),f10(x99602,x99602,x99603)),f775(f775(f10(x99602,f857(x99602,x99602),x99601),f83(x99602)),x99604))),x99605))),x99606)),x99607),f775(f775(f83(x99602),f775(f775(f8(x99601,x99602),x99604),x99607)),f775(f775(f8(x99603,x99602),x99605),x99606))) % 186.05/186.62 [9109]~P23(x91097,x91091,x91093,x91098)+E(f775(f75(x91091,x91091,x91092,f775(x91093,x91094)),f775(f75(x91091,x91091,x91092,f775(x91093,x91095)),x91096)),f775(f75(x91091,x91091,x91092,f775(x91093,x91095)),f775(f75(x91091,x91091,x91092,f775(x91093,x91094)),x91096))) % 186.05/186.62 [10013]E(f775(f775(f241(x100131,x100132),f775(x100133,f573(x100134,x100135,x100133,x100136,x100137,x100138,x100132,x100131))),f775(x100135,f574(x100134,x100135,x100133,x100136,x100137,x100138,x100132,x100131))),x100138)+~P1(f775(f775(f334(f856(x100131,x100132)),x100138),f775(f303(f856(x100137,x100136),f856(x100131,x100132),f252(x100137,x100131,x100136,x100132,x100133,x100135)),x100134))) % 186.05/186.62 [10025]~P1(f775(f775(f334(f856(x100258,x100257)),x100256),f775(f303(f856(x100251,x100252),f856(x100258,x100257),f252(x100251,x100258,x100252,x100257,x100255,x100254)),x100253)))+P1(f775(f775(f334(f856(x100251,x100252)),f775(f775(f241(x100251,x100252),f573(x100253,x100254,x100255,x100252,x100251,x100256,x100257,x100258)),f574(x100253,x100254,x100255,x100252,x100251,x100256,x100257,x100258))),x100253)) % 186.05/186.62 [9512]P1(f775(f775(f334(f856(f856(x95121,x95122),f856(x95121,x95122))),f775(f775(f241(f856(x95121,x95122),f856(x95121,x95122)),f775(f775(f241(x95121,x95122),x95123),x95124)),f775(f775(f241(x95121,x95122),x95125),x95126))),f325(x95121,x95122,x95127,x95128)))+~P1(f775(f775(f334(f856(x95121,x95121)),f775(f775(f241(x95121,x95121),x95123),x95125)),x95127)) % 186.05/186.62 [8404]E(f775(x84041,f775(x84042,x84043)),f775(x84044,f775(x84045,x84043)))+~E(f775(f75(x84046,x84047,x84048,x84041),x84042),f775(f75(x84049,x84047,x84048,x84044),x84045)) % 186.05/186.62 [9885]P1(f775(f775(f334(f856(x98851,x98852)),f775(f775(f241(x98851,x98852),f775(x98853,x98854)),f775(x98855,x98856))),f775(f303(f856(x98857,x98858),f856(x98851,x98852),f252(x98857,x98851,x98858,x98852,x98853,x98855)),x98859)))+~P1(f775(f775(f334(f856(x98857,x98858)),f775(f775(f241(x98857,x98858),x98854),x98856)),x98859)) % 186.05/186.62 [8663]~E(f775(x86634,f775(x86635,x86636)),f775(x86639,f775(x866310,x866311)))+E(f775(f775(f75(x86631,x86632,x86633,x86634),x86635),x86636),f775(f775(f75(x86637,x86632,x86638,x86639),x866310),x866311)) % 186.05/186.62 [4491]~P100(x44911)+~P92(x44911)+E(f179(x44911),f103(x44911)) % 186.05/186.62 [4492]~P100(x44921)+~P98(x44921)+E(f236(x44921),f104(x44921)) % 186.05/186.62 [4726]~P110(x47261)+~P88(x47261)+E(f775(f77(x47261),f775(f106(x47261),a99)),f80(x47261)) % 186.05/186.62 [5001]E(x50011,f2(a1))+E(f84(a1,x50011),f775(f81(a1),f80(a1)))+P1(f775(f775(f233(a1),f2(a1)),x50011)) % 186.05/186.62 [5203]E(x52031,f2(a1))+E(f84(a1,x52031),f80(a1))+~P1(f775(f775(f233(a1),f2(a1)),x52031)) % 186.05/186.62 [7248]~P38(x72481)+P1(f775(f63(a1),x72481))+~P1(f775(f63(a850),f775(f303(a1,a850,a107),x72481))) % 186.05/186.62 [8510]~P13(a5000)+~P1(f775(f775(f334(f856(a846,a845)),x85101),f775(f158(f856(a846,a845)),a29)))+P1(f775(f775(f251(a846,a845,a844),f775(f18(f857(a845,a844),a846),a26)),x85101)) % 186.05/186.62 [9482]E(x94821,f180(f857(f856(a850,a850),a844)))+~P1(f775(f63(f856(a850,a850)),x94821))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f180(f857(f856(a850,a850),a844))),x94821)),a41)) % 186.05/186.62 [9629]E(x96291,f2(a850))+E(x96291,f775(a114,f2(a850)))+~P1(f775(f775(f233(a850),x96291),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.62 [9911]E(x99111,f2(a101))+E(f775(f775(f82(a1),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(a23,f775(f775(f43(a101),x99111),f775(f106(a101),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))),f80(a1)),f775(a23,x99111))+E(f52(a101,x99111,f775(f106(a101),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f2(a101)) % 186.05/186.62 [9758]E(x97581,f2(a101))+~E(f52(a101,x97581,f775(f106(a101),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f2(a101))+E(f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(a23,f775(f775(f43(a101),x97581),f775(f106(a101),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f775(a23,x97581)) % 186.05/186.62 [4562]~P56(x45621,x45622)+P42(x45621,x45622)+~P43(a844) % 186.05/186.62 [4502]~P2(x45021)+P33(x45021,x45022)+~E(x45022,f2(x45021)) % 186.05/186.62 [4511]~P110(x45111)+~E(x45112,f2(x45111))+E(f84(x45111,x45112),f2(x45111)) % 186.05/186.62 [4512]~P82(x45121)+~E(x45122,f2(x45121))+E(f84(x45121,x45122),f2(x45121)) % 186.05/186.62 [4518]~P2(x45182)+~P33(x45182,x45181)+E(x45181,f2(x45182)) % 186.05/186.62 [4552]~P110(x45522)+~E(f84(x45522,x45521),f2(x45522))+E(x45521,f2(x45522)) % 186.05/186.62 [4570]~P10(x45702)+~P10(x45701)+P10(f188(x45701,x45702)) % 186.05/186.62 [4571]~P59(x45712)+~P59(x45711)+P59(f858(x45711,x45712)) % 186.05/186.62 [4572]~P59(x45722)+~P59(x45721)+P59(f857(x45721,x45722)) % 186.05/186.62 [4573]~P59(x45732)+~P59(x45731)+P59(f856(x45731,x45732)) % 186.05/186.62 [4574]~P139(x45742)+~P139(x45741)+P139(f856(x45741,x45742)) % 186.05/186.62 [4929]~P10(x49292)+~P10(x49291)+P10(f52(a1,x49291,x49292)) % 186.05/186.62 [4520]~P68(x45201)+~E(x45202,f2(x45201))+E(f775(f81(x45201),x45202),x45202) % 186.05/186.62 [4524]~P87(x45241)+~E(x45242,f2(a1))+E(f775(f105(x45241),x45242),f2(x45241)) % 186.05/186.62 [4525]~P133(x45251)+~E(x45252,f2(a1))+E(f775(f105(x45251),x45252),f2(x45251)) % 186.05/186.62 [4549]~P69(x45491)+~E(f2(x45491),x45492)+E(f775(f81(x45491),x45492),f2(x45491)) % 186.05/186.62 [4550]~P69(x45501)+~E(x45502,f2(x45501))+E(f775(f81(x45501),x45502),f2(x45501)) % 186.05/186.62 [4551]~P79(x45511)+~E(x45512,f2(x45511))+E(f775(f77(x45511),x45512),f2(x45511)) % 186.05/186.62 [4576]~P68(x45762)+E(x45761,f2(x45762))+~E(f775(f81(x45762),x45761),x45761) % 186.05/186.62 [4584]E(x45841,f775(a107,x45842))+~E(x45841,f2(a850))+~E(x45842,f775(f102(a1),x45841)) % 186.05/186.62 [4585]E(f775(a107,x45851),x45852)+~E(x45852,f2(a850))+~E(x45851,f775(f102(a1),x45852)) % 186.05/186.62 [4589]~P87(x45892)+E(x45891,f2(a1))+~E(f775(f105(x45892),x45891),f2(x45892)) % 186.05/186.62 [4594]~P69(x45942)+E(x45941,f2(x45942))+~E(f775(f81(x45942),x45941),f2(x45942)) % 186.05/186.62 [4595]~P79(x45952)+E(x45951,f2(x45952))+~E(f775(f77(x45952),x45951),f2(x45952)) % 186.05/186.62 [4596]~P69(x45961)+E(f2(x45961),x45962)+~E(f775(f81(x45961),x45962),f2(x45961)) % 186.05/186.62 [4730]~P13(a5000)+~E(f775(a30,x47302),f775(f227(a845),x47301))+P1(f775(a26,x47301)) % 186.05/186.62 [4769]~P100(x47691)+~P18(x47691,x47692)+P18(x47691,f775(f157(x47691),x47692)) % 186.05/186.62 [4795]~P1(x47952)+~P1(x47951)+P1(f775(f775(a331,x47951),x47952)) % 186.05/186.62 [4829]~E(f80(a850),f2(a850))+E(f775(f42(x48291),x48292),f2(a850))+~P1(f775(f63(x48291),x48292)) % 186.05/186.62 [4860]~P105(x48601)+~P136(x48601)+E(f775(f775(f242(x48601),f2(x48601)),f775(a114,x48602)),f2(x48601)) % 186.05/186.62 [4900]~P100(x49001)+P18(x49001,f130(x49001,x49002))+~P1(f775(f63(x49001),x49002)) % 186.05/186.62 [4920]~P100(x49201)+E(f775(f158(x49201),f130(x49201,x49202)),x49202)+~P1(f775(f63(x49201),x49202)) % 186.05/186.62 [4954]P1(x49541)+P1(x49542)+~P1(f775(f775(a332,x49542),x49541)) % 186.05/186.62 [4966]E(x49661,f180(f857(x49662,a844)))+~E(f775(f42(x49662),x49661),f2(a850))+~P1(f775(f63(x49662),x49661)) % 186.05/186.62 [4971]P1(x49711)+~P1(x49712)+~P1(f775(f775(a335,x49712),x49711)) % 186.05/186.62 [5019]~P65(x50191)+E(f775(f77(x50191),x50192),x50192)+P1(f775(f775(f233(x50191),x50192),f2(x50191))) % 186.05/186.62 [5116]~P1(f775(a26,x51162))+~P1(f775(a26,x51161))+P1(f775(a26,f36(x51161,x51162))) % 186.05/186.62 [5123]E(x51231,f115(x51232))+P1(f775(f127(x51232),f116(x51232,x51231)))+~P1(f775(f127(x51232),x51231)) % 186.05/186.62 [5128]~P100(x51281)+~P1(f775(f63(x51281),x51282))+P1(f775(f127(x51281),f130(x51281,x51282))) % 186.05/186.62 [5134]~P133(x51341)+E(f775(f102(x51341),f775(a107,x51342)),f775(f105(x51341),x51342))+P1(f775(f775(f233(a1),x51342),f2(a1))) % 186.05/186.62 [5160]P11(x51602,x51601)+E(f775(x51601,f504(x51601)),f775(x51601,f520(x51601)))+P1(f775(f775(x51601,f504(x51601)),f520(x51601))) % 186.05/186.62 [5173]E(f775(f102(a1),f617(x51731,x51732)),x51731)+P1(f775(x51732,f775(a107,x51731)))+~P1(f775(x51732,f2(a850))) % 186.05/186.62 [5213]~P110(x52131)+~E(f84(x52131,x52132),f775(f81(x52131),f80(x52131)))+P1(f775(f775(f233(x52131),x52132),f2(x52131))) % 186.05/186.62 [5286]~E(x52862,f2(a1))+E(f210(x52861,x52862),f775(f775(f241(a1,a1),f2(a1)),f80(a1)))+P1(f775(f775(f233(a1),x52862),f2(a1))) % 186.05/186.62 [5287]~E(x52871,f2(a1))+E(f210(x52871,x52872),f775(f775(f241(a1,a1),f2(a1)),f80(a1)))+P1(f775(f775(f233(a1),x52872),f2(a1))) % 186.05/186.62 [5338]E(f775(f102(a1),f617(x53381,x53382)),x53381)+P1(f775(x53382,f775(a107,x53381)))+P1(f775(f775(f233(a1),x53381),f2(a1))) % 186.05/186.62 [5404]~P110(x54041)+E(f84(x54041,x54042),f775(f81(x54041),f80(x54041)))+~P1(f775(f775(f233(x54041),x54042),f2(x54041))) % 186.05/186.62 [5405]~P79(x54051)+E(f775(f77(x54051),x54052),f775(f81(x54051),x54052))+~P1(f775(f775(f233(x54051),x54052),f2(x54051))) % 186.05/186.62 [5406]~P79(x54061)+E(f775(f77(x54061),x54062),f775(f81(x54061),x54062))+~P1(f775(f775(f232(x54061),x54062),f2(x54061))) % 186.05/186.62 [5407]~P65(x54071)+E(f775(f77(x54071),x54072),f775(f81(x54071),x54072))+~P1(f775(f775(f233(x54071),x54072),f2(x54071))) % 186.05/186.62 [5499]~P1(f775(x54991,f617(x54992,x54991)))+P1(f775(x54991,f775(a107,x54992)))+~P1(f775(x54991,f2(a850))) % 186.05/186.62 [5506]E(x55061,f2(a850))+E(f775(a114,f559(x55062,x55061)),x55061)+~P1(f775(f775(f233(a850),x55061),f775(a114,x55062))) % 186.05/186.62 [5509]P11(x55091,x55092)+~E(f775(x55092,f504(x55092)),f775(x55092,f520(x55092)))+~P1(f775(f775(x55092,f504(x55092)),f520(x55092))) % 186.05/186.62 [5528]~P100(x55281)+P18(x55281,x55282)+P1(f775(f775(f232(a850),f761(x55282,x55281)),f762(x55282,x55281))) % 186.05/186.62 [5614]~P79(x56141)+~E(x56142,f2(x56141))+P1(f775(f775(f232(x56141),f775(f77(x56141),x56142)),f2(x56141))) % 186.05/186.62 [5703]~P1(f775(x57031,f617(x57032,x57031)))+P1(f775(x57031,f775(a107,x57032)))+P1(f775(f775(f233(a1),x57032),f2(a1))) % 186.05/186.62 [5729]~P1(f775(x57291,f775(a107,x57292)))+P1(f775(x57291,f2(a850)))+~P1(f775(f775(f233(a1),x57292),f2(a1))) % 186.05/186.62 [6073]~P110(x60731)+~P1(f775(f775(f233(x60731),x60732),f2(x60731)))+P1(f775(f775(f233(x60731),f84(x60731,x60732)),f2(x60731))) % 186.05/186.62 [6190]~P110(x61901)+P1(f775(f775(f233(x61901),f775(f105(x61901),x61902)),f2(x61901)))+~P1(f775(f775(f233(a1),x61902),f2(a1))) % 186.05/186.62 [6191]~P110(x61911)+P1(f775(f775(f232(x61911),f775(f105(x61911),x61912)),f2(x61911)))+~P1(f775(f775(f232(a1),x61912),f2(a1))) % 186.05/186.62 [6196]~P79(x61962)+E(x61961,f2(x61962))+~P1(f775(f775(f232(x61962),f775(f77(x61962),x61961)),f2(x61962))) % 186.05/186.62 [6281]~P133(x62811)+~P1(f775(f775(f334(x62811),x62812),f112(x62811)))+P1(f775(f775(f334(x62811),f775(f81(x62811),x62812)),f112(x62811))) % 186.05/186.62 [6313]~P110(x63131)+~P1(f775(f775(f233(x63131),f84(x63131,x63132)),f2(x63131)))+P1(f775(f775(f233(x63131),x63132),f2(x63131))) % 186.05/186.62 [6394]~P99(x63941)+P50(a850,x63941,f279(a850),x63942)+P1(f775(f775(f279(a850),f377(x63942,x63941)),f393(x63942,x63941))) % 186.05/186.62 [6492]~P110(x64922)+~P1(f775(f775(f233(x64922),f775(f105(x64922),x64921)),f2(x64922)))+P1(f775(f775(f233(a1),x64921),f2(a1))) % 186.05/186.62 [6493]~P110(x64932)+~P1(f775(f775(f232(x64932),f775(f105(x64932),x64931)),f2(x64932)))+P1(f775(f775(f232(a1),x64931),f2(a1))) % 186.05/186.62 [7018]~P68(x70181)+~P1(f775(f775(f233(x70181),x70182),f2(x70181)))+P1(f775(f775(f233(x70181),f775(f775(f82(x70181),x70182),x70182)),f2(x70181))) % 186.05/186.62 [7019]~P110(x70191)+~P1(f775(f775(f233(x70191),x70192),f2(x70191)))+P1(f775(f775(f233(x70191),f775(f775(f82(x70191),x70192),x70192)),f2(x70191))) % 186.05/186.62 [7020]~P68(x70201)+~P1(f775(f775(f232(x70201),x70202),f2(x70201)))+P1(f775(f775(f232(x70201),f775(f775(f82(x70201),x70202),x70202)),f2(x70201))) % 186.05/186.62 [7615]~P68(x76151)+~P1(f775(f775(f233(x76151),f775(f775(f82(x76151),x76152),x76152)),f2(x76151)))+P1(f775(f775(f233(x76151),x76152),f2(x76151))) % 186.05/186.62 [7616]~P110(x76161)+~P1(f775(f775(f233(x76161),f775(f775(f82(x76161),x76162),x76162)),f2(x76161)))+P1(f775(f775(f233(x76161),x76162),f2(x76161))) % 186.05/186.62 [7617]~P68(x76171)+~P1(f775(f775(f232(x76171),f775(f775(f82(x76171),x76172),x76172)),f2(x76171)))+P1(f775(f775(f232(x76171),x76172),f2(x76171))) % 186.05/186.62 [4633]~E(x46332,f2(a850))+~E(x46331,f2(a850))+E(f775(f775(f82(a850),x46331),x46332),f2(a850)) % 186.05/186.62 [4634]~E(x46342,f80(a850))+~E(x46341,f80(a850))+E(f775(f775(f83(a850),x46341),x46342),f80(a850)) % 186.05/186.62 [4635]~E(x46352,f80(a1))+~E(x46351,f80(a1))+E(f775(f775(f83(a1),x46351),x46352),f80(a1)) % 186.05/186.62 [4685]~P7(x46852)+E(x46851,f2(x46852))+E(f775(f775(f43(x46852),x46851),x46851),f80(x46852)) % 186.05/186.62 [4686]~P113(x46862)+E(x46861,f2(x46862))+E(f775(f775(f283(x46862),x46861),x46861),f80(x46862)) % 186.05/186.62 [4687]~P114(x46872)+E(x46871,f2(x46872))+E(f775(f775(f283(x46872),x46871),x46871),f80(x46872)) % 186.05/186.62 [4702]~P68(x47021)+~E(x47022,f2(x47021))+E(f775(f775(f82(x47021),x47022),x47022),f2(x47021)) % 186.05/186.62 [4705]~P120(x47051)+~E(x47052,f80(x47051))+E(f775(f775(f83(x47051),x47052),x47052),f80(x47051)) % 186.05/186.62 [4706]~P114(x47061)+~E(x47062,f2(x47061))+E(f775(f775(f283(x47061),x47062),x47062),f2(x47061)) % 186.05/186.62 [4750]~E(x47502,f2(a850))+~E(x47501,f2(a850))+E(f775(f81(a1),f775(f102(a1),x47501)),f775(f102(a1),x47502)) % 186.05/186.62 [4768]E(x47681,f80(a850))+E(x47682,f2(a850))+~E(f775(f775(f83(a850),x47682),x47681),x47682) % 186.05/186.62 [4776]E(x47761,f2(a850))+E(x47762,f2(a850))+~E(f775(f775(f83(a850),x47762),x47761),f2(a850)) % 186.05/186.62 [4804]~E(x48042,f2(a850))+~E(x48041,f775(a114,f2(a850)))+E(f775(f775(f82(a850),x48041),x48042),f775(a114,f2(a850))) % 186.05/186.62 [4805]~E(x48051,f2(a850))+~E(x48052,f775(a114,f2(a850)))+E(f775(f775(f82(a850),x48051),x48052),f775(a114,f2(a850))) % 186.05/186.62 [4810]E(x48101,f80(a1))+E(x48102,f775(f106(a1),a99))+~E(f775(f775(f83(a1),x48101),x48102),f80(a1)) % 186.05/186.62 [4811]E(x48111,f80(a1))+E(x48112,f775(f106(a1),a99))+~E(f775(f775(f83(a1),x48112),x48111),f80(a1)) % 186.05/186.62 [4812]E(x48121,f80(a1))+E(x48121,f775(f106(a1),a99))+~E(f775(f775(f83(a1),x48122),x48121),f80(a1)) % 186.05/186.62 [4814]E(x48141,f80(a1))+E(x48141,f775(f106(a1),a99))+~E(f775(f775(f83(a1),x48141),x48142),f80(a1)) % 186.05/186.62 [4833]~P68(x48332)+E(x48331,f2(x48332))+~E(f775(f775(f82(x48332),x48331),x48331),f2(x48332)) % 186.05/186.62 [4839]~E(x48391,f775(f106(a1),a99))+~E(x48392,f775(f106(a1),a99))+E(f775(f775(f83(a1),x48391),x48392),f80(a1)) % 186.05/186.62 [4851]E(x48511,f2(a850))+E(x48512,f2(a850))+~E(f775(f775(f82(a850),x48512),x48511),f775(a114,f2(a850))) % 186.05/186.62 [4859]~P88(x48591)+~P60(x48591)+E(f775(f775(f283(x48591),x48592),f775(f106(x48591),a85)),f2(x48591)) % 186.05/186.62 [4866]~P120(x48661)+~E(x48662,f775(f81(x48661),f80(x48661)))+E(f775(f775(f83(x48661),x48662),x48662),f80(x48661)) % 186.05/186.62 [4871]~P10(x48712)+~P10(x48711)+P10(f775(f775(f82(a1),x48711),x48712)) % 186.05/186.62 [4872]~P10(x48722)+~P10(x48721)+P10(f775(f775(f83(a1),x48721),x48722)) % 186.05/186.62 [4873]~P10(x48732)+~P10(x48731)+P10(f775(f775(f43(a1),x48731),x48732)) % 186.05/186.62 [4875]~E(x48752,f2(a1))+E(x48751,f2(a1))+E(f53(x48751,x48752),f775(f775(f241(a1,a1),f2(a1)),x48751)) % 186.05/186.62 [4898]~E(x48982,f775(a114,f2(a850)))+~E(x48981,f775(a114,f2(a850)))+E(f775(f775(f83(a850),x48981),x48982),f775(a114,f2(a850))) % 186.05/186.62 [4911]E(x49111,f2(a850))+E(x49112,f775(a114,f2(a850)))+~E(f775(f775(f242(a850),x49112),x49111),f775(a114,f2(a850))) % 186.05/186.62 [4912]E(x49121,f2(a850))+E(x49121,f775(a114,f2(a850)))+~E(f775(f775(f82(a850),x49122),x49121),f775(a114,f2(a850))) % 186.05/186.62 [4913]E(x49131,f2(a850))+E(x49131,f775(a114,f2(a850)))+~E(f775(f775(f82(a850),x49131),x49132),f775(a114,f2(a850))) % 186.05/186.62 [4921]~P88(x49211)+~P60(x49211)+E(f775(f775(f283(x49211),x49212),f775(f106(x49211),a99)),f775(f81(x49211),x49212)) % 186.05/186.62 [4942]E(x49421,f775(a107,x49422))+~E(x49421,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x49422)) % 186.05/186.62 [4943]E(f775(a107,x49431),x49432)+~E(x49432,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x49431)) % 186.05/186.62 [4962]E(x49621,f775(a114,f2(a850)))+E(x49622,f775(a114,f2(a850)))+~E(f775(f775(f82(a850),x49621),x49622),f775(a114,f2(a850))) % 186.05/186.62 [4973]~E(x49731,f775(a107,x49732))+E(x49731,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x49732)) % 186.05/186.62 [4974]~E(f775(a107,x49742),x49741)+E(x49741,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x49742)) % 186.05/186.62 [4997]~P93(x49971)+E(f775(f65(x49971,f103(x49971)),x49972),f15(x49971,x49972))+~P1(f775(f63(x49971),x49972)) % 186.05/186.62 [4998]~P100(x49981)+E(f775(f65(x49981,f179(x49981)),x49982),f16(x49981,x49982))+~P1(f775(f63(x49981),x49982)) % 186.05/186.62 [4999]~P100(x49991)+E(f775(f65(x49991,f236(x49991)),x49992),f17(x49991,x49992))+~P1(f775(f63(x49991),x49992)) % 186.05/186.62 [5000]~P93(x50001)+E(f775(f65(x50001,f104(x50001)),x50002),f12(x50001,x50002))+~P1(f775(f63(x50001),x50002)) % 186.05/186.62 [5083]E(x50831,x50832)+~E(f775(f775(f3(a850),x50832),x50831),f2(a850))+~E(f775(f775(f3(a850),x50831),x50832),f2(a850)) % 186.05/186.62 [5093]P10(x50931)+~P38(x50932)+~P1(f775(f775(f334(a1),x50931),x50932)) % 186.05/186.62 [5124]~P110(x51241)+~E(f84(x51241,x51242),f80(x51241))+P1(f775(f775(f233(x51241),f2(x51241)),x51242)) % 186.05/186.62 [5135]~P88(x51351)+E(f775(f102(x51351),f775(f106(a850),x51352)),f775(f106(x51351),x51352))+P1(f775(a186,f775(f106(a1),x51352))) % 186.05/186.62 [5140]~P42(x51401,x51402)+P43(a844)+P1(f775(f63(f856(x51401,x51401)),x51402)) % 186.05/186.62 [5205]~P100(x52051)+E(f775(f65(x52051,f179(x52051)),x52052),f13(x52051,f179(x52051),x52052))+~P1(f775(f63(x52051),x52052)) % 186.05/186.62 [5206]~P100(x52061)+E(f775(f65(x52061,f236(x52061)),x52062),f14(x52061,f236(x52061),x52062))+~P1(f775(f63(x52061),x52062)) % 186.05/186.62 [5220]E(x52201,x52202)+P1(f775(f775(f233(a850),x52202),x52201))+P1(f775(f775(f233(a850),x52201),x52202)) % 186.05/186.62 [5221]E(x52211,x52212)+P1(f775(f775(f233(a1),x52212),x52211))+P1(f775(f775(f233(a1),x52211),x52212)) % 186.05/186.62 [5273]~P88(x52731)+E(f775(f102(x52731),f775(f106(a850),x52732)),f2(x52731))+~P1(f775(a186,f775(f106(a1),x52732))) % 186.05/186.62 [5276]~E(x52762,f775(a107,x52761))+E(x52761,f775(f102(a1),x52762))+~P1(f775(f775(f232(a1),f2(a1)),x52761)) % 186.05/186.62 [5277]~E(f775(a107,x52771),x52772)+E(x52771,f775(f102(a1),x52772))+~P1(f775(f775(f232(a1),f2(a1)),x52771)) % 186.05/186.62 [5278]~E(x52781,f775(a107,x52782))+E(f775(f102(a1),x52781),x52782)+~P1(f775(f775(f232(a1),f2(a1)),x52782)) % 186.05/186.62 [5288]E(x52881,f775(a107,x52882))+~E(x52882,f775(f102(a1),x52881))+~P1(f775(f775(f232(a1),f2(a1)),x52882)) % 186.05/186.62 [5289]E(f775(a107,x52891),x52892)+~E(x52891,f775(f102(a1),x52892))+~P1(f775(f775(f232(a1),f2(a1)),x52891)) % 186.05/186.62 [5318]~P85(x53182)+E(x53181,f2(x53182))+~P1(f775(f775(f279(x53182),f2(x53182)),x53181)) % 186.05/186.62 [5327]~P79(x53272)+E(x53271,f2(x53272))+P1(f775(f775(f233(x53272),f2(x53272)),f775(f77(x53272),x53271))) % 186.05/186.62 [5395]~P110(x53951)+E(f84(x53951,x53952),f80(x53951))+~P1(f775(f775(f233(x53951),f2(x53951)),x53952)) % 186.05/186.62 [5401]~P88(x54011)+E(f775(f102(x54011),f775(f106(a850),x54012)),f2(x54011))+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x54012))) % 186.05/186.62 [5408]~P79(x54081)+E(f775(f77(x54081),x54082),x54082)+~P1(f775(f775(f233(x54081),f2(x54081)),x54082)) % 186.05/186.62 [5409]~P79(x54091)+E(f775(f77(x54091),x54092),x54092)+~P1(f775(f775(f232(x54091),f2(x54091)),x54092)) % 186.05/186.62 [5416]E(x54161,f2(a850))+~E(f130(a850,f775(f294(a850,x54162),x54161)),f115(a850))+P1(f775(f775(f232(a850),x54161),x54162)) % 186.05/186.62 [5426]~P66(x54261)+E(f775(f775(f8(x54261,x54261),f7(x54261)),f775(f158(x54261),x54262)),f775(f155(x54261),x54262))+~P1(f775(f127(x54261),x54262)) % 186.05/186.62 [5429]~P133(x54291)+E(f775(f102(x54291),f775(a107,x54292)),f775(f105(x54291),x54292))+~P1(f775(f775(f232(a1),f2(a1)),x54292)) % 186.05/186.62 [5452]E(x54521,x54522)+P1(f775(f775(f233(a850),x54521),x54522))+~P1(f775(f775(f232(a850),x54521),x54522)) % 186.05/186.62 [5453]E(x54531,x54532)+P1(f775(f775(f233(a1),x54531),x54532))+~P1(f775(f775(f232(a1),x54531),x54532)) % 186.05/186.62 [5456]E(x54561,f80(a1))+~E(f775(f775(f83(a1),x54562),x54561),f80(a1))+~P1(f775(f775(f233(a1),f2(a1)),x54562)) % 186.05/186.62 [5457]E(x54571,f80(a1))+~E(f775(f775(f83(a1),x54571),x54572),f80(a1))+~P1(f775(f775(f233(a1),f2(a1)),x54571)) % 186.05/186.62 [5496]~P38(x54962)+P1(f775(f775(f232(a1),f2(a1)),x54961))+~P1(f775(f775(f334(a1),x54961),x54962)) % 186.05/186.62 [5514]~P56(x55141,x55142)+P36(x55141,x55142)+~P1(f775(f63(f856(x55141,x55141)),x55142)) % 186.05/186.62 [5516]~P56(x55161,x55162)+P42(x55161,x55162)+~P1(f775(f63(f856(x55161,x55161)),x55162)) % 186.05/186.62 [5556]E(x55561,f180(f857(x55562,a844)))+~P1(f775(f63(x55562),x55561))+P1(f775(f775(f233(a850),f2(a850)),f775(f42(x55562),x55561))) % 186.05/186.62 [5582]~P1(f775(x55821,x55822))+P1(f775(x55821,f2(a850)))+P1(f775(f775(f233(a850),f792(x55822,x55821)),x55822)) % 186.05/186.62 [5607]E(x56071,f2(a850))+~E(f775(f155(a850),x56072),f2(a850))+~P1(f775(f775(f334(a850),x56071),f775(f158(a850),x56072))) % 186.05/186.62 [5669]~E(x56692,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x56691))+P1(f775(f775(f279(a850),f775(a107,x56691)),x56692)) % 186.05/186.62 [5672]E(x56721,x56722)+~P1(f775(f775(f232(a850),x56722),x56721))+~P1(f775(f775(f232(a850),x56721),x56722)) % 186.05/186.62 [5673]E(x56731,x56732)+~P1(f775(f775(f232(a1),x56732),x56731))+~P1(f775(f775(f232(a1),x56731),x56732)) % 186.05/186.62 [5682]E(x56821,x56822)+~P1(f775(f775(f279(a850),x56822),x56821))+~P1(f775(f775(f279(a850),x56821),x56822)) % 186.05/186.62 [5683]E(f775(f42(x56831),x56832),f2(a850))+~P1(f775(f63(x56831),x56832))+P1(f775(f775(f334(x56831),f619(x56832,x56831)),x56832)) % 186.05/186.62 [5689]E(f57(x56891,x56892),f53(x56891,x56892))+P1(f775(f775(f232(a1),f2(a1)),x56891))+~P1(f775(f775(f233(a1),f2(a1)),x56892)) % 186.05/186.62 [5718]~P1(f775(x57181,f778(x57181)))+P1(f775(x57181,f775(a107,x57182)))+~P1(f775(f775(f232(a1),f2(a1)),x57182)) % 186.05/186.62 [5720]P1(f775(f775(f233(a850),x57201),f401(x57202)))+~P1(f775(f63(a850),x57202))+~P1(f775(f775(f334(a850),x57201),x57202)) % 186.05/186.62 [5721]P1(f775(f775(f232(a850),x57211),f376(x57212)))+~P1(f775(f63(a850),x57212))+~P1(f775(f775(f334(a850),x57211),x57212)) % 186.05/186.62 [5750]E(x57501,x57502)+~P1(f775(f775(f233(a850),x57501),f775(a114,x57502)))+P1(f775(f775(f233(a850),x57501),x57502)) % 186.05/186.62 [5788]E(x57881,f775(a114,x57882))+~P1(f775(f775(f232(a850),x57881),f775(a114,x57882)))+P1(f775(f775(f232(a850),x57881),x57882)) % 186.05/186.62 [5798]P1(f775(x57981,f779(x57981)))+~P1(f775(x57981,f775(a107,x57982)))+~P1(f775(f775(f232(a1),f2(a1)),x57982)) % 186.05/186.62 [5800]E(f775(f77(a1),x58001),f775(f77(a1),x58002))+~P1(f775(f775(f279(a1),x58002),x58001))+~P1(f775(f775(f279(a1),x58001),x58002)) % 186.05/186.62 [5812]~P1(f775(x58121,x58122))+~P1(f775(f775(f232(a1),f2(a1)),x58122))+P1(f775(x58121,f775(f102(a1),f724(x58121)))) % 186.05/186.62 [5824]~P79(x58242)+~E(x58241,f2(x58242))+~P1(f775(f775(f233(x58242),f2(x58242)),f775(f77(x58242),x58241))) % 186.05/186.62 [5849]~P56(x58491,x58492)+P36(x58491,f775(f278(x58491,x58491),x58492))+~P1(f775(f63(f856(x58491,x58491)),x58492)) % 186.05/186.62 [5857]~P88(x58571)+E(f775(f102(x58571),f775(f106(a850),x58572)),f775(f106(x58571),x58572))+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x58572))) % 186.05/186.62 [5861]E(f775(a114,x58611),x58612)+~P1(f775(f775(f233(a850),x58611),x58612))+P1(f775(f775(f233(a850),f775(a114,x58611)),x58612)) % 186.05/186.62 [5874]E(f775(f775(f43(a1),x58741),x58742),f2(a1))+~P1(f775(f775(f232(a1),x58741),f2(a1)))+~P1(f775(f775(f233(a1),x58742),x58741)) % 186.05/186.62 [5887]E(f52(a1,x58871,x58872),x58871)+~P1(f775(f775(f232(a1),x58871),f2(a1)))+~P1(f775(f775(f233(a1),x58872),x58871)) % 186.05/186.62 [5900]E(f54(x59001,x59002),f53(x59001,x59002))+~P1(f775(f775(f232(a1),f2(a1)),x59001))+~P1(f775(f775(f232(a1),f2(a1)),x59002)) % 186.05/186.62 [5908]E(f775(f775(f43(a1),x59081),x59082),f2(a1))+~P1(f775(f775(f232(a1),f2(a1)),x59081))+~P1(f775(f775(f233(a1),x59081),x59082)) % 186.05/186.62 [5922]E(f52(a850,f775(f106(a850),x59221),f775(f106(a850),x59222)),f775(f106(a850),x59221))+P1(f775(a186,f775(f106(a1),x59221)))+~P1(f775(a186,f775(f106(a1),x59222))) % 186.05/186.62 [5924]E(f52(a1,x59241,x59242),x59241)+~P1(f775(f775(f232(a1),f2(a1)),x59241))+~P1(f775(f775(f233(a1),x59241),x59242)) % 186.05/186.62 [5926]E(x59261,x59262)+~P1(f775(f775(f233(a850),x59261),f775(a114,x59262)))+~P1(f775(f775(f232(a850),x59262),x59261)) % 186.05/186.62 [5942]~P110(x59421)+~P1(f775(f775(f233(x59421),x59422),f2(x59421)))+P1(f775(f775(f233(x59421),x59422),f775(f81(x59421),x59422))) % 186.05/186.62 [5943]~P68(x59431)+~P1(f775(f775(f232(x59431),x59432),f2(x59431)))+P1(f775(f775(f232(x59431),x59432),f775(f81(x59431),x59432))) % 186.05/186.62 [5952]~P9(x59521)+E(f775(f775(f66(x59521,x59521,f104(x59521)),f239(x59521)),x59522),f45(x59521,x59522))+~P1(f775(f63(x59521),x59522)) % 186.05/186.62 [5953]~P9(x59531)+E(f775(f775(f66(x59531,x59531,f103(x59531)),f180(x59531)),x59532),f44(x59531,x59532))+~P1(f775(f63(x59531),x59532)) % 186.05/186.62 [5967]~P117(x59671)+~P1(f775(f775(f233(a850),f2(a850)),x59672))+P1(f775(f775(f233(x59671),f2(x59671)),f775(f102(x59671),x59672))) % 186.05/186.62 [5968]~P110(x59681)+~P1(f775(f775(f233(a1),f2(a1)),x59682))+P1(f775(f775(f233(x59681),f2(x59681)),f775(f105(x59681),x59682))) % 186.05/186.62 [5969]~P110(x59691)+~P1(f775(f775(f232(a1),f2(a1)),x59692))+P1(f775(f775(f232(x59691),f2(x59691)),f775(f105(x59691),x59692))) % 186.05/186.62 [5972]~P10(x59722)+~P10(x59721)+E(f775(f303(a850,a1,f102(a1)),f295(a850,f775(a107,x59721),f775(a107,x59722))),f295(a1,x59721,x59722)) % 186.05/186.62 [5978]P1(f775(x59781,x59782))+~P1(f775(f775(f232(a1),f2(a1)),x59782))+~P1(f775(x59781,f775(f102(a1),f748(x59781)))) % 186.05/186.62 [6005]E(f775(f775(f82(a850),f775(f106(a850),x60051)),f775(f106(a850),x60052)),f775(f106(a850),x60051))+P1(f775(f775(f233(a1),x60051),a85))+~P1(f775(f775(f233(a1),x60052),a85)) % 186.05/186.62 [6009]~P110(x60091)+P1(f775(f775(f233(x60091),f2(x60091)),f84(x60091,x60092)))+~P1(f775(f775(f233(x60091),f2(x60091)),x60092)) % 186.05/186.62 [6023]~P77(x60231)+~P1(f775(f775(f233(x60231),x60232),f2(x60231)))+P1(f775(f775(f233(x60231),f2(x60231)),f775(f81(x60231),x60232))) % 186.05/186.62 [6024]~P77(x60241)+~P1(f775(f775(f232(x60241),x60242),f2(x60241)))+P1(f775(f775(f232(x60241),f2(x60241)),f775(f81(x60241),x60242))) % 186.05/186.62 [6027]E(x60271,f2(a850))+P1(f775(f775(f232(a1),f2(a1)),x60272))+~P1(f775(f775(f279(a850),f775(a107,x60272)),x60271)) % 186.05/186.62 [6028]E(x60281,f239(f857(x60282,a844)))+~E(f775(f42(x60282),x60281),f775(f42(x60282),f239(f857(x60282,a844))))+~P1(f775(f63(x60282),f239(f857(x60282,a844)))) % 186.05/186.62 [6059]~P1(f775(f775(f233(a850),f2(a850)),x60592))+~P1(f775(f775(f279(a850),x60591),x60592))+P1(f775(f775(f232(a850),x60591),x60592)) % 186.05/186.62 [6060]~P1(f775(f775(f233(a1),f2(a1)),x60602))+~P1(f775(f775(f279(a1),x60601),x60602))+P1(f775(f775(f232(a1),x60601),x60602)) % 186.05/186.62 [6066]~P110(x60661)+P1(f775(f775(f233(x60661),x60662),f2(x60661)))+~P1(f775(f775(f233(x60661),x60662),f775(f81(x60661),x60662))) % 186.05/186.62 [6067]~P68(x60671)+P1(f775(f775(f232(x60671),x60672),f2(x60671)))+~P1(f775(f775(f232(x60671),x60672),f775(f81(x60671),x60672))) % 186.05/186.62 [6075]~P88(x60751)+P1(f775(f775(f334(x60751),f775(f106(x60751),x60752)),f176(x60751)))+~P1(f775(f775(f232(a1),a85),x60752)) % 186.05/186.62 [6105]E(x61051,f2(a850))+~P1(f775(f775(f233(a850),x61051),f775(a114,x61052)))+P1(f775(f775(f233(a850),f559(x61052,x61051)),x61052)) % 186.05/186.62 [6129]~P110(x61291)+~P1(f775(f775(f233(x61291),f2(x61291)),f84(x61291,x61292)))+P1(f775(f775(f233(x61291),f2(x61291)),x61292)) % 186.05/186.62 [6131]~E(f775(f106(a850),x61312),f775(f106(a850),x61311))+P1(f775(f775(f232(a1),f775(f106(a1),x61311)),f2(a1)))+~P1(f775(a186,f775(f106(a1),x61312))) % 186.05/186.62 [6159]E(f775(f240(a1,a1),f57(x61591,x61592)),f775(f775(f43(a1),x61591),x61592))+~P1(f775(f775(f233(a1),x61591),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x61592)) % 186.05/186.62 [6193]E(f775(f250(a1,a1),f57(x61931,x61932)),f52(a1,x61931,x61932))+~P1(f775(f775(f233(a1),x61931),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x61932)) % 186.05/186.62 [6195]E(x61951,f2(a1))+~P1(f775(f775(f279(a1),x61952),x61951))+P1(f775(f775(f232(a1),f775(f77(a1),x61952)),f775(f77(a1),x61951))) % 186.05/186.62 [6197]~P117(x61972)+~P1(f775(f775(f233(x61972),f2(x61972)),f775(f102(x61972),x61971)))+P1(f775(f775(f233(a850),f2(a850)),x61971)) % 186.05/186.62 [6198]~P110(x61982)+~P1(f775(f775(f233(x61982),f2(x61982)),f775(f105(x61982),x61981)))+P1(f775(f775(f233(a1),f2(a1)),x61981)) % 186.05/186.62 [6199]~P110(x61992)+~P1(f775(f775(f232(x61992),f2(x61992)),f775(f105(x61992),x61991)))+P1(f775(f775(f232(a1),f2(a1)),x61991)) % 186.05/186.62 [6203]~E(x62032,f2(a850))+P1(f775(f775(f279(a850),f775(a107,x62031)),x62032))+~P1(f775(f775(f279(a1),x62031),f775(f102(a1),x62032))) % 186.05/186.62 [6204]E(f775(f240(a1,a1),f54(x62041,x62042)),f775(f775(f43(a1),x62041),x62042))+~P1(f775(f775(f233(a1),f2(a1)),x62041))+~P1(f775(f775(f232(a1),f2(a1)),x62042)) % 186.05/186.62 [6218]E(f775(f250(a1,a1),f54(x62181,x62182)),f52(a1,x62181,x62182))+~P1(f775(f775(f233(a1),f2(a1)),x62181))+~P1(f775(f775(f232(a1),f2(a1)),x62182)) % 186.05/186.62 [6236]~P77(x62361)+P1(f775(f775(f233(x62361),x62362),f2(x62361)))+~P1(f775(f775(f233(x62361),f2(x62361)),f775(f81(x62361),x62362))) % 186.05/186.62 [6237]~P77(x62371)+P1(f775(f775(f232(x62371),x62372),f2(x62371)))+~P1(f775(f775(f232(x62371),f2(x62371)),f775(f81(x62371),x62372))) % 186.05/186.62 [6263]P1(f775(f56(x62631,x62632),f57(x62631,x62632)))+~P1(f775(f775(f233(a1),x62631),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x62632)) % 186.05/186.62 [6279]~P1(f775(f775(f233(a850),f2(a850)),x62791))+~P1(f775(f775(f279(a850),x62792),x62791))+~P1(f775(f775(f233(a850),x62791),x62792)) % 186.05/186.62 [6280]~P1(f775(f775(f233(a1),f2(a1)),x62801))+~P1(f775(f775(f279(a1),x62802),x62801))+~P1(f775(f775(f233(a1),x62801),x62802)) % 186.05/186.62 [6292]P1(f775(f56(x62921,x62922),f54(x62921,x62922)))+~P1(f775(f775(f233(a1),f2(a1)),x62922))+~P1(f775(f775(f232(a1),f2(a1)),x62921)) % 186.05/186.62 [6334]~P77(x63341)+P1(f775(f775(f233(x63341),f775(f81(x63341),x63342)),f2(x63341)))+~P1(f775(f775(f233(x63341),f2(x63341)),x63342)) % 186.05/186.62 [6335]~P77(x63351)+P1(f775(f775(f232(x63351),f775(f81(x63351),x63352)),f2(x63351)))+~P1(f775(f775(f232(x63351),f2(x63351)),x63352)) % 186.05/186.62 [6357]E(f775(f775(f3(a850),f775(a107,x63571)),f775(a107,x63572)),f775(a107,f188(x63571,x63572)))+~P1(f775(f775(f232(a1),f2(a1)),x63572))+~P1(f775(f775(f232(a1),f2(a1)),x63571)) % 186.05/186.62 [6375]P1(f775(f775(f232(a1),f2(a1)),f188(x63751,x63752)))+~P1(f775(f775(f232(a1),f2(a1)),x63752))+~P1(f775(f775(f232(a1),f2(a1)),x63751)) % 186.05/186.62 [6414]~P1(f775(x64141,x64142))+P1(f775(x64141,f2(a850)))+P1(f775(x64141,f775(f775(f82(a850),f792(x64142,x64141)),f80(a850)))) % 186.05/186.62 [6500]E(f775(f106(a850),x65001),f775(f106(a850),x65002))+~P1(f775(f775(f232(a1),f775(f106(a1),x65002)),f2(a1)))+~P1(f775(a186,f775(f106(a1),x65001))) % 186.05/186.62 [6513]~E(x65131,f2(a850))+~E(f737(x65132,x65131),f2(a850))+E(f775(f132(a850,a850,f82(a850),x65131),x65132),f2(a850)) % 186.05/186.62 [6539]~P1(f775(f63(x65391),f670(x65392,x65391)))+~P1(f775(f63(f857(x65391,a844)),x65392))+P1(f775(f63(x65391),f44(f857(x65391,a844),x65392))) % 186.05/186.62 [6545]E(x65451,x65452)+P1(f775(f775(f233(a1),x65451),x65452))+~P1(f775(f775(f233(a1),x65451),f775(f775(f82(a1),x65452),f80(a1)))) % 186.05/186.62 [6547]P1(f775(f775(f233(a850),f775(a107,x65471)),f775(a107,x65472)))+~P1(f775(f775(f233(a1),f2(a1)),x65472))+~P1(f775(f775(f233(a1),x65471),x65472)) % 186.05/186.62 [6548]P1(f775(f775(f233(a850),f775(a107,x65481)),f775(a107,x65482)))+~P1(f775(f775(f232(a1),f2(a1)),x65481))+~P1(f775(f775(f233(a1),x65481),x65482)) % 186.05/186.62 [6549]P1(f775(f775(f232(a850),f775(a107,x65491)),f775(a107,x65492)))+~P1(f775(f775(f233(a1),f2(a1)),x65491))+~P1(f775(f775(f232(a1),x65491),x65492)) % 186.05/186.62 [6550]P1(f775(f775(f232(a850),f775(a107,x65501)),f775(a107,x65502)))+~P1(f775(f775(f232(a1),f2(a1)),x65502))+~P1(f775(f775(f232(a1),x65501),x65502)) % 186.05/186.62 [6561]E(f52(a850,f775(a107,x65611),f775(a107,x65612)),f775(a107,f52(a1,x65611,x65612)))+~P1(f775(f775(f232(a1),f2(a1)),x65612))+~P1(f775(f775(f232(a1),f2(a1)),x65611)) % 186.05/186.62 [6582]~P77(x65821)+~P1(f775(f775(f233(x65821),f775(f81(x65821),x65822)),f2(x65821)))+P1(f775(f775(f233(x65821),f2(x65821)),x65822)) % 186.05/186.62 [6583]~P77(x65831)+~P1(f775(f775(f232(x65831),f775(f81(x65831),x65832)),f2(x65831)))+P1(f775(f775(f232(x65831),f2(x65831)),x65832)) % 186.05/186.62 [6600]~P1(f775(f775(f233(a1),a85),x66002))+~P1(f775(f775(f233(a1),x66001),x66002))+P1(f775(f775(f233(a850),f775(f106(a850),x66001)),f775(f106(a850),x66002))) % 186.05/186.62 [6697]~P1(f775(f775(f232(a1),f2(a1)),x66971))+P1(f775(f775(f233(a850),f775(a107,x66971)),x66972))+~P1(f775(f775(f233(a1),x66971),f775(f102(a1),x66972))) % 186.05/186.62 [6698]~P1(f775(f775(f232(a1),f2(a1)),x66981))+P1(f775(f775(f279(a850),f775(a107,x66981)),x66982))+~P1(f775(f775(f279(a1),x66981),f775(f102(a1),x66982))) % 186.05/186.62 [6714]E(x67141,f2(a1))+E(f52(a1,x67142,x67141),f2(a1))+E(f775(f775(f3(a1),f775(f81(a1),f775(f775(f43(a1),x67142),x67141))),f80(a1)),f775(f775(f43(a1),x67142),f775(f81(a1),x67141))) % 186.05/186.62 [6730]~P1(f775(f775(f232(a1),f2(a1)),x67301))+~P1(f775(f775(f233(a850),f775(a107,x67301)),x67302))+P1(f775(f775(f233(a1),x67301),f775(f102(a1),x67302))) % 186.05/186.62 [6731]~P1(f775(f775(f232(a1),f2(a1)),x67311))+~P1(f775(f775(f279(a850),f775(a107,x67311)),x67312))+P1(f775(f775(f279(a1),x67311),f775(f102(a1),x67312))) % 186.05/186.62 [6771]~P1(f775(f775(f232(a850),f775(a107,x67711)),f775(a107,x67712)))+~P1(f775(f775(f233(a1),f2(a1)),x67711))+P1(f775(f775(f232(a1),x67711),x67712)) % 186.05/186.62 [6772]~P1(f775(f775(f232(a850),f775(a107,x67721)),f775(a107,x67722)))+~P1(f775(f775(f232(a1),f2(a1)),x67722))+P1(f775(f775(f232(a1),x67721),x67722)) % 186.05/186.62 [6803]P1(f775(f775(f232(a1),x68031),x68032))+~P1(f775(f775(f232(a850),f775(f106(a850),x68031)),f775(f106(a850),x68032)))+P1(f775(f775(f232(a1),x68031),a85)) % 186.05/186.62 [6830]P1(f775(f775(f232(a1),f2(a1)),f52(a1,x68301,x68302)))+~P1(f775(f775(f232(a1),f2(a1)),x68302))+~P1(f775(f775(f232(a1),f2(a1)),x68301)) % 186.05/186.62 [6929]P1(f775(f775(f233(a1),a85),x69291))+~P1(f775(f775(f233(a1),x69292),x69291))+~P1(f775(f775(f233(a850),f775(f106(a850),x69292)),f775(f106(a850),x69291))) % 186.05/186.62 [6977]E(f775(f775(f241(a1,a1),f775(f775(f43(a1),x69771),x69772)),f52(a1,x69771,x69772)),f57(x69771,x69772))+~P1(f775(f775(f233(a1),x69771),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x69772)) % 186.05/186.62 [6998]E(f775(f775(f241(a1,a1),f775(f775(f43(a1),x69981),x69982)),f52(a1,x69981,x69982)),f54(x69981,x69982))+~P1(f775(f775(f232(a1),f2(a1)),x69982))+~P1(f775(f775(f232(a1),f2(a1)),x69981)) % 186.05/186.62 [7053]~P91(x70532)+E(x70531,f115(x70532))+E(f775(f132(x70532,x70532,f83(x70532),f775(f131(x70532),x70531)),f775(f157(x70532),x70531)),f775(f65(x70532,f83(x70532)),f775(f158(x70532),x70531))) % 186.05/186.62 [7167]~E(x71671,f2(a850))+E(f775(f132(a850,a850,f82(a850),x71671),x71672),f2(a850))+P1(f775(f775(f334(a850),f737(x71672,x71671)),f775(f158(a850),x71672))) % 186.05/186.62 [7221]~P1(f775(f775(f233(a1),x72212),f2(a1)))+P1(f775(f775(f233(a1),f775(f775(f43(a1),x72211),x72212)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x72211)) % 186.05/186.62 [7223]~P1(f775(f775(f233(a1),x72231),f2(a1)))+P1(f775(f775(f233(a1),f775(f775(f43(a1),x72231),x72232)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x72232)) % 186.05/186.62 [7224]~P1(f775(f775(f233(a1),x72242),f2(a1)))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x72241),x72242)),f2(a1)))+~P1(f775(f775(f232(a1),f2(a1)),x72241)) % 186.05/186.62 [7225]~P1(f775(f775(f232(a1),x72251),f2(a1)))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x72251),x72252)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x72252)) % 186.05/186.62 [7234]P1(f775(f775(f334(f857(x72341,a844)),f670(x72342,x72341)),x72342))+~P1(f775(f63(f857(x72341,a844)),x72342))+P1(f775(f63(x72341),f44(f857(x72341,a844),x72342))) % 186.05/186.62 [7339]P29(x73391,x73391,x73392,f239(f857(x73391,a844)))+~E(f775(f303(x73391,x73391,x73392),f239(f857(x73391,a844))),f239(f857(x73391,a844)))+~P1(f775(f63(x73391),f239(f857(x73391,a844)))) % 186.05/186.62 [7468]~P29(x74681,x74681,x74682,f239(f857(x74681,a844)))+E(f775(f303(x74681,x74681,x74682),f239(f857(x74681,a844))),f239(f857(x74681,a844)))+~P1(f775(f63(x74681),f239(f857(x74681,a844)))) % 186.05/186.62 [7609]E(f775(f775(f43(a1),x76091),x76092),f775(f106(a1),a99))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x76091),x76092)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x76091)) % 186.05/186.62 [7667]~P1(f775(f775(f233(a1),x76672),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f43(a1),x76671),x76672)),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x76671)) % 186.05/186.62 [7672]E(f775(f775(f82(a1),x76721),x76722),f52(a1,x76721,x76722))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),x76721),x76722)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x76721)) % 186.05/186.62 [7674]P1(f775(f775(f233(a1),x76741),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f43(a1),x76741),x76742)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x76742)) % 186.05/186.62 [7926]~P99(x79261)+P50(a850,x79261,f279(a850),x79262)+~P1(f775(f775(f232(x79261),f775(x79262,f377(x79262,x79261))),f775(x79262,f393(x79262,x79261)))) % 186.05/186.62 [8368]~P100(x83681)+P18(x83681,x83682)+~P1(f775(f775(f232(x83681),f775(f775(f153(x83681),x83682),f761(x83682,x83681))),f775(f775(f153(x83681),x83682),f762(x83682,x83681)))) % 186.05/186.62 [5550]E(x55501,f2(a1))+~E(f52(a1,x55502,x55501),f2(a1))+E(f775(f775(f43(a1),x55502),f775(f81(a1),x55501)),f775(f81(a1),f775(f775(f43(a1),x55502),x55501))) % 186.05/186.62 [5567]~P38(x55672)+~P38(x55671)+P38(f775(f775(f103(f857(a1,a844)),x55671),x55672)) % 186.05/186.62 [5568]~P38(x55682)+~P38(x55681)+P38(f775(f775(f104(f857(a1,a844)),x55681),x55682)) % 186.05/186.62 [5585]~P88(x55851)+~P60(x55851)+E(f775(f81(x55851),f775(f775(f283(x55851),f80(x55851)),x55852)),f775(f775(f283(x55851),f775(f106(x55851),a99)),x55852)) % 186.05/186.62 [5710]E(x57101,f2(a1))+~E(f52(a1,x57102,x57101),f2(a1))+E(f775(f775(f43(a1),f775(f81(a1),x57102)),x57101),f775(f81(a1),f775(f775(f43(a1),x57102),x57101))) % 186.05/186.62 [5844]~P100(x58441)+P18(x58441,x58442)+P1(f775(f775(f233(a850),f762(x58442,x58441)),f775(f181(f851(x58441)),x58442))) % 186.05/186.62 [6001]~P88(x60011)+~E(f775(f106(x60011),x60012),f2(x60011))+P33(x60011,f775(f106(x60011),f775(f775(f82(a1),x60012),f775(f81(a1),a85)))) % 186.05/186.62 [6002]~P88(x60021)+~E(f775(f106(x60021),x60022),f2(x60021))+P33(x60021,f775(f106(x60021),f775(f775(f82(a1),a85),f775(f81(a1),x60022)))) % 186.05/186.62 [6004]E(f775(a58,f54(f775(f81(a1),x60041),f775(f81(a1),x60042))),f53(x60041,x60042))+P1(f775(f775(f233(a1),f2(a1)),x60042))+P1(f775(f775(f232(a1),f2(a1)),x60041)) % 186.05/186.62 [6137]~E(x61372,f2(a850))+~E(x61371,f2(a850))+P1(f775(f775(f232(a1),f775(f102(a1),x61371)),f775(f81(a1),f775(f102(a1),x61372)))) % 186.05/186.62 [6163]E(f775(f775(f82(a850),f775(f106(a850),x61631)),f775(f106(a850),x61632)),f775(f106(a850),f775(f775(f82(a1),x61631),x61632)))+P1(f775(f775(f233(a1),x61631),a85))+P1(f775(f775(f233(a1),x61632),a85)) % 186.05/186.62 [6301]~P68(x63011)+~P1(f775(f775(f233(x63011),f2(x63011)),x63012))+P1(f775(f775(f233(x63011),f775(f81(x63011),x63012)),x63012)) % 186.05/186.63 [6302]~P68(x63021)+~P1(f775(f775(f232(x63021),f2(x63021)),x63022))+P1(f775(f775(f232(x63021),f775(f81(x63021),x63022)),x63022)) % 186.05/186.63 [6485]E(f775(f775(f3(a850),f775(a107,x64851)),f775(a107,x64852)),f775(a107,f775(f775(f3(a1),x64851),x64852)))+~P1(f775(f775(f232(a1),f2(a1)),x64852))+~P1(f775(f775(f232(a1),x64852),x64851)) % 186.05/186.63 [6522]E(f775(a107,f52(a1,f775(f106(a1),x65221),f775(f106(a1),x65222))),f52(a850,f775(f106(a850),x65221),f775(f106(a850),x65222)))+P1(f775(a186,f775(f106(a1),x65221)))+P1(f775(a186,f775(f106(a1),x65222))) % 186.05/186.63 [6540]~P68(x65401)+P1(f775(f775(f233(x65401),f2(x65401)),x65402))+~P1(f775(f775(f233(x65401),f775(f81(x65401),x65402)),x65402)) % 186.05/186.63 [6541]~P68(x65411)+P1(f775(f775(f232(x65411),f2(x65411)),x65412))+~P1(f775(f775(f232(x65411),f775(f81(x65411),x65412)),x65412)) % 186.05/186.63 [6552]~P68(x65521)+~P1(f775(f775(f233(x65521),f2(x65521)),x65522))+P1(f775(f775(f233(x65521),f2(x65521)),f775(f775(f82(x65521),x65522),x65522))) % 186.05/186.63 [6554]~P68(x65541)+~P1(f775(f775(f232(x65541),f2(x65541)),x65542))+P1(f775(f775(f232(x65541),f2(x65541)),f775(f775(f82(x65541),x65542),x65542))) % 186.05/186.63 [6565]E(f775(f775(f82(a850),f775(a107,x65651)),f775(a107,x65652)),f775(a107,f775(f775(f82(a1),x65651),x65652)))+~P1(f775(f775(f232(a1),f2(a1)),x65652))+~P1(f775(f775(f232(a1),f2(a1)),x65651)) % 186.05/186.63 [6578]E(x65781,f2(a850))+P1(f775(f775(f233(a850),f2(a850)),x65782))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f242(a850),x65782),x65781))) % 186.05/186.63 [6611]~P88(x66111)+E(f775(f106(x66111),x66112),f2(x66111))+~P33(x66111,f775(f106(x66111),f775(f775(f82(a1),a85),f775(f81(a1),x66112)))) % 186.05/186.63 [6612]~P88(x66121)+E(f775(f106(x66121),x66122),f2(x66121))+~P33(x66121,f775(f106(x66121),f775(f775(f82(a1),x66122),f775(f81(a1),a85)))) % 186.05/186.63 [6674]~P1(f775(f63(x66741),x66742))+~P1(f775(f63(x66741),f239(f857(x66741,a844))))+P1(f775(f63(x66741),f775(f81(f857(x66741,a844)),x66742))) % 186.05/186.63 [6699]~P1(f775(f775(f233(a1),f2(a1)),x66992))+~P1(f775(f775(f232(a1),x66992),x66991))+P1(f775(f775(f233(a1),f2(a1)),f775(f775(f43(a1),x66991),x66992))) % 186.05/186.63 [6700]~P1(f775(f775(f233(a1),x67002),f2(a1)))+~P1(f775(f775(f232(a1),x67001),f2(a1)))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f43(a1),x67001),x67002))) % 186.05/186.63 [6742]~P1(f775(f775(f233(a850),f2(a850)),x67422))+~P1(f775(f775(f233(a850),f2(a850)),x67421))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f83(a850),x67421),x67422))) % 186.05/186.63 [6743]~P1(f775(f775(f232(a1),f2(a1)),x67432))+~P1(f775(f775(f232(a1),f2(a1)),x67431))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),x67431),x67432))) % 186.05/186.63 [6744]~P1(f775(f775(f232(a1),f2(a1)),x67442))+~P1(f775(f775(f232(a1),f2(a1)),x67441))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f83(a1),x67441),x67442))) % 186.05/186.63 [6745]~P1(f775(f775(f233(a1),f2(a1)),x67452))+~P1(f775(f775(f232(a1),f2(a1)),x67451))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f43(a1),x67451),x67452))) % 186.05/186.63 [6746]~P1(f775(f775(f232(a1),f2(a1)),x67462))+~P1(f775(f775(f232(a1),f2(a1)),x67461))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f43(a1),x67461),x67462))) % 186.05/186.63 [6815]E(x68151,f2(a1))+E(f52(a1,x68152,x68151),f2(a1))+E(f775(f775(f3(a1),f775(f81(a1),f775(f775(f43(a1),x68152),x68151))),f80(a1)),f775(f775(f43(a1),f775(f81(a1),x68152)),x68151)) % 186.05/186.63 [6875]P1(f775(f775(f233(a850),f2(a850)),x68751))+P1(f775(f775(f233(a850),f2(a850)),x68752))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f82(a850),x68752),x68751))) % 186.05/186.63 [6876]~P68(x68761)+P1(f775(f775(f233(x68761),f2(x68761)),x68762))+~P1(f775(f775(f233(x68761),f2(x68761)),f775(f775(f82(x68761),x68762),x68762))) % 186.05/186.63 [6877]~P68(x68771)+P1(f775(f775(f232(x68771),f2(x68771)),x68772))+~P1(f775(f775(f232(x68771),f2(x68771)),f775(f775(f82(x68771),x68772),x68772))) % 186.05/186.63 [6930]~P1(f775(f63(x69301),x69302))+P1(f775(f63(x69301),f239(f857(x69301,a844))))+~P1(f775(f63(x69301),f775(f81(f857(x69301,a844)),x69302))) % 186.05/186.63 [6990]P1(f775(f775(f232(a1),x69901),f2(a1)))+~P1(f775(f775(f233(a1),x69902),f2(a1)))+~P1(f775(f775(f232(a1),f2(a1)),f775(f775(f43(a1),x69901),x69902))) % 186.05/186.63 [6996]~P1(f775(f775(f233(a1),f2(a1)),x69961))+P1(f775(f775(f232(a1),x69961),x69962))+~P1(f775(f775(f233(a1),f2(a1)),f775(f775(f43(a1),x69962),x69961))) % 186.05/186.63 [6997]~P1(f775(f775(f232(a1),f2(a1)),x69972))+P1(f775(f775(f232(a1),x69971),x69972))+~P1(f775(f775(f233(a1),f2(a1)),f775(f775(f43(a1),x69972),x69971))) % 186.05/186.63 [7029]P1(f775(f775(f233(a1),f2(a1)),x70291))+~P1(f775(f775(f232(a1),f2(a1)),x70292))+~P1(f775(f775(f233(a1),f2(a1)),f775(f775(f43(a1),x70292),x70291))) % 186.05/186.63 [7030]P1(f775(f775(f232(a1),f2(a1)),x70301))+~P1(f775(f775(f233(a1),f2(a1)),x70302))+~P1(f775(f775(f232(a1),f2(a1)),f775(f775(f43(a1),x70301),x70302))) % 186.05/186.63 [7499]~P1(f775(f63(x74992),f239(f857(x74992,a844))))+~P1(f775(f63(x74991),f239(f857(x74991,a844))))+P1(f775(f63(f858(x74991,x74992)),f239(f857(f858(x74991,x74992),a844)))) % 186.05/186.63 [7500]~P1(f775(f63(x75002),f239(f857(x75002,a844))))+~P1(f775(f63(x75001),f239(f857(x75001,a844))))+P1(f775(f63(f856(x75001,x75002)),f239(f857(f856(x75001,x75002),a844)))) % 186.05/186.63 [7572]~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x75721))+~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x75722))+P1(f775(f775(f233(a850),x75721),f775(f775(f83(a850),x75722),x75721))) % 186.05/186.63 [7573]~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x75731))+~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x75732))+P1(f775(f775(f233(a850),x75731),f775(f775(f83(a850),x75731),x75732))) % 186.05/186.63 [7608]E(f775(f42(x76081),f239(f857(x76081,a844))),f775(a114,f2(a850)))+P1(f775(f63(x76082),f239(f857(x76082,a844))))+~P1(f775(f63(f857(x76082,x76081)),f239(f857(f857(x76082,x76081),a844)))) % 186.05/186.63 [7733]~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x77332))+~P1(f775(f775(f233(a850),f775(a114,f2(a850))),x77331))+P1(f775(f775(f233(a850),f775(a114,f2(a850))),f775(f775(f83(a850),x77331),x77332))) % 186.05/186.63 [7734]~P1(f775(f775(f232(a850),f775(a114,f2(a850))),x77341))+~P1(f775(f775(f232(a850),f775(a114,f2(a850))),x77342))+P1(f775(f775(f232(a850),f775(a114,f2(a850))),f775(f775(f83(a850),x77341),x77342))) % 186.05/186.63 [8415]E(x84151,f115(x84152))+~P1(f775(f127(x84152),x84151))+E(f162(x84152,f775(f775(f10(a844,a844,x84152),a328),f775(f775(f9(x84152,x84152,a844),a330),f134(x84152,x84151))),x84151),f116(x84152,x84151)) % 186.05/186.63 [8513]~P38(x85132)+~P38(x85131)+E(f775(f303(a850,a1,f102(a1)),f775(f775(f103(f857(a850,a844)),f775(f303(a1,a850,a107),x85131)),f775(f303(a1,a850,a107),x85132))),f775(f775(f103(f857(a1,a844)),x85131),x85132)) % 186.05/186.63 [8514]~P38(x85142)+~P38(x85141)+E(f775(f303(a850,a1,f102(a1)),f775(f775(f104(f857(a850,a844)),f775(f303(a1,a850,a107),x85141)),f775(f303(a1,a850,a107),x85142))),f775(f775(f104(f857(a1,a844)),x85141),x85142)) % 186.05/186.63 [9103]~P88(x91031)+~E(f775(f106(x91031),x91032),f80(x91031))+P33(x91031,f775(f106(x91031),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f81(a1),x91032)))) % 186.05/186.63 [9318]~P88(x93181)+E(f775(f106(x93181),x93182),f80(x93181))+~P33(x93181,f775(f106(x93181),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f81(a1),x93182)))) % 186.05/186.63 [9732]~P99(x97322)+P52(a850,x97322,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97321)+P1(f775(f775(f279(a850),f369(x97321,x97322)),f370(x97321,x97322))) % 186.05/186.63 [9735]~P99(x97351)+P52(a850,x97351,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97352)+~P1(f775(f775(f279(a850),f370(x97352,x97351)),f369(x97352,x97351))) % 186.05/186.63 [9736]~P99(x97361)+P52(a850,x97361,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x97362)+~P1(f775(f775(f233(x97361),f775(x97362,f369(x97362,x97361))),f775(x97362,f370(x97362,x97361)))) % 186.05/186.63 [9825]~P99(x98251)+P50(a850,x98251,f279(a850),x98252)+~P52(a850,x98251,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x98252) % 186.05/186.63 [10023]E(x100231,f2(a1))+E(x100232,f2(a1))+E(f775(f252(a1,a1,a1,a1,f39(a1),f775(f83(a1),f84(a1,x100232))),f775(f775(f775(f98(f856(a1,a1)),f775(f775(a330,f84(a1,x100231)),f84(a1,x100232))),f60(x100231,x100232)),f775(f775(f251(a1,a1,f856(a1,a1)),f775(f775(f20(a1,f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f857(f856(a1,a1),f856(a1,a1))),f857(f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),a1),f20(a1,f856(a1,a1),f856(a1,a1))),f775(f775(f10(f856(a1,a1),f857(a1,f857(f856(a1,a1),f856(a1,a1))),a1),f775(f9(a1,f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),f775(f775(f10(a844,f857(f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),a1),f98(f856(a1,a1))),f775(f775(f9(a1,a1,a844),a330),f2(a1))))),f775(f775(f9(a1,a1,f856(a1,a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f775(f775(f9(a1,f857(a1,a1),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f856(a1,a1)),f857(f857(a1,a1),f857(a1,f856(a1,a1))),a1),f10(a1,f856(a1,a1),a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f775(f775(f9(a1,a1,a1),f775(f775(f10(a1,f857(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f775(f3(a1),f775(f77(a1),x100232))))),f60(x100231,x100232)))),f53(x100231,x100232)) % 186.05/186.63 [10024]E(x100241,f2(a1))+E(x100242,f2(a1))+E(f775(f252(a1,a1,a1,a1,f39(a1),f775(f83(a1),f84(a1,x100242))),f775(f775(f775(f98(f856(a1,a1)),f775(f775(a332,f775(f775(a331,f775(f775(f233(a1),f2(a1)),x100242)),f775(f775(f232(a1),f2(a1)),x100241))),f775(f775(a331,f775(f775(f233(a1),x100242),f2(a1))),f775(f775(f233(a1),x100241),f2(a1))))),f60(x100241,x100242)),f775(f775(f251(a1,a1,f856(a1,a1)),f775(f775(f20(a1,f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f857(f856(a1,a1),f856(a1,a1))),f857(f857(a1,f856(a1,a1)),f857(a1,f856(a1,a1))),a1),f20(a1,f856(a1,a1),f856(a1,a1))),f775(f775(f10(f856(a1,a1),f857(a1,f857(f856(a1,a1),f856(a1,a1))),a1),f775(f9(a1,f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),f775(f775(f10(a844,f857(f856(a1,a1),f857(f856(a1,a1),f856(a1,a1))),a1),f98(f856(a1,a1))),f775(f775(f9(a1,a1,a844),a330),f2(a1))))),f775(f775(f9(a1,a1,f856(a1,a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f775(f775(f9(a1,f857(a1,a1),f857(a1,f856(a1,a1))),f775(f775(f10(f857(a1,f856(a1,a1)),f857(f857(a1,a1),f857(a1,f856(a1,a1))),a1),f10(a1,f856(a1,a1),a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f775(f775(f9(a1,a1,a1),f775(f775(f10(a1,f857(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f775(f3(a1),f775(f77(a1),x100242))))),f60(x100241,x100242)))),f53(x100241,x100242)) % 186.05/186.63 [5575]~P110(x55751)+~P88(x55751)+E(f775(f77(x55751),f775(f775(f242(x55751),f775(f106(x55751),a99)),x55752)),f80(x55751)) % 186.05/186.63 [6076]~P133(x60761)+~P1(f775(f775(f233(a1),x60762),f2(a1)))+E(f775(f81(x60761),f775(f102(x60761),f775(a107,f775(f81(a1),x60762)))),f775(f105(x60761),x60762)) % 186.05/186.63 [6285]P1(f775(f775(f232(a101),x62851),f80(a101)))+E(f775(f775(f82(a101),f80(a101)),f267(x62851,f775(f775(f43(a101),x62852),x62851))),f267(x62851,x62852))+P1(f775(f775(f233(a101),x62852),x62851)) % 186.05/186.63 [6358]E(x63581,f2(a1))+~E(f775(f77(a1),x63582),f80(a1))+P1(f775(f775(f279(a1),f775(f775(f83(a1),x63581),x63582)),x63581)) % 186.05/186.63 [6784]~E(x67842,f80(a850))+~P1(f775(f775(f233(a850),f2(a850)),x67841))+P1(f775(f775(f279(a850),f775(f775(f83(a850),x67841),x67842)),x67841)) % 186.05/186.63 [6785]~E(x67851,f80(a850))+~P1(f775(f775(f233(a850),f2(a850)),x67852))+P1(f775(f775(f279(a850),f775(f775(f83(a850),x67851),x67852)),x67852)) % 186.05/186.63 [6918]~P87(x69181)+~P1(f775(f775(f334(x69181),x69182),f112(x69181)))+~E(f775(f775(f82(x69181),f775(f775(f82(x69181),f80(x69181)),x69182)),x69182),f2(x69181)) % 186.05/186.63 [7031]~P1(f775(f775(f233(a1),x70311),f2(a1)))+~P1(f775(f775(f232(a1),x70312),f2(a1)))+E(f775(f240(a1,a1),f775(a58,f54(f775(f81(a1),x70311),f775(f81(a1),x70312)))),f775(f775(f43(a1),x70311),x70312)) % 186.05/186.63 [7047]~P1(f775(f775(f233(a1),x70471),f2(a1)))+~P1(f775(f775(f232(a1),x70472),f2(a1)))+E(f775(f250(a1,a1),f775(a58,f54(f775(f81(a1),x70471),f775(f81(a1),x70472)))),f52(a1,x70471,x70472)) % 186.05/186.63 [7055]~P1(f775(f775(f233(a1),x70552),f2(a1)))+E(f775(f240(a1,a1),f775(a58,f57(f775(f81(a1),x70551),f775(f81(a1),x70552)))),f775(f775(f43(a1),x70551),x70552))+~P1(f775(f775(f233(a1),f2(a1)),x70551)) % 186.05/186.63 [7059]E(x70591,f2(a1))+E(f775(f77(a1),x70592),f80(a1))+~P1(f775(f775(f279(a1),f775(f775(f83(a1),x70591),x70592)),x70591)) % 186.05/186.63 [7074]~P1(f775(f775(f233(a1),x70742),f2(a1)))+E(f775(f250(a1,a1),f775(a58,f57(f775(f81(a1),x70741),f775(f81(a1),x70742)))),f52(a1,x70741,x70742))+~P1(f775(f775(f233(a1),f2(a1)),x70741)) % 186.05/186.63 [7125]E(f775(f775(f43(a1),f775(f775(f242(a1),x71251),x71252)),x71251),f775(f775(f242(a1),x71251),f775(f775(f3(a850),x71252),f775(a114,f2(a850)))))+~P1(f775(f775(f233(a850),f2(a850)),x71252))+~P1(f775(f775(f233(a1),f2(a1)),x71251)) % 186.05/186.63 [7230]~P1(f775(f775(f233(a850),f2(a850)),x72301))+~P1(f775(f775(f233(a850),f80(a850)),x72302))+P1(f775(f775(f233(a850),f775(f775(f43(a850),x72301),x72302)),x72301)) % 186.05/186.63 [7231]~P1(f775(f775(f233(a850),f2(a850)),x72311))+~P1(f775(f775(f233(a850),f2(a850)),x72312))+P1(f775(f775(f233(a850),f775(f775(f3(a850),x72311),x72312)),x72311)) % 186.05/186.63 [7232]~P1(f775(f775(f233(a1),f2(a1)),x72321))+~P1(f775(f775(f233(a1),f80(a1)),x72322))+P1(f775(f775(f233(a1),f775(f775(f43(a1),x72321),x72322)),x72321)) % 186.05/186.63 [7391]E(x73911,f2(a850))+~E(x73912,f2(a1))+~P1(f775(f775(f233(a1),f2(a1)),f775(f775(f242(a1),f775(f77(a1),x73912)),x73911))) % 186.05/186.63 [7429]E(x74291,f80(a850))+~P1(f775(f775(f233(a850),f2(a850)),x74292))+~P1(f775(f775(f279(a850),f775(f775(f83(a850),x74292),x74291)),x74292)) % 186.05/186.63 [7430]E(x74301,f80(a850))+~P1(f775(f775(f233(a850),f2(a850)),x74302))+~P1(f775(f775(f279(a850),f775(f775(f83(a850),x74301),x74302)),x74302)) % 186.05/186.63 [7816]~E(x78162,f115(f851(x78161)))+E(f775(f181(f851(f851(x78161))),f164(x78161,x78162)),f2(a850))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x78161),a850),f181(f851(x78161))),x78162))) % 186.05/186.63 [8066]P1(f775(x80661,x80662))+~P1(f775(x80661,f775(a109,f575(x80661,x80662))))+~P1(f775(f775(f334(f857(f856(a850,a850),a844)),x80662),a100)) % 186.05/186.63 [8080]E(x80801,f115(f851(x80802)))+E(f775(f181(f851(x80802)),f775(f775(f153(f851(x80802)),x80801),f2(a850))),f775(f181(f851(f851(x80802))),f164(x80802,x80801)))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x80802),a850),f181(f851(x80802))),x80801))) % 186.05/186.63 [8752]~P1(f775(f63(x87521),f775(f256(x87521),x87522)))+~P1(f775(f63(x87521),f239(f857(x87521,a844))))+P1(f775(f63(x87521),f775(f256(x87521),f775(f775(f10(a844,a844,x87521),a328),x87522)))) % 186.05/186.63 [8805]E(f775(f775(f241(a850,a850),f775(a114,f775(f775(f43(a850),f775(f775(f3(a850),x88051),x88052)),x88052))),f52(a850,f775(f775(f3(a850),x88051),x88052),x88052)),f87(f856(a850,a850),f55(x88051,x88052)))+~P1(f775(f775(f233(a850),f2(a850)),x88052))+~P1(f775(f775(f232(a850),x88052),x88051)) % 186.05/186.63 [9070]~P1(f775(f63(x90701),f775(f256(x90701),x90702)))+P1(f775(f63(x90701),f239(f857(x90701,a844))))+~P1(f775(f63(x90701),f775(f256(x90701),f775(f775(f10(a844,a844,x90701),a328),x90702)))) % 186.05/186.63 [9729]P30(x97291,x97292)+~P36(x97291,f775(f240(f857(f856(x97291,x97291),a844),f857(f856(x97291,x97291),a844)),x97292))+~P1(f775(f775(f232(f857(f856(x97291,x97291),a844)),f775(f775(f281(x97291,x97291,x97291),f775(f240(f857(f856(x97291,x97291),a844),f857(f856(x97291,x97291),a844)),x97292)),f775(f250(f857(f856(x97291,x97291),a844),f857(f856(x97291,x97291),a844)),x97292))),f775(f240(f857(f856(x97291,x97291),a844),f857(f856(x97291,x97291),a844)),x97292))) % 186.05/186.63 [9829]~E(f292(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x98292,x98291),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x98292),x98291))+P1(f775(f775(f279(a850),x98291),x98292)) % 186.05/186.63 [9830]~E(f289(a850,f279(a850),f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x98302,x98301),f180(f857(a850,a844)))+~P1(f775(f775(f279(a850),x98302),x98301))+P1(f775(f775(f279(a850),x98301),x98302)) % 186.05/186.63 [7149]~P1(f775(f775(f233(a850),f2(a850)),x71492))+P1(f775(f775(f233(a850),x71491),x71492))+E(f775(a114,f775(f775(f43(a850),f775(f775(f3(a850),x71491),x71492)),x71492)),f775(f775(f43(a850),x71491),x71492)) % 186.05/186.63 [7306]~P1(f775(f775(f233(a850),f2(a850)),x73062))+~P1(f775(f775(f232(a850),x73062),x73061))+E(f775(a114,f775(f775(f43(a850),f775(f775(f3(a850),x73061),x73062)),x73062)),f775(f775(f43(a850),x73061),x73062)) % 186.05/186.63 [8279]~P88(x82791)+~P87(x82791)+~P33(x82791,f775(f106(x82791),f775(f775(f3(a1),f775(f775(f82(a1),x82792),x82792)),a99))) % 186.05/186.63 [8980]E(x89801,f2(a850))+E(f775(f775(f251(a850,a850,f856(a850,a850)),f775(f775(f10(a850,f857(a850,f856(a850,a850)),a850),f241(a850,a850)),a114)),f87(f856(a850,a850),f55(f775(f775(f3(a850),x89802),x89801),x89801))),f87(f856(a850,a850),f55(x89802,x89801)))+P1(f775(f775(f233(a850),x89802),x89801)) % 186.05/186.63 [9377]P1(f775(x93772,f699(x93772,x93771)))+P1(f775(x93771,f699(x93772,x93771)))+E(f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93771)),f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93772))) % 186.05/186.63 [9381]~P1(f775(x93812,f699(x93812,x93811)))+~P1(f775(x93811,f699(x93812,x93811)))+E(f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93811)),f775(f256(a1),f775(f775(f20(a1,a844,a844),f775(f775(f10(a844,f857(a844,a844),a1),a331),f775(f232(a1),f2(a1)))),x93812))) % 186.05/186.63 [9912]~P1(f775(f775(f279(a850),x99122),x99121))+P1(f775(f775(f279(a850),x99121),x99122))+P1(f775(f775(f334(a850),x99121),f287(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99122))) % 186.05/186.63 [9913]~P1(f775(f775(f279(a850),x99132),x99131))+P1(f775(f775(f279(a850),x99131),x99132))+P1(f775(f775(f334(a850),x99132),f290(a850,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x99131))) % 186.05/186.63 [7529]~P88(x75291)+~P61(x75291)+E(f775(f775(f283(x75291),x75292),f775(f106(x75291),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))),x75292) % 186.05/186.63 [9102]~P88(x91021)+~E(f775(f106(x91021),x91022),f80(x91021))+P33(x91021,f775(f106(x91021),f775(f775(f82(a1),x91022),f775(f81(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.63 [9257]~P120(x92571)+~E(x92572,f2(x92571))+E(f775(f775(f242(x92571),x92572),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f2(x92571)) % 186.05/186.63 [9258]~P120(x92581)+~E(x92582,f80(x92581))+E(f775(f775(f242(x92581),x92582),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(x92581)) % 186.05/186.63 [9271]~P120(x92711)+~E(x92712,f775(f81(x92711),f80(x92711)))+E(f775(f775(f242(x92711),x92712),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(x92711)) % 186.05/186.63 [9319]~P88(x93191)+E(f775(f106(x93191),x93192),f80(x93191))+~P33(x93191,f775(f106(x93191),f775(f775(f82(a1),x93192),f775(f81(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.63 [9670]~P110(x96702)+E(x96701,f2(x96702))+P1(f775(f775(f233(x96702),f2(x96702)),f775(f775(f242(x96702),x96701),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.63 [9728]~P110(x97282)+~E(x97281,f2(x97282))+~P1(f775(f775(f233(x97282),f2(x97282)),f775(f775(f242(x97282),x97281),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.63 [9767]P1(f775(f775(f232(a1),x97671),f2(a1)))+P1(f775(f775(f233(a1),x97672),x97671))+E(f775(f50(x97671),f54(x97672,f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97671))),f54(x97672,x97671)) % 186.05/186.63 [9768]~P1(f775(f775(f233(a1),f2(a1)),x97681))+P1(f775(f775(f233(a1),x97682),x97681))+E(f775(f50(x97681),f54(x97682,f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97681))),f54(x97682,x97681)) % 186.05/186.63 [9769]P1(f775(f775(f232(a1),x97691),f2(a1)))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),x97692),x97691)))+E(f775(f50(x97691),f57(x97692,f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97691))),f57(x97692,x97691)) % 186.05/186.63 [9770]~P1(f775(f775(f233(a1),f2(a1)),x97701))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),x97702),x97701)))+E(f775(f50(x97701),f57(x97702,f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97701))),f57(x97702,x97701)) % 186.05/186.63 [9771]~P2(x97711)+~P1(f775(f775(f232(a1),f2(a1)),x97712))+E(f775(f102(x97711),f775(a107,f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x97712))),f775(f775(f82(x97711),f775(f102(x97711),f775(a107,x97712))),f775(f102(x97711),f775(a107,x97712)))) % 186.05/186.63 [4930]~P140(x49301,x49303,x49302)+~E(x49303,f2(a1))+P1(f775(x49301,x49302)) % 186.05/186.63 [5056]~P100(x50561)+~P18(x50561,x50563)+P18(x50561,f151(x50561,x50562,x50563)) % 186.05/186.63 [5057]~P100(x50571)+~P18(x50571,x50573)+P18(x50571,f162(x50571,x50572,x50573)) % 186.05/186.63 [4643]~P69(x46432)+~E(x46433,f775(f81(x46432),x46431))+E(x46431,f775(f81(x46432),x46433)) % 186.05/186.63 [4645]~P69(x46451)+~E(f775(f81(x46451),x46453),x46452)+E(f775(f81(x46451),x46452),x46453) % 186.05/186.63 [4716]~P86(x47163)+E(x47161,x47162)+~E(f775(f102(x47163),x47161),f775(f102(x47163),x47162)) % 186.05/186.63 [4717]~P87(x47173)+E(x47171,x47172)+~E(f775(f105(x47173),x47171),f775(f105(x47173),x47172)) % 186.05/186.63 [4718]~P69(x47183)+E(x47181,x47182)+~E(f775(f81(x47183),x47181),f775(f81(x47183),x47182)) % 186.05/186.63 [4719]~P90(x47193)+E(x47191,x47192)+~E(f775(f81(x47193),x47191),f775(f81(x47193),x47192)) % 186.05/186.63 [4720]~P100(x47203)+E(x47201,x47202)+~E(f775(f257(x47203),x47201),f775(f257(x47203),x47202)) % 186.05/186.63 [4721]~P100(x47213)+E(x47211,x47212)+~E(f775(f296(x47213),x47211),f775(f296(x47213),x47212)) % 186.05/186.63 [4722]~P100(x47223)+E(x47221,x47222)+~E(f775(f293(x47223),x47221),f775(f293(x47223),x47222)) % 186.05/186.63 [4723]~P100(x47233)+E(x47231,x47232)+~E(f775(f258(x47233),x47231),f775(f258(x47233),x47232)) % 186.05/186.63 [4953]~P141(x49531,x49532,x49533)+~E(x49532,f2(a1))+P1(f775(x49531,f2(a1))) % 186.05/186.63 [4992]~E(x49921,f2(a850))+E(f374(x49921,x49922,x49923),f180(f857(x49923,a844)))+~E(f775(f42(x49923),x49922),f775(a114,x49921)) % 186.05/186.63 [5139]~E(x51392,f2(a850))+E(f775(f240(a850,a850),x51391),f2(a850))+~P1(f775(f55(x51393,x51392),x51391)) % 186.05/186.63 [5183]P1(f775(x51831,x51832))+~E(x51833,f775(f102(a1),x51832))+~P1(f775(x51831,f775(a107,x51833))) % 186.05/186.63 [5637]~E(x56373,f2(a850))+~P1(f775(x56371,x56372))+P1(f775(x56371,f52(a850,x56372,x56373))) % 186.05/186.63 [5784]~P1(f775(a26,x57843))+~P1(f775(a26,x57842))+P1(f775(a26,f33(x57841,x57842,x57843))) % 186.05/186.63 [6058]~E(x60583,f2(a850))+P1(f775(x60581,x60582))+~P1(f775(x60581,f52(a850,x60582,x60583))) % 186.05/186.63 [6768]E(x67681,f2(a850))+~P1(f775(x67682,f804(x67681,x67683,x67682)))+P1(f775(x67682,f52(a850,x67683,x67681))) % 186.05/186.63 [6881]~P9(x68811)+~P1(f775(f775(f232(x68811),x68812),f672(x68813,x68812,x68811)))+P1(f775(f775(f232(x68811),x68812),f45(x68811,x68813))) % 186.05/186.63 [6883]~P1(f775(x68831,x68832))+~P1(f775(x68831,f804(x68833,x68832,x68831)))+P1(f775(x68831,f52(a850,x68832,x68833))) % 186.05/186.63 [6983]E(x69831,f115(x69832))+E(f775(f775(f140(x69832),f749(x69833,x69831,x69832)),f756(x69833,x69831,x69832)),x69831)+~P1(f775(f775(f334(f851(x69832)),x69831),f149(x69832,x69833))) % 186.05/186.63 [7017]~P133(x70171)+~P1(f775(f775(f334(x70171),x70172),f112(x70171)))+P1(f775(f775(f334(x70171),f775(f775(f242(x70171),x70172),x70173)),f112(x70171))) % 186.05/186.63 [7358]P36(x73581,x73582)+~P1(f775(f775(f334(x73581),x73583),f683(x73582,x73581)))+P1(f775(f775(f334(x73581),f698(x73582,x73581,x73583)),f683(x73582,x73581))) % 186.05/186.63 [7634]E(x76341,f115(x76342))+~P1(f775(f775(f334(f851(x76342)),x76341),f149(x76342,x76343)))+P1(f775(f775(f334(f851(x76342)),f756(x76343,x76341,x76342)),f149(x76342,x76343))) % 186.05/186.63 [7684]E(x76841,f2(a850))+E(f775(f775(f82(a850),f775(f775(f83(a850),x76841),f806(x76841,x76842,x76843))),f804(x76841,x76842,x76843)),x76842)+P1(f775(x76843,f52(a850,x76842,x76841))) % 186.05/186.63 [7727]~P1(f775(x77273,x77272))+E(f775(f775(f82(a850),f775(f775(f83(a850),x77271),f806(x77271,x77272,x77273))),f804(x77271,x77272,x77273)),x77272)+P1(f775(x77273,f52(a850,x77272,x77271))) % 186.05/186.63 [7871]P1(f775(f775(f233(a1),x78711),f794(x78712,x78713,x78711)))+P1(f775(f775(x78713,f775(f775(f43(a1),x78712),x78711)),f52(a1,x78712,x78711)))+~P1(f775(f775(f233(a1),x78711),f2(a1))) % 186.05/186.63 [8137]P1(f775(f775(x81372,f775(f775(f43(a1),x81371),x81373)),f52(a1,x81371,x81373)))+~P1(f775(f775(f233(a1),x81373),f2(a1)))+P1(f775(f775(f232(a1),f794(x81371,x81372,x81373)),f2(a1))) % 186.05/186.63 [8316]E(f775(f775(f82(a1),f775(f775(f83(a1),x83161),f797(x83162,x83163,x83161))),f794(x83162,x83163,x83161)),x83162)+P1(f775(f775(x83163,f775(f775(f43(a1),x83162),x83161)),f52(a1,x83162,x83161)))+~P1(f775(f775(f233(a1),x83161),f2(a1))) % 186.05/186.63 [8551]~P1(f775(f775(x85511,f797(x85512,x85511,x85513)),f794(x85512,x85511,x85513)))+P1(f775(f775(x85511,f775(f775(f43(a1),x85512),x85513)),f52(a1,x85512,x85513)))+~P1(f775(f775(f233(a1),x85513),f2(a1))) % 186.05/186.63 [8762]~P100(x87621)+~P18(x87621,x87623)+P18(x87621,f139(x87621,x87621,f7(x87621),x87622,x87623)) % 186.05/186.63 [9207]~P119(x92072)+E(x92071,f2(x92072))+~P1(f775(f775(f232(x92072),f775(f775(f82(x92072),f775(f775(f83(x92072),x92073),x92073)),f775(f775(f83(x92072),x92071),x92071))),f2(x92072))) % 186.05/186.63 [9208]~P119(x92082)+E(x92081,f2(x92082))+~P1(f775(f775(f232(x92082),f775(f775(f82(x92082),f775(f775(f83(x92082),x92081),x92081)),f775(f775(f83(x92082),x92083),x92083))),f2(x92082))) % 186.05/186.63 [9966]~P110(x99661)+~P1(f775(f775(f233(x99661),x99662),f2(x99661)))+P1(f775(f775(f233(x99661),f775(f775(f242(x99661),x99662),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x99663)))),f2(x99661))) % 186.05/186.63 [9976]~P110(x99762)+E(x99761,f2(x99762))+~P1(f775(f775(f232(x99762),f775(f775(f82(x99762),f775(f775(f242(x99762),x99763),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99762),x99761),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f2(x99762))) % 186.05/186.63 [9977]~P110(x99772)+E(x99771,f2(x99772))+~P1(f775(f775(f232(x99772),f775(f775(f82(x99772),f775(f775(f242(x99772),x99771),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99772),x99773),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f2(x99772))) % 186.05/186.63 [4674]~E(x46742,x46743)+~P69(x46741)+E(f775(f775(f3(x46741),x46742),x46743),f2(x46741)) % 186.05/186.63 [4675]~E(x46752,x46753)+~P6(x46751)+E(f775(f775(f3(x46751),x46752),x46753),f2(x46751)) % 186.05/186.63 [4688]~P137(x46881)+~E(x46883,f2(x46881))+E(f775(f775(f82(x46881),x46882),x46883),x46882) % 186.05/186.63 [4703]~P134(x47031)+~E(x47033,f2(x47031))+E(f775(f775(f83(x47031),x47032),x47033),f2(x47031)) % 186.05/186.63 [4704]~P134(x47041)+~E(x47042,f2(x47041))+E(f775(f775(f83(x47041),x47042),x47043),f2(x47041)) % 186.05/186.63 [4725]~E(x47253,f115(x47251))+~E(x47252,f115(x47251))+E(f775(f775(f125(x47251),x47252),x47253),f115(x47251)) % 186.05/186.63 [4808]~P137(x48082)+E(x48081,f2(x48082))+~E(f775(f775(f82(x48082),x48083),x48081),x48083) % 186.05/186.63 [4809]~P69(x48091)+~E(x48092,f775(f81(x48091),x48093))+E(f775(f775(f82(x48091),x48092),x48093),f2(x48091)) % 186.05/186.63 [4816]E(x48161,f115(x48162))+E(x48163,f2(a850))+~E(f775(f775(f159(x48162),x48163),x48161),f115(x48162)) % 186.05/186.63 [4824]~P69(x48243)+E(x48241,x48242)+~E(f775(f775(f3(x48243),x48241),x48242),f2(x48243)) % 186.05/186.63 [4825]~P6(x48253)+E(x48251,x48252)+~E(f775(f775(f3(x48253),x48251),x48252),f2(x48253)) % 186.05/186.63 [4834]~P120(x48342)+E(x48341,f2(x48342))+~E(f775(f775(f242(x48342),x48341),x48343),f2(x48342)) % 186.05/186.63 [4835]~P94(x48352)+E(x48351,f239(x48352))+~E(f775(f775(f104(x48352),x48353),x48351),f239(x48352)) % 186.05/186.63 [4836]~P94(x48362)+E(x48361,f239(x48362))+~E(f775(f775(f104(x48362),x48361),x48363),f239(x48362)) % 186.05/186.63 [4837]~P95(x48372)+E(x48371,f180(x48372))+~E(f775(f775(f103(x48372),x48373),x48371),f180(x48372)) % 186.05/186.63 [4838]~P95(x48382)+E(x48381,f180(x48382))+~E(f775(f775(f103(x48382),x48381),x48383),f180(x48382)) % 186.05/186.63 [4903]~P69(x49032)+E(x49031,f775(f81(x49032),x49033))+~E(f775(f775(f82(x49032),x49031),x49033),f2(x49032)) % 186.05/186.63 [4904]~P69(x49041)+E(f775(f81(x49041),x49042),x49043)+~E(f775(f775(f82(x49041),x49042),x49043),f2(x49041)) % 186.05/186.63 [4907]~E(x49072,x49073)+~P99(x49071)+P1(f775(f775(f232(x49071),x49072),x49073)) % 186.05/186.63 [4908]~E(x49082,x49083)+~P103(x49081)+P1(f775(f775(f232(x49081),x49082),x49083)) % 186.05/186.63 [5006]~P111(x50061)+~E(x50062,f775(f81(x50061),x50063))+E(f775(f775(f83(x50061),x50062),x50062),f775(f775(f83(x50061),x50063),x50063)) % 186.05/186.63 [5014]~P100(x50141)+~P18(x50141,x50143)+P18(x50141,f775(f775(f159(x50141),x50142),x50143)) % 186.05/186.63 [5015]~P100(x50151)+~P18(x50151,x50153)+P18(x50151,f775(f775(f128(x50151),x50152),x50153)) % 186.05/186.63 [5054]E(x50541,x50542)+E(x50543,f2(a850))+~E(f775(f775(f83(a850),x50543),x50541),f775(f775(f83(a850),x50543),x50542)) % 186.05/186.63 [5055]E(x50551,x50552)+E(x50553,f2(a850))+~E(f775(f775(f83(a850),x50551),x50553),f775(f775(f83(a850),x50552),x50553)) % 186.05/186.63 [5131]~E(x51312,x51313)+~P99(x51311)+E(f295(x51311,x51312,x51313),f775(f775(f302(x51311),x51312),f180(f857(x51311,a844)))) % 186.05/186.63 [5171]~P110(x51711)+~E(f775(f77(x51711),x51712),f775(f77(x51711),x51713))+P1(f775(f775(f279(x51711),x51712),x51713)) % 186.05/186.63 [5180]~E(x51801,x51802)+~P99(x51803)+~P1(f775(f775(f233(x51803),x51801),x51802)) % 186.05/186.63 [5181]~E(x51811,x51812)+~P100(x51813)+~P1(f775(f775(f233(x51813),x51811),x51812)) % 186.05/186.63 [5188]~P99(x51881)+E(f775(f294(x51881,x51882),x51883),f180(f857(x51881,a844)))+P1(f775(f775(f233(x51881),x51882),x51883)) % 186.05/186.63 [5234]~P99(x52341)+E(f295(x52341,x52342,x52343),f180(f857(x52341,a844)))+P1(f775(f775(f232(x52341),x52342),x52343)) % 186.05/186.63 [5235]~P99(x52351)+E(f297(x52351,x52352,x52353),f180(f857(x52351,a844)))+P1(f775(f775(f233(x52351),x52352),x52353)) % 186.05/186.63 [5236]~P99(x52361)+E(f180(f857(x52361,a844)),f295(x52361,x52362,x52363))+P1(f775(f775(f232(x52361),x52362),x52363)) % 186.05/186.63 [5237]~P99(x52371)+E(f180(f857(x52371,a844)),f297(x52371,x52372,x52373))+P1(f775(f775(f233(x52371),x52372),x52373)) % 186.05/186.63 [5245]~P100(x52451)+~E(f775(f775(f236(x52451),x52452),x52453),x52452)+P1(f775(f775(f232(x52451),x52452),x52453)) % 186.05/186.63 [5246]~P100(x52461)+~E(f775(f775(f179(x52461),x52462),x52463),x52463)+P1(f775(f775(f232(x52461),x52462),x52463)) % 186.05/186.63 [5247]~P92(x52471)+~E(f775(f775(f103(x52471),x52472),x52473),x52473)+P1(f775(f775(f232(x52471),x52472),x52473)) % 186.05/186.63 [5248]~P98(x52481)+~E(f775(f775(f104(x52481),x52482),x52483),x52482)+P1(f775(f775(f232(x52481),x52482),x52483)) % 186.05/186.63 [5264]~P100(x52641)+P18(x52641,x52642)+~P18(x52641,f775(f775(f140(x52641),x52643),x52642)) % 186.05/186.63 [5265]~P100(x52651)+P18(x52651,x52652)+~P18(x52651,f775(f775(f125(x52651),x52653),x52652)) % 186.05/186.63 [5266]~P100(x52661)+P18(x52661,x52662)+~P18(x52661,f775(f775(f125(x52661),x52662),x52663)) % 186.05/186.63 [5271]~P7(x52711)+~E(f52(x52711,x52713,x52712),f2(x52711))+P1(f775(f775(f279(x52711),x52712),x52713)) % 186.05/186.63 [5334]~P100(x53341)+P1(f775(f775(f232(x53341),x53343),x53342))+P1(f775(f775(f233(x53341),x53342),x53343)) % 186.05/186.63 [5336]~P100(x53361)+P1(f775(f775(f232(x53361),x53363),x53362))+P1(f775(f775(f232(x53361),x53362),x53363)) % 186.05/186.63 [5375]~P100(x53751)+E(f775(f775(f236(x53751),x53752),x53753),x53753)+~P1(f775(f775(f232(x53751),x53753),x53752)) % 186.05/186.63 [5377]~P100(x53771)+E(f775(f775(f236(x53771),x53772),x53773),x53772)+~P1(f775(f775(f232(x53771),x53772),x53773)) % 186.05/186.63 [5378]~P100(x53781)+E(f775(f775(f179(x53781),x53782),x53783),x53782)+~P1(f775(f775(f232(x53781),x53783),x53782)) % 186.05/186.63 [5380]~P100(x53801)+E(f775(f775(f179(x53801),x53802),x53803),x53803)+~P1(f775(f775(f232(x53801),x53802),x53803)) % 186.05/186.63 [5381]~P92(x53811)+E(f775(f775(f103(x53811),x53812),x53813),x53812)+~P1(f775(f775(f232(x53811),x53813),x53812)) % 186.05/186.63 [5383]~P92(x53831)+E(f775(f775(f103(x53831),x53832),x53833),x53833)+~P1(f775(f775(f232(x53831),x53832),x53833)) % 186.05/186.63 [5384]~P98(x53841)+E(f775(f775(f104(x53841),x53842),x53843),x53843)+~P1(f775(f775(f232(x53841),x53843),x53842)) % 186.05/186.63 [5386]~P98(x53861)+E(f775(f775(f104(x53861),x53862),x53863),x53862)+~P1(f775(f775(f232(x53861),x53862),x53863)) % 186.05/186.63 [5393]~P113(x53932)+E(x53931,f2(x53932))+E(f775(f775(f283(x53932),f775(f81(x53932),x53933)),f775(f81(x53932),x53931)),f775(f775(f283(x53932),x53933),x53931)) % 186.05/186.63 [5400]~P7(x54001)+E(f52(x54001,x54002,x54003),f2(x54001))+~P1(f775(f775(f279(x54001),x54003),x54002)) % 186.05/186.63 [5440]~P99(x54401)+E(f775(f294(x54401,x54402),x54403),f180(f857(x54401,a844)))+~P1(f775(f775(f232(x54401),x54403),x54402)) % 186.05/186.63 [5469]~P99(x54691)+E(f295(x54691,x54692,x54693),f180(f857(x54691,a844)))+~P1(f775(f775(f233(x54691),x54693),x54692)) % 186.05/186.63 [5470]~P99(x54701)+E(f297(x54701,x54702,x54703),f180(f857(x54701,a844)))+~P1(f775(f775(f232(x54701),x54703),x54702)) % 186.05/186.63 [5471]~P99(x54711)+E(f298(x54711,x54712,x54713),f180(f857(x54711,a844)))+~P1(f775(f775(f232(x54711),x54713),x54712)) % 186.05/186.63 [5520]~E(f775(f775(f3(a850),x55201),x55203),x55202)+E(x55201,f775(f775(f82(a850),x55202),x55203))+~P1(f775(f775(f232(a850),x55203),x55201)) % 186.05/186.63 [5521]~E(x55211,f775(f775(f82(a850),x55213),x55212))+E(f775(f775(f3(a850),x55211),x55212),x55213)+~P1(f775(f775(f232(a850),x55212),x55211)) % 186.05/186.63 [5564]~P1(f775(x55641,x55643))+P1(f775(x55641,f799(x55641,x55642)))+~P1(f775(f775(f232(a850),x55643),x55642)) % 186.05/186.63 [5565]~P1(f775(x55651,x55653))+P1(f775(x55651,f339(x55651,x55652)))+~P1(f775(f775(f233(a850),x55653),x55652)) % 186.05/186.63 [5573]~P99(x55731)+~E(f775(f294(x55731,x55732),x55733),f180(f857(x55731,a844)))+~P1(f775(f775(f233(x55731),x55732),x55733)) % 186.05/186.63 [5577]~P99(x55771)+~P1(f775(f775(f233(x55771),x55772),x55773))+P1(f775(f775(f232(x55771),x55772),x55773)) % 186.05/186.63 [5579]~P103(x55791)+~P1(f775(f775(f233(x55791),x55792),x55793))+P1(f775(f775(f232(x55791),x55792),x55793)) % 186.05/186.63 [5692]~P99(x56921)+~E(f295(x56921,x56922,x56923),f180(f857(x56921,a844)))+~P1(f775(f775(f232(x56921),x56922),x56923)) % 186.05/186.63 [5693]~P99(x56931)+~E(f297(x56931,x56932,x56933),f180(f857(x56931,a844)))+~P1(f775(f775(f233(x56931),x56932),x56933)) % 186.05/186.63 [5694]~P99(x56941)+~E(f180(f857(x56941,a844)),f295(x56941,x56942,x56943))+~P1(f775(f775(f232(x56941),x56942),x56943)) % 186.05/186.63 [5695]~P99(x56951)+~E(f180(f857(x56951,a844)),f297(x56951,x56952,x56953))+~P1(f775(f775(f233(x56951),x56952),x56953)) % 186.05/186.63 [5708]P1(f775(x57081,x57082))+~P1(f775(x57081,f800(x57081,x57083)))+~P1(f775(f775(f232(a850),x57082),x57083)) % 186.05/186.63 [5709]P1(f775(x57091,x57092))+~P1(f775(x57091,f342(x57091,x57093)))+~P1(f775(f775(f233(a850),x57092),x57093)) % 186.05/186.63 [5717]~E(x57171,f775(a114,x57173))+P1(f775(f775(f233(a850),x57171),f775(a114,x57172)))+~P1(f775(f775(f233(a850),x57173),x57172)) % 186.05/186.63 [5733]E(x57331,x57332)+~E(f775(f775(f83(a850),x57333),x57331),f775(f775(f83(a850),x57333),x57332))+~P1(f775(f775(f233(a850),f2(a850)),x57333)) % 186.05/186.63 [5794]E(f775(x57941,f404(x57941,x57942,x57943)),f80(a850))+~E(f775(f775(f8(x57943,a850),x57941),x57942),f80(a850))+~P1(f775(f63(x57943),x57942)) % 186.05/186.63 [5804]~P9(x58041)+P1(f775(f775(f232(x58041),x58042),f44(x58041,x58043)))+~P1(f775(f775(f334(x58041),x58042),x58043)) % 186.05/186.63 [5828]~P99(x58281)+~P1(f775(f775(f233(x58281),x58283),x58282))+~P1(f775(f775(f233(x58281),x58282),x58283)) % 186.05/186.63 [5832]~P103(x58321)+~P1(f775(f775(f233(x58321),x58323),x58322))+~P1(f775(f775(f233(x58321),x58322),x58323)) % 186.05/186.63 [5833]~P103(x58331)+~P1(f775(f775(f232(x58331),x58333),x58332))+~P1(f775(f775(f233(x58331),x58332),x58333)) % 186.05/186.63 [5834]~P100(x58341)+~P1(f775(f775(f233(x58341),x58343),x58342))+~P1(f775(f775(f233(x58341),x58342),x58343)) % 186.05/186.63 [5837]~P100(x58371)+~P1(f775(f775(f232(x58371),x58373),x58372))+~P1(f775(f775(f233(x58371),x58372),x58373)) % 186.05/186.63 [5856]~E(x58562,x58563)+~E(x58561,x58562)+E(f282(a850,f279(a850),x58561,x58562),f775(f775(f302(a850),x58563),f180(f857(a850,a844)))) % 186.05/186.63 [5864]~E(f775(x58642,f405(x58642,x58643,x58641)),f2(a850))+E(f775(f775(f8(x58641,a850),x58642),x58643),f2(a850))+~P1(f775(f63(x58641),x58643)) % 186.05/186.63 [5865]~E(f775(x58652,f450(x58652,x58653,x58651)),f80(a850))+E(f775(f775(f11(x58651,a850),x58652),x58653),f80(a850))+~P1(f775(f63(x58651),x58653)) % 186.05/186.63 [5879]~P102(x58791)+~P1(f775(f775(f233(x58791),x58793),x58792))+P1(f775(f775(f334(x58791),x58792),f775(f296(x58791),x58793))) % 186.05/186.63 [5880]~P102(x58801)+~P1(f775(f775(f232(x58801),x58803),x58802))+P1(f775(f775(f334(x58801),x58802),f775(f258(x58801),x58803))) % 186.05/186.63 [5881]~P102(x58811)+~P1(f775(f775(f233(x58811),x58812),x58813))+P1(f775(f775(f334(x58811),x58812),f775(f257(x58811),x58813))) % 186.05/186.63 [5882]~P102(x58821)+~P1(f775(f775(f232(x58821),x58822),x58823))+P1(f775(f775(f334(x58821),x58822),f775(f293(x58821),x58823))) % 186.05/186.63 [5883]~P104(x58831)+~P1(f775(f775(f279(x58831),x58832),x58833))+P1(f775(f775(f279(x58831),x58832),f775(f81(x58831),x58833))) % 186.05/186.63 [5884]~P110(x58841)+~P1(f775(f775(f279(x58841),x58842),x58843))+P1(f775(f775(f279(x58841),x58842),f775(f77(x58841),x58843))) % 186.05/186.63 [5895]E(f775(x58951,f406(x58951,x58952,x58953)),f775(a114,f2(a850)))+~E(f775(f775(f8(x58953,a850),x58951),x58952),f775(a114,f2(a850)))+~P1(f775(f63(x58953),x58952)) % 186.05/186.63 [5979]~P9(x59791)+~P1(f775(f775(f334(x59791),x59793),x59792))+P1(f775(f775(f232(x59791),f45(x59791,x59792)),x59793)) % 186.05/186.63 [5997]~P1(f775(f775(f232(a850),x59971),x59973))+P1(f775(f775(f232(a850),x59971),x59972))+~P1(f775(f775(f232(a850),x59973),x59972)) % 186.05/186.63 [5998]~P1(f775(f775(f232(a1),x59981),x59983))+P1(f775(f775(f232(a1),x59981),x59982))+~P1(f775(f775(f232(a1),x59983),x59982)) % 186.05/186.63 [5999]~P1(f775(f775(f279(a850),x59991),x59993))+P1(f775(f775(f279(a850),x59991),x59992))+~P1(f775(f775(f279(a850),x59993),x59992)) % 186.05/186.63 [6017]~P102(x60171)+~P1(f775(f775(f334(x60171),x60173),f775(f296(x60171),x60172)))+P1(f775(f775(f233(x60171),x60172),x60173)) % 186.05/186.63 [6018]~P102(x60181)+~P1(f775(f775(f334(x60181),x60182),f775(f257(x60181),x60183)))+P1(f775(f775(f233(x60181),x60182),x60183)) % 186.05/186.63 [6019]~P102(x60191)+~P1(f775(f775(f334(x60191),x60193),f775(f258(x60191),x60192)))+P1(f775(f775(f232(x60191),x60192),x60193)) % 186.05/186.63 [6020]~P102(x60201)+~P1(f775(f775(f334(x60201),x60202),f775(f293(x60201),x60203)))+P1(f775(f775(f232(x60201),x60202),x60203)) % 186.05/186.63 [6021]~P110(x60211)+~P1(f775(f775(f279(x60211),x60212),f775(f77(x60211),x60213)))+P1(f775(f775(f279(x60211),x60212),x60213)) % 186.05/186.63 [6022]~P104(x60221)+~P1(f775(f775(f279(x60221),x60222),f775(f81(x60221),x60223)))+P1(f775(f775(f279(x60221),x60222),x60223)) % 186.05/186.63 [6246]~P62(x62461)+P1(f775(f775(f233(x62461),f2(x62461)),f802(x62463,x62462,x62461)))+P1(f775(f775(f232(x62461),x62462),x62463)) % 186.05/186.63 [6247]~P63(x62471)+P1(f775(f775(f233(x62471),f2(x62471)),f809(x62473,x62472,x62471)))+P1(f775(f775(f232(x62471),x62472),x62473)) % 186.05/186.63 [6318]~P77(x63181)+~P1(f775(f775(f233(x63181),x63183),f775(f81(x63181),x63182)))+P1(f775(f775(f233(x63181),x63182),f775(f81(x63181),x63183))) % 186.05/186.63 [6320]~P77(x63201)+~P1(f775(f775(f232(x63201),x63203),f775(f81(x63201),x63202)))+P1(f775(f775(f232(x63201),x63202),f775(f81(x63201),x63203))) % 186.05/186.63 [6331]~P1(f775(f775(f233(a850),x63311),x63313))+~P1(f775(f775(f233(a850),x63313),x63312))+P1(f775(f775(f233(a850),f775(a114,x63311)),x63312)) % 186.05/186.63 [6364]~P110(x63641)+P1(f775(f775(f233(x63641),f775(f105(x63641),x63642)),f775(f105(x63641),x63643)))+~P1(f775(f775(f233(a1),x63642),x63643)) % 186.05/186.63 [6365]~P117(x63651)+P1(f775(f775(f233(x63651),f775(f102(x63651),x63652)),f775(f102(x63651),x63653)))+~P1(f775(f775(f233(a850),x63652),x63653)) % 186.05/186.63 [6366]~P117(x63661)+P1(f775(f775(f232(x63661),f775(f102(x63661),x63662)),f775(f102(x63661),x63663)))+~P1(f775(f775(f232(a850),x63662),x63663)) % 186.05/186.63 [6367]~P110(x63671)+P1(f775(f775(f232(x63671),f775(f105(x63671),x63672)),f775(f105(x63671),x63673)))+~P1(f775(f775(f232(a1),x63672),x63673)) % 186.05/186.63 [6373]~P100(x63731)+E(f775(f775(f103(f857(x63731,a844)),f775(f257(x63731),x63732)),f775(f294(x63731,x63732),x63733)),f775(f257(x63731),x63733))+~P1(f775(f775(f232(x63731),x63732),x63733)) % 186.05/186.63 [6404]~P77(x64041)+~P1(f775(f775(f233(x64041),x64043),x64042))+P1(f775(f775(f233(x64041),f775(f81(x64041),x64042)),f775(f81(x64041),x64043))) % 186.05/186.63 [6406]~P77(x64061)+~P1(f775(f775(f232(x64061),x64063),x64062))+P1(f775(f775(f232(x64061),f775(f81(x64061),x64062)),f775(f81(x64061),x64063))) % 186.05/186.63 [6408]~P90(x64081)+~P1(f775(f775(f232(x64081),x64083),x64082))+P1(f775(f775(f232(x64081),f775(f81(x64081),x64082)),f775(f81(x64081),x64083))) % 186.05/186.63 [6443]~P100(x64431)+E(f775(f775(f103(f857(x64431,a844)),f775(f257(x64431),x64432)),f295(x64431,x64432,x64433)),f775(f293(x64431),x64433))+~P1(f775(f775(f232(x64431),x64432),x64433)) % 186.05/186.63 [6444]~P100(x64441)+E(f775(f775(f103(f857(x64441,a844)),f775(f293(x64441),x64442)),f297(x64441,x64442,x64443)),f775(f293(x64441),x64443))+~P1(f775(f775(f232(x64441),x64442),x64443)) % 186.05/186.63 [6445]~P100(x64451)+E(f775(f775(f103(f857(x64451,a844)),f775(f293(x64451),x64452)),f298(x64451,x64452,x64453)),f775(f257(x64451),x64453))+~P1(f775(f775(f233(x64451),x64452),x64453)) % 186.05/186.63 [6483]~P100(x64831)+E(f775(f775(f103(f857(x64831,a844)),f775(f294(x64831,x64832),x64833)),f775(f258(x64831),x64833)),f775(f258(x64831),x64832))+~P1(f775(f775(f232(x64831),x64832),x64833)) % 186.05/186.63 [6646]~P100(x66461)+E(f775(f775(f103(f857(x66461,a844)),f295(x66461,x66462,x66463)),f775(f296(x66461),x66463)),f775(f258(x66461),x66462))+~P1(f775(f775(f232(x66461),x66462),x66463)) % 186.05/186.63 [6647]~P100(x66471)+E(f775(f775(f103(f857(x66471,a844)),f297(x66471,x66472,x66473)),f775(f296(x66471),x66473)),f775(f296(x66471),x66472))+~P1(f775(f775(f232(x66471),x66472),x66473)) % 186.05/186.63 [6648]~P100(x66481)+E(f775(f775(f103(f857(x66481,a844)),f298(x66481,x66482,x66483)),f775(f258(x66481),x66483)),f775(f296(x66481),x66482))+~P1(f775(f775(f233(x66481),x66482),x66483)) % 186.05/186.63 [6665]P1(f775(x66651,x66652))+~P1(f775(f775(f232(a850),x66652),x66653))+P1(f775(f775(f334(a850),f800(x66651,x66653)),f295(a850,f2(a850),x66653))) % 186.05/186.63 [6675]P1(f775(f775(f279(a1),x66751),f52(a1,x66752,x66753)))+~P1(f775(f775(f279(a1),x66751),x66752))+~P1(f775(f775(f279(a1),x66751),x66753)) % 186.05/186.63 [6701]E(x67011,x67012)+~E(f775(f775(f153(x67013),x67011),f731(x67013,x67012,x67011)),f775(f775(f153(x67013),x67012),f731(x67013,x67012,x67011)))+~E(f775(f181(f851(x67013)),x67011),f775(f181(f851(x67013)),x67012)) % 186.05/186.63 [6707]~E(x67073,f775(f775(f43(a850),x67071),x67072))+~P1(f775(f775(f233(a850),f2(a850)),x67072))+P1(f775(f775(f233(a850),x67071),f775(f775(f83(a850),x67072),f775(a114,x67073)))) % 186.05/186.63 [6722]~P1(f775(x67221,x67223))+~P1(f775(f775(f232(a850),x67223),x67222))+P1(f775(f775(f334(a850),f799(x67221,x67222)),f295(a850,f2(a850),x67222))) % 186.05/186.63 [6765]~P1(f775(x67651,x67653))+P1(f775(x67651,f340(x67651,x67652)))+~P1(f775(f775(f334(a850),x67653),f295(a850,f2(a850),x67652))) % 186.05/186.63 [6788]~P117(x67883)+~P1(f775(f775(f233(x67883),f775(f102(x67883),x67881)),f775(f102(x67883),x67882)))+P1(f775(f775(f233(a850),x67881),x67882)) % 186.05/186.63 [6789]~P110(x67893)+~P1(f775(f775(f233(x67893),f775(f105(x67893),x67891)),f775(f105(x67893),x67892)))+P1(f775(f775(f233(a1),x67891),x67892)) % 186.05/186.63 [6790]~P117(x67903)+~P1(f775(f775(f232(x67903),f775(f102(x67903),x67901)),f775(f102(x67903),x67902)))+P1(f775(f775(f232(a850),x67901),x67902)) % 186.05/186.63 [6791]~P110(x67913)+~P1(f775(f775(f232(x67913),f775(f105(x67913),x67911)),f775(f105(x67913),x67912)))+P1(f775(f775(f232(a1),x67911),x67912)) % 186.05/186.63 [6807]~P117(x68071)+~P1(f775(f775(f233(x68071),f80(x68071)),x68072))+P1(f775(f775(f233(x68071),f80(x68071)),f775(f775(f242(x68071),x68072),f775(a114,x68073)))) % 186.05/186.63 [6811]~P77(x68111)+~P1(f775(f775(f233(x68111),f775(f81(x68111),x68113)),f775(f81(x68111),x68112)))+P1(f775(f775(f233(x68111),x68112),x68113)) % 186.05/186.63 [6812]~P77(x68121)+~P1(f775(f775(f232(x68121),f775(f81(x68121),x68123)),f775(f81(x68121),x68122)))+P1(f775(f775(f232(x68121),x68122),x68123)) % 186.05/186.63 [6813]~P90(x68131)+~P1(f775(f775(f232(x68131),f775(f81(x68131),x68133)),f775(f81(x68131),x68132)))+P1(f775(f775(f232(x68131),x68132),x68133)) % 186.05/186.63 [6839]P1(f775(x68391,x68392))+~P1(f775(x68391,f839(x68391,x68393)))+~P1(f775(f775(f334(a850),x68392),f295(a850,f2(a850),x68393))) % 186.05/186.63 [6860]~P62(x68601)+P1(f775(f775(f233(x68601),f802(x68603,x68602,x68601)),f80(x68601)))+P1(f775(f775(f232(x68601),x68602),x68603)) % 186.05/186.63 [6879]~E(f52(a850,x68793,x68792),f52(a850,x68791,x68792))+E(f775(f775(f82(a850),x68791),f775(f775(f83(a850),x68792),f811(x68791,x68792,x68793))),x68793)+~P1(f775(f775(f232(a850),x68791),x68793)) % 186.05/186.63 [6897]E(f775(x68971,f607(x68971,x68972,x68973)),f183(x68972))+~P1(f775(f63(x68973),f169(x68973,x68972,x68971)))+P1(f775(f63(x68973),f239(f857(x68973,a844)))) % 186.05/186.63 [6938]E(f775(f775(f8(x69381,a850),x69382),x69383),f2(a850))+~P1(f775(f63(x69381),x69383))+P1(f775(f775(f334(x69381),f405(x69382,x69383,x69381)),x69383)) % 186.05/186.63 [6939]E(f775(f775(f11(x69391,a850),x69392),x69393),f80(a850))+~P1(f775(f63(x69391),x69393))+P1(f775(f775(f334(x69391),f450(x69392,x69393,x69391)),x69393)) % 186.05/186.63 [6961]~P100(x69611)+~P1(f775(f775(f233(x69611),x69612),x69613))+P1(f775(f775(f233(f857(x69611,a844)),f775(f257(x69611),x69612)),f775(f257(x69611),x69613))) % 186.05/186.63 [6962]~P100(x69621)+~P1(f775(f775(f232(x69621),x69622),x69623))+P1(f775(f775(f232(f857(x69621,a844)),f775(f257(x69621),x69622)),f775(f257(x69621),x69623))) % 186.05/186.63 [6963]~P100(x69631)+~P1(f775(f775(f232(x69631),x69633),x69632))+P1(f775(f775(f232(f857(x69631,a844)),f775(f296(x69631),x69632)),f775(f296(x69631),x69633))) % 186.05/186.63 [6964]~P99(x69641)+~P1(f775(f775(f232(x69641),x69642),x69643))+P1(f775(f775(f232(f857(x69641,a844)),f775(f293(x69641),x69642)),f775(f293(x69641),x69643))) % 186.05/186.63 [6965]~P99(x69651)+~P1(f775(f775(f232(x69651),x69653),x69652))+P1(f775(f775(f232(f857(x69651,a844)),f775(f258(x69651),x69652)),f775(f258(x69651),x69653))) % 186.05/186.63 [6970]~P9(x69701)+P1(f775(f775(f232(x69701),x69702),f45(x69701,x69703)))+P1(f775(f775(f334(x69701),f672(x69703,x69702,x69701)),x69703)) % 186.05/186.63 [6975]~P77(x69751)+P1(f775(f775(f233(x69751),f775(f775(f3(x69751),x69752),x69753)),f2(x69751)))+~P1(f775(f775(f233(x69751),x69752),x69753)) % 186.05/186.63 [6976]~P77(x69761)+P1(f775(f775(f232(x69761),f775(f775(f3(x69761),x69762),x69763)),f2(x69761)))+~P1(f775(f775(f232(x69761),x69762),x69763)) % 186.05/186.63 [7014]~P1(f775(f775(f279(a1),x70141),f52(a1,x70142,x70143)))+~P1(f775(f775(f279(a1),x70141),x70143))+P1(f775(f775(f279(a1),x70141),x70142)) % 186.05/186.63 [7021]P1(f775(x70211,x70212))+P1(f775(f775(f232(a850),f839(x70211,x70213)),x70213))+~P1(f775(f775(f334(a850),x70212),f295(a850,f2(a850),x70213))) % 186.05/186.63 [7063]~E(f775(f775(f8(x70631,a850),x70632),x70633),f80(a850))+~P1(f775(f63(x70631),x70633))+P1(f775(f775(f334(x70631),f404(x70632,x70633,x70631)),x70633)) % 186.05/186.63 [7064]~P1(f775(x70641,x70643))+P1(f775(f775(f232(a850),f340(x70641,x70642)),x70642))+~P1(f775(f775(f334(a850),x70643),f295(a850,f2(a850),x70642))) % 186.05/186.63 [7102]~P9(x71021)+P1(f775(f775(f334(x71021),f673(x71023,x71022,x71021)),x71022))+P1(f775(f775(f232(x71021),f44(x71021,x71022)),x71023)) % 186.05/186.63 [7132]~E(f775(f775(f8(x71321,a850),x71322),x71323),f775(a114,f2(a850)))+~P1(f775(f63(x71321),x71323))+P1(f775(f775(f334(x71321),f406(x71322,x71323,x71321)),x71323)) % 186.05/186.63 [7143]E(x71431,f2(a850))+P1(f775(x71432,f52(a850,x71433,x71431)))+P1(f775(f775(f233(a850),f804(x71431,x71433,x71432)),x71431)) % 186.05/186.63 [7267]~P1(f775(x72671,x72672))+P1(f775(x72671,f52(a850,x72672,x72673)))+P1(f775(f775(f233(a850),f804(x72673,x72672,x72671)),x72673)) % 186.05/186.63 [7394]E(x73941,f115(x73942))+~P1(f775(f775(f334(f851(x73942)),x73941),f149(x73942,x73943)))+P1(f775(f775(f334(x73942),f749(x73943,x73941,x73942)),x73943)) % 186.05/186.63 [7414]~P100(x74141)+E(f775(f775(f103(f857(x74141,a844)),f775(f775(f302(x74141),x74142),f180(f857(x74141,a844)))),f298(x74141,x74142,x74143)),f775(f294(x74141,x74142),x74143))+~P1(f775(f775(f233(x74141),x74142),x74143)) % 186.05/186.63 [7439]~P100(x74391)+E(f775(f775(f103(f857(x74391,a844)),f775(f775(f302(x74391),x74392),f180(f857(x74391,a844)))),f297(x74391,x74392,x74393)),f295(x74391,x74392,x74393))+~P1(f775(f775(f232(x74391),x74392),x74393)) % 186.05/186.63 [7551]~P100(x75511)+P1(f775(f775(f233(x75511),x75512),x75513))+~P1(f775(f775(f233(f857(x75511,a844)),f775(f257(x75511),x75512)),f775(f257(x75511),x75513))) % 186.05/186.63 [7552]~P99(x75521)+P1(f775(f775(f232(x75521),x75522),x75523))+~P1(f775(f775(f232(f857(x75521,a844)),f775(f258(x75521),x75523)),f775(f258(x75521),x75522))) % 186.05/186.63 [7553]~P100(x75531)+P1(f775(f775(f232(x75531),x75532),x75533))+~P1(f775(f775(f232(f857(x75531,a844)),f775(f296(x75531),x75533)),f775(f296(x75531),x75532))) % 186.05/186.63 [7554]~P99(x75541)+P1(f775(f775(f232(x75541),x75542),x75543))+~P1(f775(f775(f232(f857(x75541,a844)),f775(f293(x75541),x75542)),f775(f293(x75541),x75543))) % 186.05/186.63 [7555]~P100(x75551)+P1(f775(f775(f232(x75551),x75552),x75553))+~P1(f775(f775(f232(f857(x75551,a844)),f775(f257(x75551),x75552)),f775(f257(x75551),x75553))) % 186.05/186.63 [7579]~P77(x75791)+~P1(f775(f775(f233(x75791),f775(f775(f3(x75791),x75792),x75793)),f2(x75791)))+P1(f775(f775(f233(x75791),x75792),x75793)) % 186.05/186.63 [7580]~P77(x75801)+~P1(f775(f775(f232(x75801),f775(f775(f3(x75801),x75802),x75803)),f2(x75801)))+P1(f775(f775(f232(x75801),x75802),x75803)) % 186.05/186.63 [7740]E(x77401,f2(a850))+~E(f775(f132(a850,a850,f82(a850),x77402),x77403),f2(a850))+~P1(f775(f775(f334(a850),x77401),f775(f158(a850),x77403))) % 186.05/186.63 [7744]~P9(x77441)+~P1(f775(f775(f232(x77441),f673(x77443,x77442,x77441)),x77443))+P1(f775(f775(f232(x77441),f44(x77441,x77442)),x77443)) % 186.05/186.63 [7895]P1(f775(f775(f232(a1),f2(a1)),f795(x78951,x78952,x78953)))+P1(f775(f775(x78952,f775(f775(f43(a1),x78951),x78953)),f52(a1,x78951,x78953)))+~P1(f775(f775(f233(a1),f2(a1)),x78953)) % 186.05/186.63 [7988]E(x79881,x79882)+~E(f775(f181(f851(x79883)),x79881),f775(f181(f851(x79883)),x79882))+~P1(f775(f775(f251(x79883,x79883,a844),a330),f714(x79883,x79881,x79882))) % 186.05/186.63 [8054]~P36(x80542,x80543)+E(x80541,f180(f857(x80542,a844)))+~P1(f775(f775(f232(f857(x80542,a844)),x80541),f775(f277(x80542,x80542,x80543),x80541))) % 186.05/186.63 [8082]~P63(x80821)+~P1(f775(f775(f232(x80821),x80822),f775(f775(f82(x80821),x80823),f809(x80823,x80822,x80821))))+P1(f775(f775(f232(x80821),x80822),x80823)) % 186.05/186.63 [8118]P47(x81181,x81182,x81183)+P1(f775(f775(f334(x81181),f506(x81183,x81182,x81181)),x81182))+P1(f775(f775(f334(f856(x81181,x81181)),f507(x81183,x81182,x81181)),x81183)) % 186.05/186.63 [8141]P1(f775(f775(x81412,f775(f775(f43(a1),x81411),x81413)),f52(a1,x81411,x81413)))+~P1(f775(f775(f233(a1),f2(a1)),x81413))+P1(f775(f775(f233(a1),f795(x81411,x81412,x81413)),x81413)) % 186.05/186.63 [8165]E(f775(f303(a850,a850,f775(f775(f9(a850,a850,a850),f3(a850)),x81651)),f775(f294(a850,x81652),x81653)),f180(f857(a850,a844)))+P1(f775(f775(f233(a850),x81651),x81653))+P1(f775(f775(f233(a850),x81652),x81653)) % 186.05/186.63 [8267]E(f775(f303(a850,a850,f775(f775(f9(a850,a850,a850),f3(a850)),x82671)),f775(f294(a850,x82672),x82673)),f775(f775(f302(a850),f2(a850)),f180(f857(a850,a844))))+P1(f775(f775(f233(a850),x82671),x82673))+~P1(f775(f775(f233(a850),x82672),x82673)) % 186.05/186.63 [8282]~P100(x82821)+E(f139(x82821,x82821,f7(x82821),x82822,x82823),x82823)+~P1(f775(f775(f334(x82821),x82822),f775(f158(x82821),x82823))) % 186.05/186.63 [8297]P29(x82971,x82971,x82972,x82973)+~P1(f775(f63(x82971),x82973))+~P1(f775(f775(f232(f857(x82971,a844)),x82973),f775(f303(x82971,x82971,x82972),x82973))) % 186.05/186.63 [8324]E(f775(f775(f82(a1),f775(f775(f83(a1),x83241),f796(x83242,x83243,x83241))),f795(x83242,x83243,x83241)),x83242)+P1(f775(f775(x83243,f775(f775(f43(a1),x83242),x83241)),f52(a1,x83242,x83241)))+~P1(f775(f775(f233(a1),f2(a1)),x83241)) % 186.05/186.63 [8556]~P1(f775(f775(x85561,f796(x85562,x85561,x85563)),f795(x85562,x85561,x85563)))+P1(f775(f775(x85561,f775(f775(f43(a1),x85562),x85563)),f52(a1,x85562,x85563)))+~P1(f775(f775(f233(a1),f2(a1)),x85563)) % 186.05/186.63 [9346]~P1(f775(f63(x93461),x93462))+~P1(f775(f775(f334(x93461),x93463),x93462))+P1(f775(f775(f233(a850),f775(f42(x93461),f775(f775(f3(f857(x93461,a844)),x93462),f775(f775(f302(x93461),x93463),f180(f857(x93461,a844)))))),f775(f42(x93461),x93462))) % 186.05/186.63 [9922]P47(x99221,x99222,x99223)+~P1(f775(f775(f251(x99221,x99221,a844),f775(f775(f9(x99221,f857(x99221,a844),f857(x99221,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x99221,a844),f857(x99221,a844)),x99221),f10(a844,a844,x99221)),f775(f775(f10(a844,f857(a844,a844),x99221),a331),f775(f775(f9(x99221,f857(x99221,a844),a844),f334(x99221)),x99222)))),f775(f775(f9(x99221,f857(x99221,a844),a844),f334(x99221)),x99222))),f507(x99223,x99222,x99221)))+P1(f775(f775(f334(x99221),f506(x99223,x99222,x99221)),x99222)) % 186.05/186.63 [5354]~P113(x53542)+E(x53541,f2(x53542))+E(f775(f775(f283(x53542),x53543),f775(f81(x53542),x53541)),f775(f81(x53542),f775(f775(f283(x53542),x53543),x53541))) % 186.05/186.63 [5485]~E(x54853,f180(f857(x54851,a844)))+~E(x54852,f180(f857(x54851,a844)))+E(f775(f775(f103(f857(x54851,a844)),x54852),x54853),f180(f857(x54851,a844))) % 186.05/186.63 [5539]~E(x55393,f2(a850))+~P1(f775(x55391,f2(a850)))+P1(f775(x55391,f775(f775(f43(a850),x55392),x55393))) % 186.05/186.63 [5687]~P63(x56872)+E(x56871,f2(x56872))+E(f775(f775(f283(x56872),f775(f77(x56872),x56873)),f775(f77(x56872),x56871)),f775(f77(x56872),f775(f775(f283(x56872),x56873),x56871))) % 186.05/186.63 [5782]~P85(x57821)+~E(x57822,f80(x57821))+P1(f775(f775(f279(x57821),x57822),f775(f775(f242(x57821),x57822),x57823))) % 186.05/186.63 [5799]~P7(x57991)+E(f775(f775(f83(x57991),x57992),f775(f775(f43(x57991),x57993),x57992)),x57993)+~P1(f775(f775(f279(x57991),x57992),x57993)) % 186.05/186.63 [5853]~P1(f775(f63(x58531),x58533))+E(f775(f42(x58531),f775(f775(f302(x58531),x58532),x58533)),f775(a114,f775(f42(x58531),x58533)))+P1(f775(f775(f334(x58531),x58532),x58533)) % 186.05/186.63 [5929]~E(x59292,f2(a850))+P1(f775(x59291,f2(a850)))+~P1(f775(x59291,f775(f775(f43(a850),x59293),x59292))) % 186.05/186.63 [5947]~P1(f775(f63(x59471),x59473))+E(f775(f42(x59471),f775(f775(f302(x59471),x59472),x59473)),f775(f42(x59471),x59473))+~P1(f775(f775(f334(x59471),x59472),x59473)) % 186.05/186.63 [5981]~P1(f775(f63(x59811),x59813))+E(f775(f42(x59811),f775(f775(f302(x59811),x59812),x59813)),f775(f775(f82(a850),f80(a850)),f775(f42(x59811),x59813)))+P1(f775(f775(f334(x59811),x59812),x59813)) % 186.05/186.63 [5988]~P8(x59881)+E(f775(f775(f43(x59881),x59882),f775(f81(x59881),x59883)),f775(f81(x59881),f775(f775(f43(x59881),x59882),x59883)))+~P1(f775(f775(f279(x59881),x59883),x59882)) % 186.05/186.63 [6103]E(f775(f775(f82(a850),x61031),f801(x61031,x61032,x61033)),x61032)+~P1(f775(x61033,f2(a850)))+P1(f775(x61033,f775(f775(f3(a850),x61032),x61031))) % 186.05/186.63 [6104]E(f775(f775(f82(a850),x61041),f808(x61041,x61042,x61043)),x61042)+~P1(f775(x61043,f2(a850)))+P1(f775(x61043,f775(f775(f3(a850),x61042),x61041))) % 186.05/186.63 [6128]~P8(x61281)+E(f775(f775(f43(x61281),f775(f81(x61281),x61282)),x61283),f775(f81(x61281),f775(f775(f43(x61281),x61282),x61283)))+~P1(f775(f775(f279(x61281),x61283),x61282)) % 186.05/186.63 [6151]~P9(x61511)+~P1(f775(f63(x61511),x61513))+E(f775(f775(f66(x61511,x61511,f103(x61511)),x61512),x61513),f775(f775(f103(x61511),x61512),f44(x61511,x61513))) % 186.05/186.63 [6152]~P9(x61521)+~P1(f775(f63(x61521),x61523))+E(f775(f775(f66(x61521,x61521,f104(x61521)),x61522),x61523),f775(f775(f104(x61521),x61522),f45(x61521,x61523))) % 186.05/186.63 [6158]~P88(x61581)+~E(f775(f106(x61581),x61582),f775(f106(x61581),x61583))+P33(x61581,f775(f106(x61581),f775(f775(f82(a1),x61582),f775(f81(a1),x61583)))) % 186.05/186.63 [6165]~P133(x61651)+E(f775(f775(f3(x61651),f775(f102(x61651),x61652)),f775(f102(x61651),x61653)),f775(f102(x61651),f775(f775(f3(a850),x61652),x61653)))+~P1(f775(f775(f232(a850),x61653),x61652)) % 186.05/186.63 [6171]~P104(x61711)+~P1(f775(f775(f279(x61711),x61712),x61713))+P1(f775(f775(f279(x61711),f775(f81(x61711),x61712)),x61713)) % 186.05/186.63 [6172]~P110(x61721)+~P1(f775(f775(f279(x61721),x61722),x61723))+P1(f775(f775(f279(x61721),f775(f77(x61721),x61722)),x61723)) % 186.05/186.63 [6257]E(f775(f775(f82(a850),x62571),f801(x62571,x62572,x62573)),x62572)+P1(f775(f775(f233(a850),x62572),x62571))+P1(f775(x62573,f775(f775(f3(a850),x62572),x62571))) % 186.05/186.63 [6258]E(f775(f775(f82(a850),x62581),f808(x62581,x62582,x62583)),x62582)+P1(f775(f775(f233(a850),x62582),x62581))+P1(f775(x62583,f775(f775(f3(a850),x62582),x62581))) % 186.05/186.63 [6276]~P110(x62761)+E(f775(f775(f83(x62761),f775(f77(x62761),x62762)),x62763),f775(f77(x62761),f775(f775(f83(x62761),x62762),x62763)))+~P1(f775(f775(f232(x62761),f2(x62761)),x62763)) % 186.05/186.63 [6277]~P62(x62771)+E(f775(f775(f283(x62771),f775(f77(x62771),x62772)),x62773),f775(f77(x62771),f775(f775(f283(x62771),x62772),x62773)))+~P1(f775(f775(f233(x62771),f2(x62771)),x62773)) % 186.05/186.63 [6286]~P93(x62861)+~P1(f775(f63(x62861),x62863))+E(f775(f775(f66(x62861,x62861,f103(x62861)),x62862),x62863),f15(x62861,f775(f775(f302(x62861),x62862),x62863))) % 186.05/186.63 [6287]~P100(x62871)+~P1(f775(f63(x62871),x62873))+E(f775(f775(f66(x62871,x62871,f179(x62871)),x62872),x62873),f16(x62871,f775(f775(f302(x62871),x62872),x62873))) % 186.05/186.63 [6288]~P100(x62881)+~P1(f775(f63(x62881),x62883))+E(f775(f775(f66(x62881,x62881,f236(x62881)),x62882),x62883),f17(x62881,f775(f775(f302(x62881),x62882),x62883))) % 186.05/186.63 [6289]~P93(x62891)+~P1(f775(f63(x62891),x62893))+E(f775(f775(f66(x62891,x62891,f104(x62891)),x62892),x62893),f12(x62891,f775(f775(f302(x62891),x62892),x62893))) % 186.05/186.63 [6333]E(x63331,f115(x63332))+~E(f164(x63332,x63333),f115(f851(x63332)))+~P1(f775(f775(f334(f851(x63332)),x63331),f775(f158(f851(x63332)),x63333))) % 186.05/186.63 [6352]~P85(x63521)+~P1(f775(f775(f233(a850),f2(a850)),x63523))+P1(f775(f775(f279(x63521),x63522),f775(f775(f242(x63521),x63522),x63523))) % 186.05/186.63 [6383]~P1(f775(f127(x63831),x63833))+P1(f775(f775(f334(x63831),x63832),f775(f158(x63831),x63833)))+P1(f775(f127(x63831),f775(f775(f140(x63831),x63832),x63833))) % 186.05/186.63 [6395]~P91(x63951)+~P1(f775(f63(x63951),x63953))+E(f775(f65(x63951,f83(x63951)),f775(f775(f302(x63951),x63952),x63953)),f775(f775(f66(x63951,x63951,f83(x63951)),x63952),x63953)) % 186.05/186.63 [6416]~P100(x64161)+~P1(f775(f63(x64161),x64163))+E(f13(x64161,f179(x64161),f775(f775(f302(x64161),x64162),x64163)),f775(f775(f66(x64161,x64161,f179(x64161)),x64162),x64163)) % 186.05/186.63 [6417]~P100(x64171)+~P1(f775(f63(x64171),x64173))+E(f14(x64171,f236(x64171),f775(f775(f302(x64171),x64172),x64173)),f775(f775(f66(x64171,x64171,f236(x64171)),x64172),x64173)) % 186.05/186.63 [6419]P1(f775(x64191,f2(a850)))+~P1(f775(f775(f233(a850),x64192),x64193))+~P1(f775(x64191,f775(f775(f3(a850),x64192),x64193))) % 186.05/186.63 [6438]~P110(x64381)+P1(f775(f775(f233(x64381),x64382),x64383))+~P1(f775(f775(f233(x64381),f775(f77(x64381),x64382)),x64383)) % 186.05/186.63 [6440]~P79(x64401)+P1(f775(f775(f232(x64401),x64402),x64403))+~P1(f775(f775(f232(x64401),f775(f77(x64401),x64402)),x64403)) % 186.05/186.63 [6441]~P110(x64411)+P1(f775(f775(f279(x64411),x64412),x64413))+~P1(f775(f775(f279(x64411),f775(f77(x64411),x64412)),x64413)) % 186.05/186.63 [6442]~P104(x64421)+P1(f775(f775(f279(x64421),x64422),x64423))+~P1(f775(f775(f279(x64421),f775(f81(x64421),x64422)),x64423)) % 186.05/186.63 [6461]E(x64611,f115(x64612))+E(f775(f131(x64612),f775(f775(f128(x64612),x64613),x64611)),f775(f775(f153(x64612),x64611),x64613))+~P1(f775(f775(f233(a850),x64613),f775(f181(f851(x64612)),x64611))) % 186.05/186.63 [6515]~P1(f775(x65151,x65153))+P1(f775(x65151,f343(x65151,x65152)))+~P1(f775(f775(f334(a850),x65153),f775(f294(a850,f2(a850)),x65152))) % 186.05/186.63 [6538]P1(f775(x65381,x65382))+~P1(f775(f775(f233(a850),x65382),x65383))+P1(f775(f775(f334(a850),f342(x65381,x65383)),f775(f294(a850,f2(a850)),x65383))) % 186.05/186.63 [6553]~P117(x65531)+~P1(f775(f775(f233(x65531),f2(x65531)),x65532))+P1(f775(f775(f233(x65531),f2(x65531)),f775(f775(f242(x65531),x65532),x65533))) % 186.05/186.63 [6555]~P117(x65551)+~P1(f775(f775(f232(x65551),f2(x65551)),x65552))+P1(f775(f775(f232(x65551),f2(x65551)),f775(f775(f242(x65551),x65552),x65553))) % 186.05/186.63 [6556]~P117(x65561)+~P1(f775(f775(f232(x65561),f80(x65561)),x65562))+P1(f775(f775(f232(x65561),f80(x65561)),f775(f775(f242(x65561),x65562),x65563))) % 186.05/186.63 [6581]~P1(f775(x65811,x65813))+~P1(f775(f775(f233(a850),x65813),x65812))+P1(f775(f775(f334(a850),f339(x65811,x65812)),f775(f294(a850,f2(a850)),x65812))) % 186.05/186.63 [6586]P1(f775(f63(x65861),x65862))+~P1(f775(f63(x65861),x65863))+~P1(f775(f775(f232(f857(x65861,a844)),x65862),x65863)) % 186.05/186.63 [6595]~P1(f775(f775(f279(a850),x65951),x65952))+~P1(f775(f775(f279(a850),x65951),x65953))+P1(f775(f775(f279(a850),x65951),f775(f775(f3(a850),x65952),x65953))) % 186.05/186.63 [6596]P1(f775(x65961,x65962))+~P1(f775(x65961,f344(x65961,x65963)))+~P1(f775(f775(f334(a850),x65962),f775(f294(a850,f2(a850)),x65963))) % 186.05/186.63 [6609]E(x66091,f2(a850))+P1(f775(x66092,f793(x66091,x66093,x66092)))+~P1(f775(x66092,f775(f775(f43(a850),x66093),x66091))) % 186.05/186.63 [6618]~P119(x66182)+E(x66181,f2(x66182))+~E(f775(f775(f82(x66182),f775(f775(f83(x66182),x66183),x66183)),f775(f775(f83(x66182),x66181),x66181)),f2(x66182)) % 186.05/186.63 [6619]~P119(x66192)+E(x66191,f2(x66192))+~E(f775(f775(f82(x66192),f775(f775(f83(x66192),x66191),x66191)),f775(f775(f83(x66192),x66193),x66193)),f2(x66192)) % 186.05/186.63 [6666]E(x66661,f2(a850))+~P1(f775(x66662,f803(x66661,x66663,x66662)))+P1(f775(x66662,f775(f775(f43(a850),x66663),x66661))) % 186.05/186.63 [6671]~P100(x66711)+~P18(x66711,x66713)+P18(x66711,f775(f775(f138(x66711,x66711,f7(x66711)),x66712),x66713)) % 186.05/186.63 [6715]P1(f775(x67151,f793(x67152,x67153,x67151)))+P1(f775(x67151,f2(a850)))+~P1(f775(x67151,f775(f775(f43(a850),x67153),x67152))) % 186.05/186.63 [6721]~P88(x67211)+E(f775(f106(x67211),x67212),f775(f106(x67211),x67213))+~P33(x67211,f775(f106(x67211),f775(f775(f82(a1),x67212),f775(f81(a1),x67213)))) % 186.05/186.63 [6794]E(x67941,f2(a1))+E(x67942,f2(a1))+~P1(f775(f56(x67942,x67942),f775(f775(f241(a1,a1),x67943),x67941))) % 186.05/186.63 [6795]E(x67951,f80(a1))+E(x67952,f2(a1))+~P1(f775(f56(x67952,x67952),f775(f775(f241(a1,a1),x67951),x67953))) % 186.05/186.63 [6809]P1(f775(x68091,x68092))+P1(f775(f775(f233(a850),f344(x68091,x68093)),x68093))+~P1(f775(f775(f334(a850),x68092),f775(f294(a850,f2(a850)),x68093))) % 186.05/186.63 [6834]~P1(f775(x68341,f803(x68343,x68342,x68341)))+~P1(f775(x68341,f2(a850)))+P1(f775(x68341,f775(f775(f43(a850),x68342),x68343))) % 186.05/186.63 [6835]~P1(f775(x68351,f801(x68353,x68352,x68351)))+~P1(f775(x68351,f2(a850)))+P1(f775(x68351,f775(f775(f3(a850),x68352),x68353))) % 186.05/186.63 [6836]~P1(f775(x68361,f808(x68363,x68362,x68361)))+~P1(f775(x68361,f2(a850)))+P1(f775(x68361,f775(f775(f3(a850),x68362),x68363))) % 186.05/186.63 [6856]~P1(f775(x68561,x68563))+P1(f775(f775(f233(a850),f343(x68561,x68562)),x68562))+~P1(f775(f775(f334(a850),x68563),f775(f294(a850,f2(a850)),x68562))) % 186.05/186.63 [6857]E(f775(f775(f3(a850),f775(f775(f3(a850),x68571),x68572)),f775(f775(f3(a850),x68573),x68572)),f775(f775(f3(a850),x68571),x68573))+~P1(f775(f775(f232(a850),x68572),x68571))+~P1(f775(f775(f232(a850),x68572),x68573)) % 186.05/186.63 [6891]~P77(x68911)+~P1(f775(f775(f233(x68911),f775(f81(x68911),x68913)),x68912))+P1(f775(f775(f233(x68911),f775(f81(x68911),x68912)),x68913)) % 186.05/186.63 [6892]~P110(x68921)+~P1(f775(f775(f233(x68921),f775(f77(x68921),x68922)),x68923))+P1(f775(f775(f233(x68921),f775(f81(x68921),x68922)),x68923)) % 186.05/186.63 [6894]~P77(x68941)+~P1(f775(f775(f232(x68941),f775(f81(x68941),x68943)),x68942))+P1(f775(f775(f232(x68941),f775(f81(x68941),x68942)),x68943)) % 186.05/186.63 [6896]~P79(x68961)+~P1(f775(f775(f232(x68961),f775(f77(x68961),x68962)),x68963))+P1(f775(f775(f232(x68961),f775(f81(x68961),x68962)),x68963)) % 186.05/186.63 [6899]~P1(f775(f775(f279(a1),x68991),x68993))+P1(f775(f775(f279(a1),x68991),x68992))+~P1(f775(f775(f279(a1),x68991),f775(f775(f3(a1),x68992),x68993))) % 186.05/186.63 [6932]~P1(f775(x69323,f801(x69322,x69321,x69323)))+P1(f775(f775(f233(a850),x69321),x69322))+P1(f775(x69323,f775(f775(f3(a850),x69321),x69322))) % 186.05/186.63 [6933]~P1(f775(x69333,f808(x69332,x69331,x69333)))+P1(f775(f775(f233(a850),x69331),x69332))+P1(f775(x69333,f775(f775(f3(a850),x69331),x69332))) % 186.05/186.63 [6979]~E(f685(x69793,x69792,x69791),f680(x69793,x69792,x69791))+E(f775(f775(f104(f857(x69791,a844)),x69792),f44(f857(x69791,a844),x69793)),f180(f857(x69791,a844)))+P1(f775(f775(f334(f857(x69791,a844)),x69792),x69793)) % 186.05/186.63 [6988]~P1(f775(f63(x69881),x69883))+P1(f775(f63(x69881),f45(f857(x69881,a844),x69882)))+~P1(f775(f775(f334(f857(x69881,a844)),x69883),x69882)) % 186.05/186.63 [7049]~P100(x70491)+E(f775(f775(f103(f857(x70491,a844)),f775(f294(x70491,x70492),x70493)),f775(f775(f302(x70491),x70493),f180(f857(x70491,a844)))),f295(x70491,x70492,x70493))+~P1(f775(f775(f232(x70491),x70492),x70493)) % 186.05/186.63 [7052]E(x70521,f2(a850))+P1(f775(f775(f233(a850),f805(x70521,x70523,x70522)),x70521))+P1(f775(x70522,f775(f775(f43(a850),x70523),x70521))) % 186.05/186.63 [7087]E(x70871,x70872)+~P1(f775(f775(f232(f857(x70873,a844)),x70871),x70872))+P1(f775(f775(f233(f857(x70873,a844)),x70871),x70872)) % 186.05/186.63 [7099]E(x70991,x70992)+~E(f775(f181(f851(x70993)),x70991),f775(f181(f851(x70993)),x70992))+P1(f775(f775(f233(a850),f731(x70993,x70991,x70992)),f775(f181(f851(x70993)),x70992))) % 186.05/186.63 [7144]P12(x71441,x71442,x71443)+~E(f775(f261(x71441,x71441),x71443),x71442)+~E(f775(f775(f281(x71441,x71441,x71441),f775(f278(x71441,x71441),x71443)),x71443),x71443) % 186.05/186.63 [7226]E(x72261,f2(a1))+~P1(f775(f775(f279(a1),x72262),x72263))+P1(f775(f775(f279(a1),f775(f775(f83(a1),x72261),x72262)),f775(f775(f83(a1),x72261),x72263))) % 186.05/186.63 [7229]~P1(f775(x72291,f2(a850)))+P1(f775(f775(f233(a850),f805(x72293,x72292,x72291)),x72293))+P1(f775(x72291,f775(f775(f43(a850),x72292),x72293))) % 186.05/186.63 [7242]~P100(x72421)+E(f775(f775(f103(f857(x72421,a844)),f298(x72421,x72422,x72423)),f775(f775(f302(x72421),x72423),f180(f857(x72421,a844)))),f297(x72421,x72422,x72423))+~P1(f775(f775(f233(x72421),x72422),x72423)) % 186.05/186.63 [7347]~P1(f775(f63(x73471),x73473))+P1(f775(f775(f233(a850),f775(f42(x73471),x73472)),f775(f42(x73471),x73473)))+~P1(f775(f775(f233(f857(x73471,a844)),x73472),x73473)) % 186.05/186.63 [7348]~P1(f775(f63(x73481),x73483))+P1(f775(f775(f232(a850),f775(f42(x73481),x73482)),f775(f42(x73481),x73483)))+~P1(f775(f775(f232(f857(x73481,a844)),x73482),x73483)) % 186.05/186.63 [7389]~P1(f775(x73893,x73892))+P1(f775(f775(f187(x73891),x73892),f415(x73892,x73891,x73893)))+~P1(f775(f775(f187(f35(x73893,x73891)),x73892),x73892)) % 186.05/186.63 [7487]E(x74871,x74872)+~P1(f775(f775(f232(f857(x74873,a844)),x74872),x74871))+~P1(f775(f775(f232(f857(x74873,a844)),x74871),x74872)) % 186.05/186.63 [7490]~P100(x74901)+P18(x74901,x74902)+~P18(x74901,f775(f775(f138(x74901,x74901,f7(x74901)),x74903),x74902)) % 186.05/186.63 [7559]~P1(f775(f775(f233(a850),x75593),x75592))+~P1(f775(f775(f233(a850),x75593),x75591))+P1(f775(f775(f233(a850),f775(f775(f3(a850),x75591),x75592)),f775(f775(f3(a850),x75591),x75593))) % 186.05/186.63 [7560]~P1(f775(f775(f233(a850),x75601),x75603))+~P1(f775(f775(f232(a850),x75602),x75601))+P1(f775(f775(f233(a850),f775(f775(f3(a850),x75601),x75602)),f775(f775(f3(a850),x75603),x75602))) % 186.05/186.63 [7577]~P1(f775(f775(f233(a1),x75772),f2(a1)))+~P1(f775(f775(f232(a1),x75773),x75771))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x75771),x75772)),f775(f775(f43(a1),x75773),x75772))) % 186.05/186.63 [7597]~P1(f775(f775(f233(a850),f2(a850)),x75972))+~P1(f775(f775(f233(a850),x75971),x75973))+P1(f775(f775(f233(a850),f775(f775(f83(a850),x75971),x75972)),f775(f775(f83(a850),x75973),x75972))) % 186.05/186.63 [7598]~P1(f775(f775(f233(a850),f2(a850)),x75981))+~P1(f775(f775(f233(a850),x75982),x75983))+P1(f775(f775(f233(a850),f775(f775(f83(a850),x75981),x75982)),f775(f775(f83(a850),x75981),x75983))) % 186.05/186.63 [7599]~P1(f775(f775(f233(a1),f2(a1)),x75991))+~P1(f775(f775(f233(a1),x75992),x75993))+P1(f775(f775(f233(a1),f775(f775(f83(a1),x75991),x75992)),f775(f775(f83(a1),x75991),x75993))) % 186.05/186.63 [7601]~P1(f775(f775(f233(a850),f2(a850)),x76013))+~P1(f775(f775(f232(a850),x76013),x76012))+P1(f775(f775(f232(a850),f775(f775(f43(a850),x76011),x76012)),f775(f775(f43(a850),x76011),x76013))) % 186.05/186.63 [7602]~P1(f775(f775(f233(a1),f2(a1)),x76022))+~P1(f775(f775(f232(a1),x76021),x76023))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x76021),x76022)),f775(f775(f43(a1),x76023),x76022))) % 186.05/186.63 [7651]E(x76511,f2(a850))+E(f775(f775(f82(a850),f775(f775(f83(a850),x76511),f803(x76511,x76512,x76513))),f805(x76511,x76512,x76513)),x76512)+P1(f775(x76513,f775(f775(f43(a850),x76512),x76511))) % 186.05/186.63 [7709]E(f775(f775(f82(a850),f775(f775(f83(a850),x77091),f803(x77091,x77092,x77093))),f805(x77091,x77092,x77093)),x77092)+~P1(f775(x77093,f2(a850)))+P1(f775(x77093,f775(f775(f43(a850),x77092),x77091))) % 186.05/186.63 [7725]~P1(f775(f63(x77251),x77253))+P1(f775(f775(f334(x77251),f460(x77252,x77253,x77251)),x77253))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f11(x77251,a850),x77252),x77253))) % 186.05/186.63 [7726]~P1(f775(f63(x77261),x77263))+P1(f775(f775(f334(x77261),f572(x77262,x77263,x77261)),x77263))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f11(x77261,a850),x77262),x77263))) % 186.05/186.63 [7831]E(x78311,f2(a850))+P1(f775(f775(f279(a850),x78312),x78313))+~P1(f775(f775(f279(a850),f775(f775(f83(a850),x78311),x78312)),f775(f775(f83(a850),x78311),x78313))) % 186.05/186.63 [7833]E(x78331,f2(a1))+P1(f775(f775(f279(a1),x78332),x78333))+~P1(f775(f775(f279(a1),f775(f775(f83(a1),x78331),x78332)),f775(f775(f83(a1),x78331),x78333))) % 186.05/186.63 [8019]E(x80191,f180(f857(x80192,a844)))+E(x80191,f775(f775(f302(x80192),x80193),f180(f857(x80192,a844))))+~P1(f775(f775(f232(f857(x80192,a844)),x80191),f775(f775(f302(x80192),x80193),f180(f857(x80192,a844))))) % 186.05/186.63 [8056]~P1(f775(f775(f233(a850),f2(a850)),x80563))+P1(f775(f775(f233(a850),x80561),x80562))+~P1(f775(f775(f233(a850),f775(f775(f242(a850),x80563),x80561)),f775(f775(f242(a850),x80563),x80562))) % 186.05/186.63 [8058]~P1(f775(f775(f233(a850),f2(a850)),x80583))+P1(f775(f775(f232(a850),x80581),x80582))+~P1(f775(f775(f232(a850),f775(f775(f83(a850),x80583),x80581)),f775(f775(f83(a850),x80583),x80582))) % 186.05/186.63 [8059]~P1(f775(f775(f233(a850),f80(a850)),x80593))+P1(f775(f775(f232(a850),x80591),x80592))+~P1(f775(f775(f279(a850),f775(f775(f242(a850),x80593),x80591)),f775(f775(f242(a850),x80593),x80592))) % 186.05/186.63 [8060]~P1(f775(f775(f233(a850),f2(a850)),x80603))+P1(f775(f775(f232(a850),x80601),x80602))+~P1(f775(f775(f232(a850),f775(f775(f83(a850),x80601),x80603)),f775(f775(f83(a850),x80602),x80603))) % 186.05/186.63 [8062]~P1(f775(f775(f233(a850),f2(a850)),x80623))+P1(f775(f775(f279(a850),x80621),x80622))+~P1(f775(f775(f279(a850),f775(f775(f83(a850),x80623),x80621)),f775(f775(f83(a850),x80623),x80622))) % 186.05/186.63 [8090]~P1(f775(x80901,x80903))+P1(f775(f775(f187(f35(x80901,x80902)),f415(x80903,x80902,x80901)),x80903))+~P1(f775(f775(f187(f35(x80901,x80902)),x80903),x80903)) % 186.05/186.63 [8098]~E(f775(f775(f104(f857(x80981,a844)),f680(x80983,x80982,x80981)),f685(x80983,x80982,x80981)),f180(f857(x80981,a844)))+E(f775(f775(f104(f857(x80981,a844)),x80982),f44(f857(x80981,a844),x80983)),f180(f857(x80981,a844)))+P1(f775(f775(f334(f857(x80981,a844)),x80982),x80983)) % 186.05/186.63 [8113]E(x81131,f115(x81132))+~E(f775(f132(f851(x81132),f851(x81132),f125(x81132),f115(x81132)),x81133),f115(x81132))+~P1(f775(f775(f334(f851(x81132)),x81131),f775(f158(f851(x81132)),x81133))) % 186.05/186.63 [8170]E(x81701,f180(f857(f857(x81702,a844),a844)))+P1(f775(f775(f334(f857(x81702,a844)),f687(x81703,x81701,x81702)),x81701))+P1(f775(f775(f232(f857(x81702,a844)),f45(f857(x81702,a844),x81701)),x81703)) % 186.05/186.63 [8176]~P66(x81761)+~P70(x81761)+E(f775(f775(f8(a1,x81761),f775(f775(f10(a850,x81761,a1),x81762),a107)),f775(f303(a850,a1,f102(a1)),x81763)),f775(f775(f8(a850,x81761),x81762),x81763)) % 186.05/186.63 [8177]~P66(x81771)+~P70(x81771)+E(f775(f775(f11(a1,x81771),f775(f775(f10(a850,x81771,a1),x81772),a107)),f775(f303(a850,a1,f102(a1)),x81773)),f775(f775(f11(a850,x81771),x81772),x81773)) % 186.05/186.63 [8214]~P1(f775(f63(x82141),x82143))+~P1(f775(f775(f233(a850),f2(a850)),f775(x82142,f460(x82142,x82143,x82141))))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f11(x82141,a850),x82142),x82143))) % 186.05/186.63 [8215]~P1(f775(f63(x82151),x82153))+~P1(f775(f775(f233(a850),f2(a850)),f775(x82152,f572(x82152,x82153,x82151))))+P1(f775(f775(f233(a850),f2(a850)),f775(f775(f11(x82151,a850),x82152),x82153))) % 186.05/186.63 [8250]~P61(x82502)+E(x82501,f80(x82502))+E(f775(f775(f283(x82502),f775(f775(f3(x82502),f775(f775(f242(x82502),x82501),x82503)),f80(x82502))),f775(f775(f3(x82502),x82501),f80(x82502))),f775(f775(f8(a850,x82502),f775(f242(x82502),x82501)),f775(f294(a850,f2(a850)),x82503))) % 186.05/186.63 [8309]E(x83091,f2(a850))+~P1(f775(x83093,f775(f775(f43(a850),x83092),x83091)))+P1(f775(f775(f233(a850),x83092),f775(f775(f83(a850),x83091),f775(a114,f793(x83091,x83092,x83093))))) % 186.05/186.63 [8330]P1(f775(x83301,f2(a850)))+~P1(f775(x83301,f775(f775(f43(a850),x83302),x83303)))+P1(f775(f775(f233(a850),x83302),f775(f775(f83(a850),x83303),f775(a114,f793(x83303,x83302,x83301))))) % 186.05/186.63 [8369]E(x83691,f2(a850))+~P1(f775(x83693,f775(f775(f43(a850),x83692),x83691)))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x83691),f793(x83691,x83692,x83693))),x83692)) % 186.05/186.63 [8406]P1(f775(x84061,f2(a850)))+~P1(f775(x84061,f775(f775(f43(a850),x84063),x84062)))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x84062),f793(x84062,x84063,x84061))),x84063)) % 186.05/186.63 [8409]~P100(x84091)+E(f775(f775(f138(x84091,x84091,f7(x84091)),x84092),x84093),f139(x84091,x84091,f7(x84091),x84092,x84093))+P1(f775(f775(f334(x84091),x84092),f775(f158(x84091),x84093))) % 186.05/186.63 [8449]~E(f775(x84493,f610(x84492,x84493,x84491)),f775(x84493,f612(x84492,x84493,x84491)))+~P58(x84491,f775(x84493,f611(x84492,x84493,x84491)))+P58(x84491,f775(f775(f46(x84492,f857(x84491,f857(x84491,a844))),f239(f857(x84492,a844))),x84493)) % 186.05/186.63 [8457]E(x84571,f180(f857(f857(x84572,a844),a844)))+~P1(f775(f775(f232(f857(x84572,a844)),f687(x84573,x84571,x84572)),x84573))+P1(f775(f775(f232(f857(x84572,a844)),f45(f857(x84572,a844),x84571)),x84573)) % 186.05/186.63 [8516]~P63(x85161)+~P1(f775(f775(f233(x85161),x85162),x85163))+P1(f775(f775(f233(x85161),x85162),f775(f775(f283(x85161),f775(f775(f82(x85161),x85162),x85163)),f775(f775(f82(x85161),f80(x85161)),f80(x85161))))) % 186.05/186.63 [8559]~P1(f775(f775(x85591,f825(x85591,x85593,x85592)),f826(x85591,x85593,x85592)))+P1(f775(f775(x85591,x85592),x85593))+~P1(f775(f321(f856(a1,a1),a59),f775(f775(f241(a1,a1),x85592),x85593))) % 186.05/186.63 [8560]~P1(f775(f775(x85601,f827(x85601,x85603,x85602)),f828(x85601,x85603,x85602)))+P1(f775(f775(x85601,x85602),x85603))+~P1(f775(f321(f856(a1,a1),a62),f775(f775(f241(a1,a1),x85602),x85603))) % 186.05/186.63 [8561]~P1(f775(f775(x85611,f830(x85611,x85613,x85612)),f833(x85611,x85613,x85612)))+P1(f775(f775(x85611,x85612),x85613))+~P1(f775(f321(f856(a1,a1),a216),f775(f775(f241(a1,a1),x85612),x85613))) % 186.05/186.63 [8562]~P1(f775(f775(x85621,f834(x85621,x85623,x85622)),f835(x85621,x85623,x85622)))+P1(f775(f775(x85621,x85622),x85623))+~P1(f775(f321(f856(a850,a850),a214),f775(f775(f241(a850,a850),x85622),x85623))) % 186.05/186.63 [8563]~P1(f775(f775(x85631,f394(x85631,x85633,x85632)),f395(x85631,x85633,x85632)))+P1(f775(f775(x85631,x85632),x85633))+~P1(f775(f321(f856(a1,a1),a168),f775(f775(f241(a1,a1),x85632),x85633))) % 186.05/186.63 [8797]P1(f775(f775(x87971,x87972),x87973))+P1(f775(f321(f856(a850,a850),a214),f775(f775(f241(a850,a850),f834(x87971,x87973,x87972)),f835(x87971,x87973,x87972))))+~P1(f775(f321(f856(a850,a850),a214),f775(f775(f241(a850,a850),x87972),x87973))) % 186.05/186.63 [8798]P1(f775(f775(x87981,x87982),x87983))+P1(f775(f321(f856(a1,a1),a59),f775(f775(f241(a1,a1),f825(x87981,x87983,x87982)),f826(x87981,x87983,x87982))))+~P1(f775(f321(f856(a1,a1),a59),f775(f775(f241(a1,a1),x87982),x87983))) % 186.05/186.63 [8799]P1(f775(f775(x87991,x87992),x87993))+P1(f775(f321(f856(a1,a1),a62),f775(f775(f241(a1,a1),f827(x87991,x87993,x87992)),f828(x87991,x87993,x87992))))+~P1(f775(f321(f856(a1,a1),a62),f775(f775(f241(a1,a1),x87992),x87993))) % 186.05/186.63 [8800]P1(f775(f775(x88001,x88002),x88003))+P1(f775(f321(f856(a1,a1),a216),f775(f775(f241(a1,a1),f830(x88001,x88003,x88002)),f833(x88001,x88003,x88002))))+~P1(f775(f321(f856(a1,a1),a216),f775(f775(f241(a1,a1),x88002),x88003))) % 186.05/186.63 [8801]P1(f775(f775(x88011,x88012),x88013))+P1(f775(f321(f856(a1,a1),a168),f775(f775(f241(a1,a1),f394(x88011,x88013,x88012)),f395(x88011,x88013,x88012))))+~P1(f775(f321(f856(a1,a1),a168),f775(f775(f241(a1,a1),x88012),x88013))) % 186.05/186.63 [9113]~P1(f775(f63(x91131),x91133))+P1(f775(f775(f334(f856(f857(x91131,a844),f857(x91131,a844))),f775(f775(f241(f857(x91131,a844),f857(x91131,a844)),x91132),x91133)),f299(x91131)))+~P1(f775(f775(f233(f857(x91131,a844)),x91132),x91133)) % 186.05/186.63 [9166]~P58(x91661,f775(x91663,f611(x91662,x91663,x91661)))+P58(x91661,f775(f775(f46(x91662,f857(x91661,f857(x91661,a844))),f239(f857(x91662,a844))),x91663))+~E(f775(f775(f104(f857(x91661,a844)),f246(x91661,x91661,f775(x91663,f610(x91662,x91663,x91661)))),f247(x91661,x91661,f775(x91663,f612(x91662,x91663,x91661)))),f180(f857(x91661,a844))) % 186.05/186.63 [9359]P47(x93591,x93592,x93593)+P1(f775(f775(f334(f856(x93591,x93591)),f507(x93593,x93592,x93591)),x93593))+~P1(f775(f775(f334(f856(x93591,x93591)),f775(f775(f241(x93591,x93591),f506(x93593,x93592,x93591)),f506(x93593,x93592,x93591))),x93593)) % 186.05/186.63 [9924]P47(x99241,x99242,x99243)+~P1(f775(f775(f251(x99241,x99241,a844),f775(f775(f9(x99241,f857(x99241,a844),f857(x99241,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x99241,a844),f857(x99241,a844)),x99241),f10(a844,a844,x99241)),f775(f775(f10(a844,f857(a844,a844),x99241),a331),f775(f775(f9(x99241,f857(x99241,a844),a844),f334(x99241)),x99242)))),f775(f775(f9(x99241,f857(x99241,a844),a844),f334(x99241)),x99242))),f507(x99243,x99242,x99241)))+~P1(f775(f775(f334(f856(x99241,x99241)),f775(f775(f241(x99241,x99241),f506(x99243,x99242,x99241)),f506(x99243,x99242,x99241))),x99243)) % 186.05/186.63 [5522]~P7(x55222)+E(x55221,f2(x55222))+E(f775(f775(f43(x55222),f775(f775(f83(x55222),x55223),x55221)),x55221),x55223) % 186.05/186.63 [5523]~P7(x55232)+E(x55231,f2(x55232))+E(f775(f775(f43(x55232),f775(f775(f83(x55232),x55231),x55233)),x55231),x55233) % 186.05/186.63 [6166]~P7(x61661)+E(f775(f775(f83(x61661),f775(f775(f43(x61661),x61662),x61663)),x61663),x61662)+~P1(f775(f775(f279(x61661),x61663),x61662)) % 186.05/186.63 [6332]~P66(x63321)+~E(f775(x63322,f2(a850)),f2(x63321))+E(f775(f775(f8(a850,x63321),x63322),f775(f294(a850,f775(a114,f2(a850))),x63323)),f775(f775(f8(a850,x63321),x63322),f775(f294(a850,f2(a850)),x63323))) % 186.05/186.63 [6475]~P7(x64752)+E(x64751,f2(x64752))+E(f775(f775(f43(x64752),f775(f775(f82(x64752),x64753),x64751)),x64751),f775(f775(f82(x64752),f775(f775(f43(x64752),x64753),x64751)),f80(x64752))) % 186.05/186.63 [6476]~P7(x64762)+E(x64761,f2(x64762))+E(f775(f775(f43(x64762),f775(f775(f82(x64762),x64761),x64763)),x64761),f775(f775(f82(x64762),f775(f775(f43(x64762),x64763),x64761)),f80(x64762))) % 186.05/186.63 [6705]~P1(f775(x67053,f2(a1)))+P1(f775(f775(f232(a850),x67051),x67052))+P1(f775(x67053,f775(f102(a1),f775(f775(f3(a850),x67052),x67051)))) % 186.05/186.63 [6816]P1(f775(f775(f232(a850),x68162),x68161))+P1(f775(f775(f233(a850),x68161),x68162))+P1(f775(x68163,f775(f102(a1),f775(f775(f3(a850),x68161),x68162)))) % 186.05/186.63 [6889]E(f775(f775(f82(a850),f775(f106(a850),x68891)),f775(f775(f82(a850),f775(f106(a850),x68892)),x68893)),f775(f775(f82(a850),f775(f106(a850),x68891)),x68893))+P1(f775(a186,f775(f106(a1),x68891)))+~P1(f775(a186,f775(f106(a1),x68892))) % 186.05/186.63 [6967]~E(x69672,f775(f775(f43(a850),x69673),x69671))+~P1(f775(f775(f233(a850),f2(a850)),x69671))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x69671),x69672)),x69673)) % 186.05/186.63 [7085]~P1(f775(f63(x70851),x70853))+~P1(f775(f63(x70851),x70852))+P1(f775(f63(x70851),f775(f775(f103(f857(x70851,a844)),x70852),x70853))) % 186.05/186.63 [7400]~P100(x74001)+~P1(f775(f63(x74001),x74002))+E(f130(x74001,f775(f775(f3(f857(x74001,a844)),x74002),f775(f775(f302(x74001),x74003),f180(f857(x74001,a844))))),f151(x74001,x74003,f130(x74001,x74002))) % 186.05/186.63 [7466]P1(f775(x74661,f2(a1)))+~P1(f775(f775(f233(a850),x74662),x74663))+~P1(f775(x74661,f775(f102(a1),f775(f775(f3(a850),x74662),x74663)))) % 186.05/186.63 [7484]~P1(f775(f63(x74841),x74842))+E(f775(f42(x74841),f775(f775(f3(f857(x74841,a844)),x74842),f775(f775(f302(x74841),x74843),f180(f857(x74841,a844))))),f775(f42(x74841),x74842))+P1(f775(f775(f334(x74841),x74843),x74842)) % 186.05/186.63 [7618]~P117(x76181)+~P1(f775(f775(f233(x76181),f80(x76181)),x76182))+P1(f775(f775(f233(x76181),f80(x76181)),f775(f775(f83(x76181),x76182),f775(f775(f242(x76181),x76182),x76183)))) % 186.05/186.63 [7662]~P1(f775(f63(x76621),x76623))+E(f775(f775(f3(a850),f775(f42(x76621),x76622)),f775(f42(x76621),x76623)),f775(f42(x76621),f775(f775(f3(f857(x76621,a844)),x76622),x76623)))+~P1(f775(f775(f232(f857(x76621,a844)),x76623),x76622)) % 186.05/186.63 [7717]~P1(f775(f775(f232(a850),x77172),x77173))+~P1(f775(f775(f232(a850),x77171),f775(f775(f3(a850),x77173),x77172)))+P1(f775(f775(f232(a850),f775(f775(f82(a850),x77171),x77172)),x77173)) % 186.05/186.63 [7774]P1(f775(f63(x77741),x77742))+~P1(f775(f63(x77741),x77743))+~P1(f775(f63(x77741),f775(f775(f3(f857(x77741,a844)),x77742),x77743))) % 186.05/186.63 [7781]~P1(f775(f63(x77811),x77812))+E(f775(f42(x77811),f775(f775(f3(f857(x77811,a844)),x77812),f775(f775(f302(x77811),x77813),f180(f857(x77811,a844))))),f775(f775(f3(a850),f775(f42(x77811),x77812)),f80(a850)))+~P1(f775(f775(f334(x77811),x77813),x77812)) % 186.05/186.63 [7856]P58(x78561,x78562)+~P58(x78561,x78563)+~P1(f775(f775(f232(f857(x78561,f857(x78561,a844))),x78562),x78563)) % 186.05/186.63 [7894]~P1(f775(f775(f232(a850),x78943),x78942))+P1(f775(f775(f232(a850),x78941),f775(f775(f3(a850),x78942),x78943)))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),x78941),x78943)),x78942)) % 186.05/186.63 [7914]P36(x79141,x79142)+~P36(x79141,x79143)+~P1(f775(f775(f232(f857(f856(x79141,x79141),a844)),x79142),x79143)) % 186.05/186.63 [7915]P56(x79151,x79152)+~P56(x79151,x79153)+~P1(f775(f775(f232(f857(f856(x79151,x79151),a844)),x79152),x79153)) % 186.05/186.63 [8148]~P117(x81481)+~P1(f775(f775(f233(x81481),f80(x81481)),x81482))+P1(f775(f775(f233(x81481),f775(f775(f242(x81481),x81482),x81483)),f775(f775(f83(x81481),x81482),f775(f775(f242(x81481),x81482),x81483)))) % 186.05/186.63 [8234]~P1(f775(x82341,f2(a1)))+~P1(f775(x82341,f775(f775(f3(a1),f775(f102(a1),x82342)),f775(f102(a1),x82343))))+P1(f775(x82341,f775(f102(a1),f775(f775(f3(a850),x82342),x82343)))) % 186.05/186.63 [8247]~P1(f775(f775(f232(a850),x82473),x82472))+P1(f775(x82471,f775(f775(f3(a1),f775(f102(a1),x82472)),f775(f102(a1),x82473))))+~P1(f775(x82471,f775(f102(a1),f775(f775(f3(a850),x82472),x82473)))) % 186.05/186.63 [8264]P1(f775(f775(f233(a850),x82641),x82642))+~P1(f775(x82643,f775(f775(f3(a1),f775(f102(a1),x82641)),f775(f102(a1),x82642))))+P1(f775(x82643,f775(f102(a1),f775(f775(f3(a850),x82641),x82642)))) % 186.05/186.63 [8321]~P119(x83212)+E(x83211,f2(x83212))+P1(f775(f775(f233(x83212),f2(x83212)),f775(f775(f82(x83212),f775(f775(f83(x83212),x83213),x83213)),f775(f775(f83(x83212),x83211),x83211)))) % 186.05/186.63 [8322]~P119(x83222)+E(x83221,f2(x83222))+P1(f775(f775(f233(x83222),f2(x83222)),f775(f775(f82(x83222),f775(f775(f83(x83222),x83221),x83221)),f775(f775(f83(x83222),x83223),x83223)))) % 186.05/186.63 [8428]~P1(f775(f775(f233(a850),f2(a850)),x84281))+~P1(f775(f775(f233(a1),x84282),x84283))+P1(f775(f775(f233(a1),f775(f775(f83(a1),f775(f102(a1),x84281)),x84282)),f775(f775(f83(a1),f775(f102(a1),x84281)),x84283))) % 186.05/186.63 [8488]E(f775(f775(f104(f857(x84881,a844)),x84882),f44(f857(x84881,a844),x84883)),f180(f857(x84881,a844)))+P1(f775(f775(f334(f857(x84881,a844)),x84882),x84883))+P1(f775(f775(f334(f857(x84881,a844)),f680(x84883,x84882,x84881)),f775(f775(f302(f857(x84881,a844)),x84882),x84883))) % 186.05/186.63 [8489]E(f775(f775(f104(f857(x84891,a844)),x84892),f44(f857(x84891,a844),x84893)),f180(f857(x84891,a844)))+P1(f775(f775(f334(f857(x84891,a844)),x84892),x84893))+P1(f775(f775(f334(f857(x84891,a844)),f685(x84893,x84892,x84891)),f775(f775(f302(f857(x84891,a844)),x84892),x84893))) % 186.05/186.63 [8515]E(x85151,x85152)+~E(f775(f181(f851(x85153)),x85151),f775(f181(f851(x85153)),x85152))+P1(f775(f775(f334(f856(x85153,x85153)),f714(x85153,x85151,x85152)),f775(f158(f856(x85153,x85153)),f775(f775(f167(x85153,x85153),x85152),x85151)))) % 186.05/186.63 [8725]E(f300(x87251,x87252),f300(x87251,x87253))+~P1(f775(f775(f232(f857(f856(x87251,x87251),a844)),x87253),f300(x87251,x87252)))+~P1(f775(f775(f232(f857(f856(x87251,x87251),a844)),x87252),x87253)) % 186.05/186.63 [8778]~P47(x87781,f239(f857(x87781,a844)),x87783)+P1(f775(f775(f232(f857(f856(f851(x87781),f851(x87781)),a844)),f146(x87781,x87782)),f147(x87781,x87783)))+~P1(f775(f775(f232(f857(f856(x87781,x87781),a844)),x87782),x87783)) % 186.05/186.63 [8957]P36(x89571,x89572)+~P1(f775(f775(f334(x89571),x89573),f683(x89572,x89571)))+P1(f775(f775(f334(f856(x89571,x89571)),f775(f775(f241(x89571,x89571),f698(x89572,x89571,x89573)),x89573)),x89572)) % 186.05/186.63 [8996]~P1(f775(f63(x89961),x89962))+P1(f775(f63(f857(x89961,a844)),f775(f775(f61(x89961),x89962),x89963)))+~P1(f775(f775(f232(f857(f856(x89961,x89961),a844)),x89963),f775(f775(f248(x89961,x89961),x89962),f775(f18(f857(x89961,a844),x89961),x89962)))) % 186.05/186.63 [9027]P47(x90271,x90272,x90273)+P1(f775(f775(f334(x90271),f550(x90273,x90272,x90271)),x90272))+~P1(f775(f775(f232(f857(f856(x90271,x90271),a844)),x90273),f775(f775(f248(x90271,x90271),x90272),f775(f18(f857(x90271,a844),x90271),x90272)))) % 186.05/186.63 [9028]P47(x90281,x90282,x90283)+P1(f775(f775(f334(x90281),f555(x90282,x90283,x90281)),x90282))+~P1(f775(f775(f232(f857(f856(x90281,x90281),a844)),x90283),f775(f775(f248(x90281,x90281),x90282),f775(f18(f857(x90281,a844),x90281),x90282)))) % 186.05/186.63 [9061]~P63(x90611)+~P1(f775(f775(f233(x90611),x90612),x90613))+P1(f775(f775(f233(x90611),f775(f775(f283(x90611),f775(f775(f82(x90611),x90612),x90613)),f775(f775(f82(x90611),f80(x90611)),f80(x90611)))),x90613)) % 186.05/186.63 [9088]~P62(x90881)+P1(f775(f775(f232(x90881),x90882),x90883))+~P1(f775(f775(f232(x90881),f775(f775(f83(x90881),f802(x90883,x90882,x90881)),x90882)),x90883)) % 186.05/186.63 [9198]E(f775(f181(f851(f851(x91981))),f775(f126(f851(x91981),f775(f775(f10(a850,a844,f851(x91981)),f775(f233(a850),x91982)),f181(f851(x91981)))),f164(x91981,x91983))),f775(f181(f851(x91981)),f775(f775(f153(f851(x91981)),x91983),x91982)))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x91981),a850),f181(f851(x91981))),x91983)))+~P1(f775(f775(f233(a850),x91982),f775(f181(f851(f851(x91981))),x91983))) % 186.05/186.63 [9309]~P36(x93091,x93092)+P30(x93091,f775(f775(f241(f857(f856(x93091,x93091),a844),f857(f856(x93091,x93091),a844)),x93092),x93093))+~P1(f775(f775(f232(f857(f856(x93091,x93091),a844)),f775(f775(f281(x93091,x93091,x93091),x93092),x93093)),x93092)) % 186.05/186.63 [9316]E(f775(f775(f143(f851(x93161),x93161),f775(f775(f9(f851(x93161),a850,x93161),f153(x93161)),x93162)),f775(f126(f851(x93161),f775(f775(f10(a850,a844,f851(x93161)),f775(f233(a850),x93162)),f181(f851(x93161)))),f164(x93161,x93163))),f775(f775(f153(f851(x93161)),x93163),x93162))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x93161),a850),f181(f851(x93161))),x93163)))+~P1(f775(f775(f233(a850),x93162),f775(f181(f851(f851(x93161))),x93163))) % 186.05/186.63 [9443]P47(x94431,x94432,x94433)+~P1(f775(f775(f334(f856(x94431,x94431)),f775(f775(f241(x94431,x94431),f550(x94433,x94432,x94431)),f550(x94433,x94432,x94431))),x94433))+~P1(f775(f775(f232(f857(f856(x94431,x94431),a844)),x94433),f775(f775(f248(x94431,x94431),x94432),f775(f18(f857(x94431,a844),x94431),x94432)))) % 186.05/186.63 [9444]P47(x94441,x94442,x94443)+~P1(f775(f775(f334(f856(x94441,x94441)),f775(f775(f241(x94441,x94441),f555(x94442,x94443,x94441)),f555(x94442,x94443,x94441))),x94443))+~P1(f775(f775(f232(f857(f856(x94441,x94441),a844)),x94443),f775(f775(f248(x94441,x94441),x94442),f775(f18(f857(x94441,a844),x94441),x94442)))) % 186.05/186.63 [9603]~P133(x96031)+~P116(x96031)+E(f775(f775(f283(x96031),f775(f105(x96031),f775(f775(f75(f856(a1,a1),a1,x96032,f240(a1,a1)),f207(x96032)),x96033))),f775(f105(x96031),f775(f775(f75(f856(a1,a1),a1,x96032,f250(a1,a1)),f207(x96032)),x96033))),f217(x96032,x96031,x96033)) % 186.05/186.63 [9799]~E(x97993,f2(a850))+~E(f775(f181(f851(x97991)),f775(f775(f153(f851(x97991)),x97992),f767(x97993,x97991,x97992))),x97993)+E(f775(f775(f143(a850,f851(x97991)),f775(f775(f9(a850,f851(a850),f851(x97991)),f775(f775(f10(f857(a850,x97991),f857(f851(a850),f851(x97991)),a850),f143(a850,x97991)),f775(f9(a850,a850,x97991),f775(f775(f10(f851(x97991),f857(a850,x97991),a850),f153(x97991)),f775(f153(f851(x97991)),x97992))))),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(f851(x97991))),x97992))))),f130(a850,f775(f294(a850,f2(a850)),x97993))),f164(x97991,x97992)) % 186.05/186.63 [9800]E(x98001,f115(f851(x98002)))+~E(f775(f181(f851(x98002)),f775(f775(f153(f851(x98002)),x98001),f767(x98003,x98002,x98001))),x98003)+E(f775(f775(f143(a850,f851(x98002)),f775(f775(f9(a850,f851(a850),f851(x98002)),f775(f775(f10(f857(a850,x98002),f857(f851(a850),f851(x98002)),a850),f143(a850,x98002)),f775(f9(a850,a850,x98002),f775(f775(f10(f851(x98002),f857(a850,x98002),a850),f153(x98002)),f775(f153(f851(x98002)),x98001))))),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(f851(x98002))),x98001))))),f130(a850,f775(f294(a850,f2(a850)),x98003))),f164(x98002,x98001)) % 186.05/186.63 [9801]~E(x98013,f2(a850))+E(f775(f775(f143(a850,f851(x98011)),f775(f775(f9(a850,f851(a850),f851(x98011)),f775(f775(f10(f857(a850,x98011),f857(f851(a850),f851(x98011)),a850),f143(a850,x98011)),f775(f9(a850,a850,x98011),f775(f775(f10(f851(x98011),f857(a850,x98011),a850),f153(x98011)),f775(f153(f851(x98011)),x98012))))),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(f851(x98011))),x98012))))),f130(a850,f775(f294(a850,f2(a850)),x98013))),f164(x98011,x98012))+P1(f775(f775(f233(a850),f767(x98013,x98011,x98012)),f775(f181(f851(f851(x98011))),x98012))) % 186.05/186.63 [9802]E(x98021,f115(f851(x98022)))+E(f775(f775(f143(a850,f851(x98022)),f775(f775(f9(a850,f851(a850),f851(x98022)),f775(f775(f10(f857(a850,x98022),f857(f851(a850),f851(x98022)),a850),f143(a850,x98022)),f775(f9(a850,a850,x98022),f775(f775(f10(f851(x98022),f857(a850,x98022),a850),f153(x98022)),f775(f153(f851(x98022)),x98021))))),f130(a850,f775(f294(a850,f2(a850)),f775(f181(f851(f851(x98022))),x98021))))),f130(a850,f775(f294(a850,f2(a850)),x98023))),f164(x98022,x98021))+P1(f775(f775(f233(a850),f767(x98023,x98022,x98021)),f775(f181(f851(f851(x98022))),x98021))) % 186.05/186.63 [7659]E(f775(f775(f82(a850),f775(f106(a850),x76591)),f775(f775(f82(a850),f775(f106(a850),x76592)),x76593)),f775(f775(f82(a850),f775(f106(a850),f775(f775(f82(a1),x76591),x76592))),x76593))+P1(f775(a186,f775(f106(a1),x76591)))+P1(f775(a186,f775(f106(a1),x76592))) % 186.05/186.63 [8419]~P1(f775(f63(x84191),x84192))+~P1(f775(f775(f334(x84191),x84193),x84192))+E(f775(a114,f775(f42(x84191),f775(f775(f3(f857(x84191,a844)),x84192),f775(f775(f302(x84191),x84193),f180(f857(x84191,a844)))))),f775(f42(x84191),x84192)) % 186.05/186.63 [8439]~P1(f775(f63(x84391),x84392))+~P1(f775(f775(f334(x84391),x84393),x84392))+E(f775(f775(f82(a850),f80(a850)),f775(f42(x84391),f775(f775(f3(f857(x84391,a844)),x84392),f775(f775(f302(x84391),x84393),f180(f857(x84391,a844)))))),f775(f42(x84391),x84392)) % 186.05/186.63 [8523]~P100(x85231)+~P1(f775(f63(x85231),x85233))+E(f775(f775(f138(x85231,x85231,f7(x85231)),x85232),f130(x85231,f775(f775(f3(f857(x85231,a844)),x85233),f775(f775(f302(x85231),x85232),f180(f857(x85231,a844)))))),f130(x85231,f775(f775(f302(x85231),x85232),x85233))) % 186.05/186.63 [8661]~P1(f775(f63(x86611),x86613))+~P1(f775(f63(x86611),x86612))+E(f775(f775(f82(a850),f775(f42(x86611),f775(f775(f103(f857(x86611,a844)),x86612),x86613))),f775(f42(x86611),f775(f775(f104(f857(x86611,a844)),x86612),x86613))),f775(f775(f82(a850),f775(f42(x86611),x86612)),f775(f42(x86611),x86613))) % 186.05/186.63 [9748]~P29(x97481,f857(f857(x97481,a844),a844),f775(f775(f9(x97481,f857(f856(x97481,x97481),a844),f857(f857(x97481,a844),a844)),f775(f775(f10(f857(x97481,a844),f857(f857(f856(x97481,x97481),a844),f857(f857(x97481,a844),a844)),x97481),f61(x97481)),f775(f775(f9(x97481,f857(x97481,a844),f857(x97481,a844)),f302(x97481)),f180(f857(x97481,a844))))),x97483),x97482)+~P1(f775(f63(x97481),x97482))+E(f775(f42(f857(x97481,a844)),f775(f775(f61(x97481),x97482),x97483)),f775(f42(x97481),x97482)) % 186.05/186.63 [7931]~P88(x79311)+P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x79313)))+E(f775(f775(f242(x79311),x79312),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x79313),x79313)),a99))),f80(x79311)) % 186.05/186.63 [9292]~P88(x92921)+~P1(f775(f775(f232(a1),f2(a1)),f775(f106(a1),x92923)))+E(f775(f775(f242(x92921),x92922),f775(f106(a850),f775(f775(f3(a1),f775(f775(f82(a1),x92923),x92923)),a99))),f775(f775(f88(x92921,x92921),f775(f775(f242(x92921),x92922),f775(f106(a850),x92923))),f775(f775(f20(x92921,x92921,x92921),f775(f775(f10(x92921,f857(x92921,x92921),x92921),f83(x92921)),f775(f83(x92921),x92922))),f7(x92921)))) % 186.05/186.63 [9713]P1(f775(f775(f232(f857(f856(x97131,x97131),a844)),f300(x97131,x97132)),x97133))+~P1(f775(f775(f232(f857(f856(x97131,x97131),a844)),f300(x97131,f180(f857(f856(x97131,x97131),a844)))),x97133))+~P1(f775(f775(f232(f857(f856(x97131,x97131),a844)),f775(f775(f281(x97131,x97131,x97131),f775(f775(f104(f857(f856(x97131,x97131),a844)),f300(x97131,x97132)),x97133)),x97132)),x97133)) % 186.05/186.63 [9579]~P1(f775(f63(x95791),f775(f256(x95791),x95793)))+~P1(f775(f63(x95791),f775(f256(x95791),x95792)))+P1(f775(f63(x95791),f775(f256(x95791),f775(f775(f20(x95791,a844,a844),f775(f775(f10(a844,f857(a844,a844),x95791),a332),x95792)),x95793)))) % 186.05/186.63 [9867]P1(f775(f775(f232(f857(f856(x98671,x98671),a844)),f775(f775(f281(x98671,x98671,x98671),x98672),f300(x98671,x98672))),x98673))+~P1(f775(f775(f232(f857(f856(x98671,x98671),a844)),x98672),x98673))+~P1(f775(f775(f232(f857(f856(x98671,x98671),a844)),f775(f775(f281(x98671,x98671,x98671),f775(f775(f104(f857(f856(x98671,x98671),a844)),f775(f775(f281(x98671,x98671,x98671),x98672),f300(x98671,x98672))),x98673)),x98672)),x98673)) % 186.05/186.63 [9815]~P110(x98152)+E(x98151,f2(x98152))+~E(f775(f775(f82(x98152),f775(f775(f242(x98152),x98153),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x98152),x98151),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f2(x98152)) % 186.05/186.63 [9816]~P110(x98162)+E(x98161,f2(x98162))+~E(f775(f775(f82(x98162),f775(f775(f242(x98162),x98161),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x98162),x98163),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f2(x98162)) % 186.05/186.63 [9909]~P110(x99092)+E(x99091,f2(x99092))+P1(f775(f775(f233(x99092),f2(x99092)),f775(f775(f82(x99092),f775(f775(f242(x99092),x99093),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99092),x99091),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))) % 186.05/186.63 [9910]~P110(x99102)+E(x99101,f2(x99102))+P1(f775(f775(f233(x99102),f2(x99102)),f775(f775(f82(x99102),f775(f775(f242(x99102),x99101),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99102),x99103),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))) % 186.05/186.63 [9958]~P110(x99581)+P1(f775(f775(f232(x99581),f2(x99581)),x99582))+~P1(f775(f775(f232(x99581),f2(x99581)),f775(f775(f242(x99581),x99582),f775(a114,f775(f775(f83(a850),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),x99583))))) % 186.05/186.63 [5367]~P28(x53671,x53674,x53673)+P28(x53671,x53672,x53673)+~P28(x53671,x53672,x53674) % 186.05/186.63 [4844]~E(x48442,f92(x48443,x48441))+P1(f775(x48441,x48442))+~P1(f775(x48441,x48444)) % 186.05/186.63 [6610]~P36(x66102,x66104)+~P36(x66101,x66103)+P36(f856(x66101,x66102),f325(x66101,x66102,x66103,x66104)) % 186.05/186.63 [8002]~P39(f35(x80024,x80021),x80022,x80023,x80022)+P39(x80021,x80022,x80023,f560(x80023,x80022,x80021,x80024))+~P1(f775(x80024,x80022)) % 186.05/186.63 [8029]~P39(f35(x80291,x80292),x80294,x80293,x80294)+P39(f35(x80291,x80292),f560(x80293,x80294,x80292,x80291),x80293,x80294)+~P1(f775(x80291,x80294)) % 186.05/186.63 [5025]~P11(x50254,x50251)+~E(f775(x50251,x50252),f775(x50251,x50253))+P1(f775(f775(x50251,x50252),x50253)) % 186.05/186.63 [5186]~P11(x51864,x51861)+E(f775(x51861,x51862),f775(x51861,x51863))+~P1(f775(f775(x51861,x51862),x51863)) % 186.05/186.63 [5274]~P22(x52743,x52744,x52741)+E(f775(x52741,x52742),f775(f65(x52743,x52744),x52742))+~P1(f775(f63(x52743),x52742)) % 186.05/186.63 [5275]~P14(x52753,x52754,x52751)+E(f775(x52751,x52752),f775(f65(x52753,x52754),x52752))+~P1(f775(f63(x52753),x52752)) % 186.05/186.63 [5402]~P11(x54024,x54021)+~P1(f775(f775(x54021,x54023),x54022))+P1(f775(f775(x54021,x54022),x54023)) % 186.05/186.63 [5466]E(x54661,x54662)+~E(f775(f240(x54663,x54664),x54661),f775(f240(x54663,x54664),x54662))+~E(f775(f250(x54663,x54664),x54661),f775(f250(x54663,x54664),x54662)) % 186.05/186.63 [5492]E(x54921,x54922)+~P1(f775(f55(x54923,x54924),x54922))+~P1(f775(f55(x54923,x54924),x54921)) % 186.05/186.63 [5686]~P66(x56862)+E(f225(x56861,x56862,x56863,x56864),f2(x56862))+P1(f775(f63(x56861),x56864)) % 186.05/186.63 [5823]~P1(f775(f321(x58231,x58232),x58234))+P1(f775(f321(x58231,x58232),x58233))+~P1(f775(f775(x58232,x58233),x58234)) % 186.05/186.63 [8073]~P1(f775(f63(x80732),x80734))+~P1(f775(f63(x80731),x80733))+P1(f775(f63(f858(x80731,x80732)),f314(x80731,x80732,x80733,x80734))) % 186.05/186.63 [8076]P1(f775(f775(f334(f851(x80761)),f775(f775(f125(x80761),x80762),x80763)),f149(x80761,x80764)))+~P1(f775(f775(f334(f851(x80761)),x80763),f149(x80761,x80764)))+~P1(f775(f775(f334(f851(x80761)),x80762),f149(x80761,x80764))) % 186.05/186.63 [8651]~P1(f775(f775(f334(f856(x86511,x86511)),f775(f775(f241(x86511,x86511),x86512),x86514)),f300(x86511,x86513)))+P1(f775(f775(f334(x86511),x86512),f322(x86511,x86513)))+~P1(f775(f775(f334(x86511),x86514),f322(x86511,x86513))) % 186.05/186.63 [5009]~P66(x50092)+E(f775(f775(f8(x50091,x50092),x50093),x50094),f2(x50092))+P1(f775(f63(x50091),x50094)) % 186.05/186.63 [5012]~P70(x50122)+E(f775(f775(f11(x50121,x50122),x50123),x50124),f80(x50122))+P1(f775(f63(x50121),x50124)) % 186.05/186.63 [5155]~P3(x51553)+E(x51551,x51552)+~E(f775(f775(f82(x51553),x51554),x51551),f775(f775(f82(x51553),x51554),x51552)) % 186.05/186.63 [5156]~P4(x51563)+E(x51561,x51562)+~E(f775(f775(f82(x51563),x51564),x51561),f775(f775(f82(x51563),x51564),x51562)) % 186.05/186.63 [5158]~P3(x51583)+E(x51581,x51582)+~E(f775(f775(f82(x51583),x51581),x51584),f775(f775(f82(x51583),x51582),x51584)) % 186.05/186.63 [5244]~P112(x52441)+~E(x52443,f775(f775(f83(x52441),x52442),x52444))+P1(f775(f775(f279(x52441),x52442),x52443)) % 186.05/186.63 [5269]~P9(x52693)+E(x52691,f180(f857(x52692,a844)))+E(f775(f775(f46(x52692,x52693),x52691),f775(f18(x52693,x52692),x52694)),x52694) % 186.05/186.63 [5270]~P9(x52703)+E(x52701,f180(f857(x52702,a844)))+E(f775(f775(f47(x52702,x52703),x52701),f775(f18(x52703,x52702),x52704)),x52704) % 186.05/186.63 [5480]~P99(x54803)+E(x54801,x54802)+~E(f295(x54803,x54804,x54801),f775(f775(f302(x54803),x54802),f180(f857(x54803,a844)))) % 186.05/186.63 [5481]~P99(x54813)+E(x54811,x54812)+~E(f295(x54813,x54811,x54812),f775(f775(f302(x54813),x54814),f180(f857(x54813,a844)))) % 186.05/186.63 [5785]P1(f775(x57851,x57852))+~P1(f775(f245(x57853,x57851),x57854))+~P1(f775(f775(f334(x57853),x57852),x57854)) % 186.05/186.63 [5814]E(x58141,x58142)+~P1(f775(f775(f187(x58143),x58144),x58142))+~P1(f775(f775(f187(x58143),x58144),x58141)) % 186.05/186.63 [5896]~P66(x58961)+E(f775(f775(f8(a850,x58961),x58962),f775(f294(a850,x58963),f775(a114,x58964))),f2(x58961))+~P1(f775(f775(f233(a850),x58964),x58963)) % 186.05/186.63 [5901]~P8(x59011)+~E(f52(x59011,x59012,x59013),f52(x59011,x59014,x59013))+E(f52(x59011,f775(f81(x59011),x59012),x59013),f52(x59011,f775(f81(x59011),x59014),x59013)) % 186.05/186.63 [5970]P1(f775(x59701,x59702))+~E(f775(f126(x59703,x59701),x59704),x59704)+~P1(f775(f775(f334(x59703),x59702),f775(f158(x59703),x59704))) % 186.05/186.63 [5989]~E(f775(f775(f82(a850),x59893),x59892),f775(f775(f82(a850),x59891),x59894))+~P1(f775(f775(f233(a850),x59893),x59894))+P1(f775(f775(f233(a850),x59891),x59892)) % 186.05/186.63 [5996]~P7(x59961)+E(f52(x59961,f52(x59961,x59962,x59963),x59964),f52(x59961,x59962,x59964))+~P1(f775(f775(f279(x59961),x59964),x59963)) % 186.05/186.63 [6034]~E(f775(f126(x60341,x60342),x60343),f115(x60341))+~P1(f775(x60342,x60344))+~P1(f775(f775(f334(x60341),x60344),f775(f158(x60341),x60343))) % 186.05/186.63 [6035]~E(f162(x60353,x60351,x60354),x60354)+P1(f775(x60351,x60352))+~P1(f775(f775(f334(x60353),x60352),f775(f158(x60353),x60354))) % 186.05/186.63 [6070]~E(x60704,f180(f857(x60702,a844)))+~E(x60703,f180(f857(x60701,a844)))+E(f314(x60701,x60702,x60703,x60704),f180(f857(f858(x60701,x60702),a844))) % 186.05/186.63 [6504]~P66(x65041)+E(f775(f775(f8(a850,x65041),x65042),f295(a850,x65043,f775(a114,x65044))),f2(x65041))+~P1(f775(f775(f233(a850),f775(a114,x65044)),x65043)) % 186.05/186.63 [6653]~P100(x66531)+E(f775(f775(f3(f857(x66531,a844)),f775(f294(x66531,x66532),x66533)),f775(f294(x66531,x66532),x66534)),f775(f294(x66531,x66534),x66533))+~P1(f775(f775(f232(x66531),x66532),x66534)) % 186.05/186.63 [7015]~P1(f775(f775(f334(f851(x70151)),x70154),f149(x70151,x70153)))+P1(f775(f775(f334(x70151),x70152),x70153))+~P1(f775(f775(f334(x70151),x70152),f775(f158(x70151),x70154))) % 186.05/186.63 [7022]~P36(x70221,x70222)+P1(f775(f775(f334(x70221),f695(x70222,x70221,x70223)),x70223))+~P1(f775(f775(f334(x70221),x70224),x70223)) % 186.05/186.63 [7079]~P66(x70791)+E(f775(f775(f775(f67(x70791,x70792,f82(x70791)),x70793),f2(x70791)),x70794),f775(f775(f8(x70792,x70791),x70793),x70794))+~P1(f775(f63(x70792),x70794)) % 186.05/186.63 [7081]~P70(x70811)+E(f775(f775(f775(f67(x70811,x70812,f83(x70811)),x70813),f80(x70811)),x70814),f775(f775(f11(x70812,x70811),x70813),x70814))+~P1(f775(f63(x70812),x70814)) % 186.05/186.63 [7108]P29(x71081,x71082,x71083,x71084)+~E(f775(f42(x71082),f775(f303(x71081,x71082,x71083),x71084)),f775(f42(x71081),x71084))+~P1(f775(f63(x71081),x71084)) % 186.05/186.63 [7312]~P66(x73121)+E(f775(f775(f82(x73121),f775(x73122,x73123)),f775(f775(f8(a850,x73121),x73122),f297(a850,x73123,x73124))),f775(f775(f8(a850,x73121),x73122),f295(a850,x73123,x73124)))+~P1(f775(f775(f232(a850),x73123),x73124)) % 186.05/186.63 [7322]~P66(x73221)+~P29(x73222,x73221,x73223,x73224)+E(f775(f775(f8(x73221,x73221),f39(x73221)),f775(f303(x73222,x73221,x73223),x73224)),f775(f775(f8(x73222,x73221),x73223),x73224)) % 186.05/186.63 [7323]~P70(x73231)+~P29(x73232,x73231,x73233,x73234)+E(f775(f775(f11(x73231,x73231),f39(x73231)),f775(f303(x73232,x73231,x73233),x73234)),f775(f775(f11(x73232,x73231),x73233),x73234)) % 186.05/186.63 [7382]E(f775(f42(f858(x73821,x73822)),f314(x73821,x73822,x73823,x73824)),f775(f775(f82(a850),f775(f42(x73821),x73823)),f775(f42(x73822),x73824)))+~P1(f775(f63(x73822),x73824))+~P1(f775(f63(x73821),x73823)) % 186.05/186.63 [7467]E(x74671,x74672)+P1(f775(f775(f334(x74673),x74671),f775(f158(x74673),f151(x74673,x74672,x74674))))+~P1(f775(f775(f334(x74673),x74671),f775(f158(x74673),x74674))) % 186.05/186.63 [7693]~P66(x76931)+E(f775(f775(f82(x76931),f775(f775(f8(a850,x76931),x76932),f775(f294(a850,x76933),x76934))),f775(x76932,x76934)),f775(f775(f8(a850,x76931),x76932),f775(f294(a850,x76933),f775(a114,x76934))))+P1(f775(f775(f233(a850),x76934),x76933)) % 186.05/186.63 [7750]~P29(x77501,x77502,x77503,f239(f857(x77501,a844)))+~P1(f775(f63(x77502),x77504))+P1(f775(f63(x77501),f775(f305(x77501,x77502,x77503),x77504))) % 186.05/186.63 [7864]P1(f775(f775(f334(f851(x78641)),f775(f775(f140(x78641),x78642),x78643)),f149(x78641,x78644)))+~P1(f775(f775(f334(f851(x78641)),x78643),f149(x78641,x78644)))+~P1(f775(f775(f334(x78641),x78642),x78644)) % 186.05/186.63 [7955]~E(f775(f303(x79553,x79551,x79554),f239(f857(x79553,a844))),f239(f857(x79551,a844)))+P1(f775(f63(x79551),x79552))+~P1(f775(f63(x79553),f775(f305(x79553,x79551,x79554),x79552))) % 186.05/186.63 [8045]~P29(x80451,x80453,x80454,x80452)+P1(f775(f63(x80451),x80452))+~P1(f775(f63(x80453),f775(f303(x80451,x80453,x80454),x80452))) % 186.05/186.63 [8068]~E(x80682,x80683)+P1(f775(f775(f334(f856(x80681,x80681)),f775(f775(f241(x80681,x80681),x80682),x80683)),f260(x80681,x80684)))+~P1(f775(f775(f334(x80681),x80682),x80684)) % 186.05/186.63 [8099]~P66(x80991)+E(f775(f775(f82(x80991),f775(f775(f8(a850,x80991),x80992),f295(a850,x80993,x80994))),f775(x80992,f775(a114,x80994))),f775(f775(f8(a850,x80991),x80992),f295(a850,x80993,f775(a114,x80994))))+P1(f775(f775(f233(a850),f775(a114,x80994)),x80993)) % 186.05/186.63 [8162]P1(f775(x81621,x81622))+~P1(f775(x81621,f775(f775(f153(x81623),x81624),f726(x81621,x81624,x81623))))+~P1(f775(f775(f334(x81623),x81622),f775(f158(x81623),x81624))) % 186.05/186.63 [8296]~P1(f775(f775(f334(x82961),x82962),f322(x82961,x82964)))+P1(f775(f775(f334(f851(x82961)),f775(f775(f140(x82961),x82962),x82963)),f322(f851(x82961),f146(x82961,x82964))))+~P1(f775(f775(f334(f851(x82961)),x82963),f322(f851(x82961),f146(x82961,x82964)))) % 186.05/186.63 [8312]~P29(x83122,x83123,x83124,f688(x83124,x83123,x83122,x83121))+P29(x83122,x83123,x83124,f45(f857(x83122,a844),x83121))+E(x83121,f180(f857(f857(x83122,a844),a844))) % 186.05/186.63 [8573]E(x85731,x85732)+~P1(f775(f775(f334(f856(x85733,x85733)),f775(f775(f241(x85733,x85733),x85731),x85732)),f300(x85733,x85734)))+P1(f775(f775(f334(x85733),x85731),f775(f261(x85733,x85733),x85734))) % 186.05/186.63 [8820]P29(x88202,x88203,x88204,f45(f857(x88202,a844),x88201))+E(x88201,f180(f857(f857(x88202,a844),a844)))+P1(f775(f775(f334(f857(x88202,a844)),f688(x88204,x88203,x88202,x88201)),x88201)) % 186.05/186.63 [8948]P1(f775(f63(x89481),x89482))+~P1(f775(f63(x89484),f775(f303(x89481,x89484,x89483),x89482)))+P1(f775(f775(f334(x89481),f599(x89483,x89484,x89482,x89481)),x89482)) % 186.05/186.63 [9040]~P9(x90402)+E(f775(f775(f66(x90401,x90402,f775(f775(f10(x90402,f857(x90402,x90402),x90401),f103(x90402)),x90403)),f180(x90402)),x90404),f775(f775(f46(x90401,x90402),x90404),x90403))+~P1(f775(f63(x90401),x90404)) % 186.05/186.63 [9041]~P9(x90412)+E(f775(f775(f66(x90411,x90412,f775(f775(f10(x90412,f857(x90412,x90412),x90411),f104(x90412)),x90413)),f239(x90412)),x90414),f775(f775(f47(x90411,x90412),x90414),x90413))+~P1(f775(f63(x90411),x90414)) % 186.05/186.63 [9067]~P1(f775(f775(f279(a850),x90673),x90674))+P1(f775(f775(f279(a850),x90671),x90672))+P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x90671,x90672)),f282(a850,f279(a850),x90673,x90674))) % 186.05/186.63 [9078]~P1(f775(f775(f279(a850),x90782),x90784))+~P1(f775(f775(f279(a850),x90783),x90781))+P1(f775(f775(f232(f857(a850,a844)),f282(a850,f279(a850),x90781,x90782)),f282(a850,f279(a850),x90783,x90784))) % 186.05/186.63 [9136]E(x91361,x91362)+~P1(f775(f775(f334(f856(x91363,x91363)),f775(f775(f241(x91363,x91363),x91361),x91362)),f300(x91363,x91364)))+P1(f775(f775(f334(f856(x91363,x91363)),f775(f775(f241(x91363,x91363),x91361),x91362)),f775(f775(f281(x91363,x91363,x91363),x91364),f300(x91363,x91364)))) % 186.05/186.63 [9167]~E(f775(f181(f851(x91671)),x91672),f775(f181(f851(x91671)),x91673))+~P1(f775(f775(f334(f856(f851(x91671),f851(x91671))),f775(f775(f241(f851(x91671),f851(x91671)),x91672),x91673)),f137(x91671,x91674)))+P1(f775(f775(f334(f856(f851(x91671),f851(x91671))),f775(f775(f241(f851(x91671),f851(x91671)),x91672),x91673)),f135(x91671,x91674))) % 186.05/186.63 [9279]P1(f775(f775(f279(a850),x92791),x92792))+~P1(f775(f775(f279(a850),x92793),x92791))+~P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x92793,x92791)),f282(a850,f279(a850),x92794,x92792))) % 186.05/186.63 [9280]P1(f775(f775(f279(a850),x92801),x92802))+~P1(f775(f775(f279(a850),x92803),x92801))+~P1(f775(f775(f232(f857(a850,a844)),f282(a850,f279(a850),x92803,x92801)),f282(a850,f279(a850),x92804,x92802))) % 186.05/186.63 [9281]P1(f775(f775(f279(a850),x92811),x92812))+~P1(f775(f775(f279(a850),x92812),x92813))+~P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x92812,x92813)),f282(a850,f279(a850),x92811,x92814))) % 186.05/186.63 [9282]P1(f775(f775(f279(a850),x92821),x92822))+~P1(f775(f775(f279(a850),x92822),x92823))+~P1(f775(f775(f232(f857(a850,a844)),f282(a850,f279(a850),x92822,x92823)),f282(a850,f279(a850),x92821,x92824))) % 186.05/186.63 [9582]~P6(x95821)+E(f775(f775(f8(a850,x95821),f775(f775(f20(a850,x95821,x95821),f775(f775(f10(x95821,f857(x95821,x95821),a850),f3(x95821)),x95822)),f775(f775(f10(a850,x95821,a850),x95822),f775(f775(f9(a850,a850,a850),f82(a850)),f80(a850))))),f295(a850,x95823,x95824)),f2(x95821))+P1(f775(f775(f232(a850),x95823),x95824)) % 186.05/186.63 [9813]~P36(x98132,x98134)+~P29(x98132,x98131,x98133,f239(f857(x98132,a844)))+P36(x98131,f775(f303(f856(x98132,x98132),f856(x98131,x98131),f252(x98132,x98131,x98132,x98131,x98133,x98133)),x98134)) % 186.05/186.63 [9986]~E(f775(f181(f851(x99861)),x99863),f775(f181(f851(x99861)),x99862))+P1(f775(f775(f334(f856(f851(x99861),f851(x99861))),f775(f775(f241(f851(x99861),f851(x99861)),x99862),x99863)),f147(x99861,x99864)))+~P1(f775(f775(f251(x99861,x99861,a844),f775(f775(f9(x99861,f857(f856(x99861,x99861),a844),f857(x99861,a844)),f775(f775(f10(f857(x99861,f857(f857(f856(x99861,x99861),a844),a844)),f857(f857(f856(x99861,x99861),a844),f857(x99861,a844)),x99861),f9(x99861,f857(f856(x99861,x99861),a844),a844)),f775(f775(f10(f857(x99861,f856(x99861,x99861)),f857(x99861,f857(f857(f856(x99861,x99861),a844),a844)),x99861),f775(f10(f856(x99861,x99861),f857(f857(f856(x99861,x99861),a844),a844),x99861),f334(f856(x99861,x99861)))),f241(x99861,x99861)))),x99864)),f717(x99864,x99863,x99862,x99861))) % 186.05/186.63 [5860]~E(x58604,x58602)+P1(f775(x58601,x58602))+P1(f775(f775(f187(f35(x58601,x58603)),x58602),x58604)) % 186.05/186.63 [5954]~P7(x59541)+~E(x59542,f2(x59541))+E(f775(f775(f43(x59541),f775(f775(f83(x59541),x59542),x59543)),f775(f775(f83(x59541),x59542),x59544)),f2(x59541)) % 186.05/186.63 [5993]E(x59931,f115(x59932))+E(x59933,f775(f775(f3(a850),f775(f181(f851(x59932)),x59931)),f80(a850)))+E(f134(x59932,f775(f775(f148(x59932,x59931),x59933),x59934)),f134(x59932,x59931)) % 186.05/186.63 [6025]E(x60251,x60252)+P1(f775(x60253,x60252))+~P1(f775(f775(f775(f302(x60254),x60251),x60253),x60252)) % 186.05/186.63 [6039]~P66(x60391)+~P1(f775(f127(x60392),x60394))+E(f775(f155(x60391),f775(f775(f143(x60392,x60391),x60393),x60394)),f775(f775(f8(x60392,x60391),x60393),f775(f158(x60392),x60394))) % 186.05/186.63 [6063]~P70(x60632)+~P1(f775(f63(x60631),x60634))+E(f775(f775(f11(x60631,x60632),f775(f18(x60632,x60631),x60633)),x60634),f775(f775(f242(x60632),x60633),f775(f42(x60631),x60634))) % 186.05/186.63 [6117]~P7(x61172)+E(x61171,f2(x61172))+E(f775(f775(f43(x61172),f775(f775(f83(x61172),x61173),x61171)),f775(f775(f83(x61172),x61174),x61171)),f775(f775(f43(x61172),x61173),x61174)) % 186.05/186.63 [6119]~P60(x61192)+E(x61191,f2(x61192))+E(f775(f775(f283(x61192),f775(f775(f83(x61192),x61193),x61191)),f775(f775(f83(x61192),x61194),x61191)),f775(f775(f283(x61192),x61193),x61194)) % 186.05/186.63 [6120]~P60(x61202)+E(x61201,f2(x61202))+E(f775(f775(f283(x61202),f775(f775(f83(x61202),x61201),x61203)),f775(f775(f83(x61202),x61201),x61204)),f775(f775(f283(x61202),x61203),x61204)) % 186.05/186.63 [6121]~P7(x61212)+E(x61211,f2(x61212))+E(f775(f775(f43(x61212),f775(f775(f83(x61212),x61211),x61213)),f775(f775(f83(x61212),x61211),x61214)),f775(f775(f43(x61212),x61213),x61214)) % 186.05/186.63 [6187]P1(f775(x61871,x61872))+~E(x61873,f775(f775(f82(a850),x61874),x61872))+~P1(f775(x61871,f775(f775(f3(a850),x61873),x61874))) % 186.05/186.63 [6270]P32(x62701,x62702,x62703)+P31(x62701,f841(x62703,x62702,x62701),x62704)+~P1(f775(f775(f334(f849(x62701)),x62704),x62702)) % 186.05/186.63 [6316]E(x63161,f115(x63162))+~E(x63163,f775(f775(f3(a850),f775(f181(f851(x63162)),x63161)),f80(a850)))+E(f134(x63162,f775(f775(f148(x63162,x63161),x63163),x63164)),x63164) % 186.05/186.63 [6339]~P100(x63391)+~P1(f775(f775(f233(x63391),x63392),x63394))+P1(f775(f775(f233(x63391),x63392),f775(f775(f179(x63391),x63393),x63394))) % 186.05/186.63 [6341]~P100(x63411)+~P1(f775(f775(f233(x63411),x63412),x63413))+P1(f775(f775(f233(x63411),x63412),f775(f775(f179(x63411),x63413),x63414))) % 186.05/186.63 [6342]~P92(x63421)+~P1(f775(f775(f233(x63421),x63422),x63424))+P1(f775(f775(f233(x63421),x63422),f775(f775(f103(x63421),x63423),x63424))) % 186.05/186.63 [6343]~P92(x63431)+~P1(f775(f775(f233(x63431),x63432),x63433))+P1(f775(f775(f233(x63431),x63432),f775(f775(f103(x63431),x63433),x63434))) % 186.05/186.63 [6345]~P100(x63451)+~P1(f775(f775(f232(x63451),x63452),x63454))+P1(f775(f775(f232(x63451),x63452),f775(f775(f179(x63451),x63453),x63454))) % 186.05/186.63 [6347]~P100(x63471)+~P1(f775(f775(f232(x63471),x63472),x63473))+P1(f775(f775(f232(x63471),x63472),f775(f775(f179(x63471),x63473),x63474))) % 186.05/186.63 [6348]~P92(x63481)+~P1(f775(f775(f232(x63481),x63482),x63484))+P1(f775(f775(f232(x63481),x63482),f775(f775(f103(x63481),x63483),x63484))) % 186.05/186.63 [6349]~P92(x63491)+~P1(f775(f775(f232(x63491),x63492),x63493))+P1(f775(f775(f232(x63491),x63492),f775(f775(f103(x63491),x63493),x63494))) % 186.05/186.63 [6350]~P85(x63501)+~P1(f775(f775(f279(x63501),x63502),x63504))+P1(f775(f775(f279(x63501),x63502),f775(f775(f83(x63501),x63503),x63504))) % 186.05/186.63 [6351]~P85(x63511)+~P1(f775(f775(f279(x63511),x63512),x63513))+P1(f775(f775(f279(x63511),x63512),f775(f775(f83(x63511),x63513),x63514))) % 186.05/186.63 [6446]~E(f775(f775(f153(x64461),x64462),x64463),x64464)+E(f775(f775(f148(x64461,x64462),x64463),x64464),x64462)+~P1(f775(f775(f233(a850),x64463),f775(f181(f851(x64461)),x64462))) % 186.05/186.63 [6466]E(x64661,x64662)+P1(f775(x64663,x64661))+~P1(f775(f775(f187(f35(x64663,x64664)),x64661),x64662)) % 186.05/186.63 [6487]P1(f775(x64871,x64872))+~P1(f775(x64873,x64872))+~P1(f775(f775(f232(f857(x64874,a844)),x64873),x64871)) % 186.05/186.63 [6523]~E(f775(f775(f148(x65231,x65232),x65233),x65234),x65232)+E(f775(f775(f153(x65231),x65232),x65233),x65234)+~P1(f775(f775(f233(a850),x65233),f775(f181(f851(x65231)),x65232))) % 186.05/186.63 [6641]P31(x66411,x66412,x66413)+~P31(x66411,f775(a114,x66412),f350(x66412,x66414,x66411))+~P1(f775(f775(f334(f849(x66411)),x66413),x66414)) % 186.05/186.63 [6650]E(x66501,f180(f857(x66502,a844)))+E(x66503,f180(f857(x66504,a844)))+~E(f775(f775(f248(x66504,x66502),x66503),f775(f18(f857(x66502,a844),x66504),x66501)),f180(f857(f856(x66504,x66502),a844))) % 186.05/186.63 [6668]E(x66681,x66682)+P1(f775(f775(f334(x66683),x66681),x66684))+~P1(f775(f775(f334(x66683),x66681),f775(f775(f302(x66683),x66682),x66684))) % 186.05/186.63 [6685]~P100(x66851)+P1(f775(f775(f233(x66851),x66852),x66853))+~P1(f775(f775(f233(x66851),x66852),f775(f775(f236(x66851),x66854),x66853))) % 186.05/186.63 [6686]~P100(x66861)+P1(f775(f775(f233(x66861),x66862),x66863))+~P1(f775(f775(f233(x66861),x66862),f775(f775(f236(x66861),x66863),x66864))) % 186.05/186.63 [6688]~P100(x66881)+P1(f775(f775(f232(x66881),x66882),x66883))+~P1(f775(f775(f232(x66881),x66882),f775(f775(f236(x66881),x66884),x66883))) % 186.05/186.63 [6690]~P100(x66901)+P1(f775(f775(f232(x66901),x66902),x66903))+~P1(f775(f775(f232(x66901),x66902),f775(f775(f236(x66901),x66903),x66904))) % 186.05/186.63 [6692]~P98(x66921)+P1(f775(f775(f232(x66921),x66922),x66923))+~P1(f775(f775(f232(x66921),x66922),f775(f775(f104(x66921),x66924),x66923))) % 186.05/186.63 [6694]~P98(x66941)+P1(f775(f775(f232(x66941),x66942),x66943))+~P1(f775(f775(f232(x66941),x66942),f775(f775(f104(x66941),x66943),x66944))) % 186.05/186.63 [6716]~E(f775(f775(f153(x67161),x67163),x67164),x67162)+P1(f775(f775(f334(x67161),x67162),f775(f158(x67161),x67163)))+~P1(f775(f775(f233(a850),x67164),f775(f181(f851(x67161)),x67163))) % 186.05/186.63 [6728]~P100(x67281)+~P18(x67281,f775(f775(f140(x67281),x67282),f775(f775(f140(x67281),x67283),x67284)))+P1(f775(f775(f232(x67281),x67282),x67283)) % 186.05/186.63 [6898]E(x68981,f2(a1))+E(f775(f775(f43(a1),x68982),x68981),x68983)+~P1(f775(f56(x68982,x68981),f775(f775(f241(a1,a1),x68983),x68984))) % 186.05/186.63 [6921]E(f52(a1,x69212,x69211),x69213)+E(x69211,f2(a1))+~P1(f775(f56(x69212,x69211),f775(f775(f241(a1,a1),x69214),x69213))) % 186.05/186.63 [7036]P1(f775(f775(f334(x70361),x70362),x70363))+~P1(f775(f775(f334(x70361),x70362),x70364))+~P1(f775(f775(f233(f857(x70361,a844)),x70364),x70363)) % 186.05/186.63 [7040]P1(f775(f775(f334(x70401),x70402),x70403))+~P1(f775(f775(f334(x70401),x70402),x70404))+~P1(f775(f775(f232(f857(x70401,a844)),x70404),x70403)) % 186.05/186.63 [7050]~P111(x70501)+~E(x70503,f2(x70501))+P1(f775(f775(f279(x70501),f775(f775(f83(x70501),x70502),x70503)),f775(f775(f83(x70501),x70504),x70503))) % 186.05/186.63 [7051]~P111(x70511)+~E(x70512,f2(x70511))+P1(f775(f775(f279(x70511),f775(f775(f83(x70511),x70512),x70513)),f775(f775(f83(x70511),x70512),x70514))) % 186.05/186.63 [7276]~P102(x72762)+~P1(f775(f775(f233(f857(x72761,x72762)),x72763),x72764))+P1(f775(f775(f232(f857(x72761,x72762)),x72763),x72764)) % 186.05/186.63 [7371]~P28(x73711,x73712,x73714)+P28(x73711,x73712,f775(f775(f302(f849(x73711)),x73713),x73714))+~P28(x73711,x73712,f775(f775(f302(f849(x73711)),x73713),f180(f857(f849(x73711),a844)))) % 186.05/186.63 [7410]~P1(f775(f775(f334(x74101),x74102),x74104))+P1(f775(f775(f334(x74101),x74102),f44(f857(x74101,a844),x74103)))+~P1(f775(f775(f334(f857(x74101,a844)),x74104),x74103)) % 186.05/186.63 [7412]~P85(x74121)+~P1(f775(f775(f232(a850),x74123),x74124))+P1(f775(f775(f279(x74121),f775(f775(f242(x74121),x74122),x74123)),f775(f775(f242(x74121),x74122),x74124))) % 186.05/186.63 [7423]P31(x74231,x74232,x74233)+P1(f775(f775(f334(f849(x74231)),f350(x74232,x74234,x74231)),x74234))+~P1(f775(f775(f334(f849(x74231)),x74233),x74234)) % 186.05/186.63 [7442]~P74(x74421)+~P1(f775(f775(f233(x74421),x74423),x74424))+P1(f775(f775(f233(x74421),f775(f775(f82(x74421),x74422),x74423)),f775(f775(f82(x74421),x74422),x74424))) % 186.05/186.63 [7443]~P80(x74431)+~P1(f775(f775(f233(x74431),x74433),x74434))+P1(f775(f775(f233(x74431),f775(f775(f82(x74431),x74432),x74433)),f775(f775(f82(x74431),x74432),x74434))) % 186.05/186.63 [7444]~P74(x74441)+~P1(f775(f775(f233(x74441),x74442),x74444))+P1(f775(f775(f233(x74441),f775(f775(f82(x74441),x74442),x74443)),f775(f775(f82(x74441),x74444),x74443))) % 186.05/186.63 [7445]~P80(x74451)+~P1(f775(f775(f233(x74451),x74452),x74454))+P1(f775(f775(f233(x74451),f775(f775(f82(x74451),x74452),x74453)),f775(f775(f82(x74451),x74454),x74453))) % 186.05/186.63 [7446]~P74(x74461)+~P1(f775(f775(f232(x74461),x74463),x74464))+P1(f775(f775(f232(x74461),f775(f775(f82(x74461),x74462),x74463)),f775(f775(f82(x74461),x74462),x74464))) % 186.05/186.63 [7447]~P78(x74471)+~P1(f775(f775(f232(x74471),x74473),x74474))+P1(f775(f775(f232(x74471),f775(f775(f82(x74471),x74472),x74473)),f775(f775(f82(x74471),x74472),x74474))) % 186.05/186.63 [7448]~P74(x74481)+~P1(f775(f775(f232(x74481),x74482),x74484))+P1(f775(f775(f232(x74481),f775(f775(f82(x74481),x74482),x74483)),f775(f775(f82(x74481),x74484),x74483))) % 186.05/186.63 [7449]~P78(x74491)+~P1(f775(f775(f232(x74491),x74492),x74494))+P1(f775(f775(f232(x74491),f775(f775(f82(x74491),x74492),x74493)),f775(f775(f82(x74491),x74494),x74493))) % 186.05/186.63 [7450]~P111(x74501)+~P1(f775(f775(f279(x74501),x74503),x74504))+P1(f775(f775(f279(x74501),f775(f775(f83(x74501),x74502),x74503)),f775(f775(f83(x74501),x74502),x74504))) % 186.05/186.63 [7451]~P111(x74511)+~P1(f775(f775(f279(x74511),x74512),x74514))+P1(f775(f775(f279(x74511),f775(f775(f83(x74511),x74512),x74513)),f775(f775(f83(x74511),x74514),x74513))) % 186.05/186.63 [7452]~P85(x74521)+~P1(f775(f775(f279(x74521),x74522),x74524))+P1(f775(f775(f279(x74521),f775(f775(f242(x74521),x74522),x74523)),f775(f775(f242(x74521),x74524),x74523))) % 186.05/186.63 [7461]~P135(x74611)+~P89(x74611)+E(f775(f775(f82(x74611),f775(f775(f83(x74611),x74612),f775(f106(x74611),x74613))),f775(f775(f83(x74611),x74614),f775(f106(x74611),x74613))),f775(f775(f83(x74611),f775(f775(f82(x74611),x74612),x74614)),f775(f106(x74611),x74613))) % 186.05/186.63 [7462]~P121(x74621)+~P89(x74621)+E(f775(f775(f3(x74621),f775(f775(f83(x74621),x74622),f775(f106(x74621),x74623))),f775(f775(f83(x74621),x74624),f775(f106(x74621),x74623))),f775(f775(f83(x74621),f775(f775(f3(x74621),x74622),x74624)),f775(f106(x74621),x74623))) % 186.05/186.63 [7498]~P66(x74981)+E(f775(f775(f82(x74981),f775(x74982,x74983)),f775(f775(f8(a850,x74981),x74982),f295(a850,f775(a114,x74983),x74984))),f775(f775(f8(a850,x74981),x74982),f295(a850,x74983,x74984)))+~P1(f775(f775(f232(a850),x74983),x74984)) % 186.05/186.63 [7509]~P29(x75092,x75091,x75093,f775(f158(x75092),x75094))+~P1(f775(f127(x75092),x75094))+P1(f775(f127(x75091),f775(f775(f143(x75092,x75091),x75093),x75094))) % 186.05/186.63 [7558]~P1(f775(f775(f233(a850),x75582),x75584))+~P1(f775(f775(f233(a850),x75581),x75583))+P1(f775(f775(f233(a850),f775(f775(f82(a850),x75581),x75582)),f775(f775(f82(a850),x75583),x75584))) % 186.05/186.63 [7561]~P1(f775(f775(f233(a1),x75611),x75613))+~P1(f775(f775(f232(a1),x75612),x75614))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x75611),x75612)),f775(f775(f82(a1),x75613),x75614))) % 186.05/186.63 [7562]~P1(f775(f775(f232(a850),x75622),x75624))+~P1(f775(f775(f232(a850),x75621),x75623))+P1(f775(f775(f232(a850),f775(f775(f82(a850),x75621),x75622)),f775(f775(f82(a850),x75623),x75624))) % 186.05/186.63 [7563]~P1(f775(f775(f232(a850),x75632),x75634))+~P1(f775(f775(f232(a850),x75631),x75633))+P1(f775(f775(f232(a850),f775(f775(f83(a850),x75631),x75632)),f775(f775(f83(a850),x75633),x75634))) % 186.05/186.63 [7613]P1(f775(f775(f334(x76131),x76132),x76133))+~P1(f775(f775(f334(x76131),x76132),f45(f857(x76131,a844),x76134)))+~P1(f775(f775(f334(f857(x76131,a844)),x76133),x76134)) % 186.05/186.63 [7629]~P1(f775(x76291,f725(x76291,x76293,x76292)))+P1(f775(x76291,f775(f775(f153(x76292),x76293),x76294)))+~P1(f775(f775(f233(a850),x76294),f775(f181(f851(x76292)),x76293))) % 186.05/186.63 [7633]P1(f775(x76331,x76332))+~P1(f775(f775(f334(x76334),x76332),f775(f158(x76334),x76333)))+P1(f775(f775(f233(a850),f726(x76331,x76333,x76334)),f775(f181(f851(x76334)),x76333))) % 186.05/186.63 [7652]~P1(f775(f775(f187(x76522),x76523),x76524))+~P1(f775(f775(f187(f35(x76521,x76522)),x76524),x76523))+P1(f775(f775(f187(f35(x76521,x76522)),x76523),x76523)) % 186.05/186.63 [7680]~P102(x76801)+~P1(f775(f775(f232(f857(x76802,x76801)),x76804),x76803))+~P1(f775(f775(f233(f857(x76802,x76801)),x76803),x76804)) % 186.05/186.63 [7723]~P1(f775(x77234,x77232))+~P1(f775(f775(f334(x77231),x77232),x77233))+P1(f775(f775(f334(x77231),x77232),f775(f775(f104(f857(x77231,a844)),x77233),f775(f256(x77231),x77234)))) % 186.05/186.63 [7872]~P1(f775(f775(f334(x78721),x78723),x78724))+~P1(f775(f775(f233(f857(x78721,a844)),x78722),x78724))+P1(f775(f775(f233(f857(x78721,a844)),x78722),f775(f775(f302(x78721),x78723),x78724))) % 186.05/186.63 [7874]E(f775(f775(f104(f857(x78741,a844)),x78742),x78743),f180(f857(x78741,a844)))+~E(f775(f775(f104(f857(x78741,a844)),f44(f857(x78741,a844),x78744)),x78743),f180(f857(x78741,a844)))+~P1(f775(f775(f334(f857(x78741,a844)),x78742),x78744)) % 186.05/186.63 [7951]P1(f775(f775(f334(x79511),x79512),x79513))+~P1(f775(f775(f232(f857(x79511,a844)),x79513),f775(f775(f302(x79511),x79512),x79514)))+P1(f775(f775(f232(f857(x79511,a844)),x79513),x79514)) % 186.05/186.63 [7971]P1(f775(f775(f334(x79712),f725(x79711,x79713,x79712)),f775(f158(x79712),x79713)))+P1(f775(x79711,f775(f775(f153(x79712),x79713),x79714)))+~P1(f775(f775(f233(a850),x79714),f775(f181(f851(x79712)),x79713))) % 186.05/186.63 [7979]~P1(f775(f775(f233(f857(x79791,a844)),x79792),x79794))+P1(f775(f775(f233(f857(x79791,a844)),x79792),x79793))+~P1(f775(f775(f233(f857(x79791,a844)),x79794),x79793)) % 186.05/186.63 [7980]~P1(f775(f775(f232(f857(x79801,a844)),x79802),x79804))+P1(f775(f775(f233(f857(x79801,a844)),x79802),x79803))+~P1(f775(f775(f233(f857(x79801,a844)),x79804),x79803)) % 186.05/186.63 [7981]~P1(f775(f775(f232(f857(x79811,a844)),x79814),x79813))+~P1(f775(f775(f233(f857(x79811,a844)),x79812),x79814))+P1(f775(f775(f233(f857(x79811,a844)),x79812),x79813)) % 186.05/186.63 [7982]~P1(f775(f775(f232(f857(x79821,a844)),x79822),x79824))+P1(f775(f775(f232(f857(x79821,a844)),x79822),x79823))+~P1(f775(f775(f232(f857(x79821,a844)),x79824),x79823)) % 186.05/186.63 [8018]~P1(f775(f775(f334(x80181),x80184),x80183))+~P1(f775(f775(f233(f857(x80181,a844)),x80182),f775(f775(f302(x80181),x80184),x80183)))+P1(f775(f775(f233(f857(x80181,a844)),x80182),x80183)) % 186.05/186.63 [8031]~P74(x80311)+P1(f775(f775(f233(x80311),x80312),x80313))+~P1(f775(f775(f233(x80311),f775(f775(f82(x80311),x80314),x80312)),f775(f775(f82(x80311),x80314),x80313))) % 186.05/186.63 [8033]~P74(x80331)+P1(f775(f775(f233(x80331),x80332),x80333))+~P1(f775(f775(f233(x80331),f775(f775(f82(x80331),x80332),x80334)),f775(f775(f82(x80331),x80333),x80334))) % 186.05/186.63 [8035]~P74(x80351)+P1(f775(f775(f232(x80351),x80352),x80353))+~P1(f775(f775(f232(x80351),f775(f775(f82(x80351),x80354),x80352)),f775(f775(f82(x80351),x80354),x80353))) % 186.05/186.63 [8037]~P74(x80371)+P1(f775(f775(f232(x80371),x80372),x80373))+~P1(f775(f775(f232(x80371),f775(f775(f82(x80371),x80372),x80374)),f775(f775(f82(x80371),x80373),x80374))) % 186.05/186.63 [8201]P1(f775(x82011,x82012))+~P1(f775(f775(f334(x82013),x82012),f775(f158(x82013),x82014)))+P1(f775(f775(f233(a850),f775(f181(f851(x82013)),f775(f126(x82013,x82011),x82014))),f775(f181(f851(x82013)),x82014))) % 186.05/186.63 [8331]E(x83311,x83312)+P1(f775(f775(f187(x83313),x83311),f422(x83312,x83311,x83313,x83314)))+~P1(f775(f775(f187(f35(x83314,x83313)),x83311),x83312)) % 186.05/186.63 [8332]E(x83321,x83322)+P1(f775(f775(f187(x83323),x83321),f528(x83322,x83321,x83323,x83324)))+~P1(f775(f775(f187(f35(x83324,x83323)),x83321),x83322)) % 186.05/186.63 [8359]~P1(f775(x83594,x83592))+P1(f775(f775(f187(x83591),x83592),f422(x83593,x83592,x83591,x83594)))+~P1(f775(f775(f187(f35(x83594,x83591)),x83592),x83593)) % 186.05/186.63 [8360]~P1(f775(x83604,x83602))+P1(f775(f775(f187(x83601),x83602),f528(x83603,x83602,x83601,x83604)))+~P1(f775(f775(f187(f35(x83604,x83601)),x83602),x83603)) % 186.05/186.63 [8684]~P29(x86844,x86843,x86841,f239(f857(x86844,a844)))+E(f775(x86841,f523(x86842,x86841,x86843,x86844)),x86842)+~P1(f775(f775(f334(x86843),x86842),f775(f303(x86844,x86843,x86841),f239(f857(x86844,a844))))) % 186.05/186.63 [8822]~P1(f775(f63(x88221),x88224))+P1(f775(f775(f334(x88221),f561(x88222,x88223,x88224,x88221)),x88224))+P1(f775(f63(f856(x88221,x88223)),f775(f775(f248(x88221,x88223),x88224),x88222))) % 186.05/186.63 [8866]E(x88661,x88662)+P1(f775(f775(f187(f35(x88663,x88664)),f422(x88661,x88662,x88664,x88663)),x88661))+~P1(f775(f775(f187(f35(x88663,x88664)),x88662),x88661)) % 186.05/186.63 [8867]E(x88671,x88672)+P1(f775(f775(f187(f35(x88673,x88674)),f528(x88671,x88672,x88674,x88673)),x88671))+~P1(f775(f775(f187(f35(x88673,x88674)),x88672),x88671)) % 186.05/186.63 [8887]~P1(f775(x88871,x88874))+P1(f775(f775(f187(f35(x88871,x88872)),f422(x88873,x88874,x88872,x88871)),x88873))+~P1(f775(f775(f187(f35(x88871,x88872)),x88874),x88873)) % 186.05/186.63 [8888]~P1(f775(x88881,x88884))+P1(f775(f775(f187(f35(x88881,x88882)),f528(x88883,x88884,x88882,x88881)),x88883))+~P1(f775(f775(f187(f35(x88881,x88882)),x88884),x88883)) % 186.05/186.63 [9127]~P1(f775(f63(x91271),x91273))+~P1(f775(f63(x91272),f775(x91274,f561(x91274,x91272,x91273,x91271))))+P1(f775(f63(f856(x91271,x91272)),f775(f775(f248(x91271,x91272),x91273),x91274))) % 186.05/186.63 [9141]~E(f775(f181(f851(x91414)),x91412),f775(f181(f851(x91414)),x91413))+P1(f775(f775(f334(f856(f851(x91414),f851(x91414))),f775(f775(f241(f851(x91414),f851(x91414)),x91413),x91412)),f147(x91414,x91411)))+P1(f775(f775(f233(a850),f733(x91411,x91412,x91413,x91414)),f775(f181(f851(x91414)),x91413))) % 186.05/186.63 [9254]E(f775(f775(f159(x92541),f740(x92542,x92543,x92544,x92541)),x92543),f775(f775(f159(x92541),f740(x92542,x92543,x92544,x92541)),x92544))+~P1(f775(f775(f334(f856(f851(x92541),f851(x92541))),f775(f775(f241(f851(x92541),f851(x92541)),x92544),x92543)),f137(x92541,x92542)))+P1(f775(f775(f233(a850),f775(f181(f851(x92541)),x92544)),f775(f181(f851(x92541)),x92543))) % 186.05/186.63 [9312]~P1(f775(f775(f233(a850),f2(a850)),x93123))+~P1(f775(f775(f233(a850),x93124),x93121))+P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),x93121),f52(a850,x93122,x93123))),x93124)),f775(f775(f83(a850),x93121),x93123))) % 186.05/186.63 [9494]~P102(x94942)+~P1(f775(f775(f232(x94942),f775(x94943,f705(x94944,x94943,x94941,x94942))),f775(x94944,f705(x94944,x94943,x94941,x94942))))+P1(f775(f775(f232(f857(x94941,x94942)),x94943),x94944)) % 186.05/186.63 [9585]~P6(x95851)+E(f775(f775(f8(a850,x95851),f775(f775(f20(a850,x95851,x95851),f775(f775(f10(x95851,f857(x95851,x95851),a850),f3(x95851)),x95852)),f775(f775(f10(a850,x95851,a850),x95852),f775(f775(f9(a850,a850,a850),f82(a850)),f80(a850))))),f295(a850,x95853,x95854)),f775(f775(f3(x95851),f775(x95852,x95853)),f775(x95852,f775(f775(f82(a850),x95854),f80(a850)))))+~P1(f775(f775(f232(a850),x95853),x95854)) % 186.05/186.63 [6630]~P7(x66301)+E(f775(f775(f43(x66301),f775(f775(f83(x66301),x66302),x66303)),x66304),f775(f775(f83(x66301),x66302),f775(f775(f43(x66301),x66303),x66304)))+~P1(f775(f775(f279(x66301),x66304),x66303)) % 186.05/186.63 [6720]E(f775(f775(f125(x67201),x67202),x67203),x67204)+~E(x67203,f775(f775(f128(x67201),f775(f181(f851(x67201)),x67202)),x67204))+~E(f775(f775(f159(x67201),f775(f181(f851(x67201)),x67202)),x67204),x67202) % 186.05/186.63 [6781]~P61(x67812)+E(x67811,f2(x67812))+E(f775(f775(f283(x67812),f775(f775(f242(x67812),x67813),x67814)),f775(f775(f242(x67812),x67811),x67814)),f775(f775(f242(x67812),f775(f775(f283(x67812),x67813),x67811)),x67814)) % 186.05/186.63 [6931]~P7(x69311)+E(f775(f775(f43(x69311),f775(f775(f83(x69311),x69312),x69313)),x69314),f775(f775(f83(x69311),f775(f775(f43(x69311),x69312),x69314)),x69313))+~P1(f775(f775(f279(x69311),x69314),x69312)) % 186.05/186.63 [6941]~P100(x69411)+~P1(f775(f775(f233(x69411),x69413),x69414))+P1(f775(f775(f233(x69411),f775(f775(f236(x69411),x69412),x69413)),x69414)) % 186.05/186.63 [6943]~P100(x69431)+~P1(f775(f775(f233(x69431),x69432),x69434))+P1(f775(f775(f233(x69431),f775(f775(f236(x69431),x69432),x69433)),x69434)) % 186.05/186.63 [6944]~P98(x69441)+~P1(f775(f775(f233(x69441),x69443),x69444))+P1(f775(f775(f233(x69441),f775(f775(f104(x69441),x69442),x69443)),x69444)) % 186.05/186.63 [6945]~P98(x69451)+~P1(f775(f775(f233(x69451),x69452),x69454))+P1(f775(f775(f233(x69451),f775(f775(f104(x69451),x69452),x69453)),x69454)) % 186.05/186.63 [6947]~P100(x69471)+~P1(f775(f775(f232(x69471),x69473),x69474))+P1(f775(f775(f232(x69471),f775(f775(f236(x69471),x69472),x69473)),x69474)) % 186.05/186.63 [6949]~P100(x69491)+~P1(f775(f775(f232(x69491),x69492),x69494))+P1(f775(f775(f232(x69491),f775(f775(f236(x69491),x69492),x69493)),x69494)) % 186.05/186.63 [6950]~P98(x69501)+~P1(f775(f775(f232(x69501),x69503),x69504))+P1(f775(f775(f232(x69501),f775(f775(f104(x69501),x69502),x69503)),x69504)) % 186.05/186.63 [6951]~P98(x69511)+~P1(f775(f775(f232(x69511),x69512),x69514))+P1(f775(f775(f232(x69511),f775(f775(f104(x69511),x69512),x69513)),x69514)) % 186.05/186.63 [6968]~P1(f775(x69683,x69684))+~P1(f775(x69682,x69684))+P1(f775(f775(f775(f104(f857(x69681,a844)),x69682),x69683),x69684)) % 186.05/186.63 [7000]~E(f775(f181(f851(x70001)),x70003),f775(f181(f851(x70002)),x70004))+~P1(f775(f127(x70001),x70003))+E(f169(x70001,x70002,f166(x70001,x70002,f775(f775(f167(x70001,x70002),x70003),x70004))),f775(f158(x70001),x70003)) % 186.05/186.63 [7094]P28(x70941,x70942,x70943)+~P28(x70941,x70944,x70943)+~P1(f775(f775(f232(f857(f849(x70941),a844)),x70944),x70942)) % 186.05/186.63 [7095]P28(x70951,x70952,x70953)+~P28(x70951,x70952,x70954)+~P1(f775(f775(f232(f857(f849(x70951),a844)),x70953),x70954)) % 186.05/186.63 [7233]~P7(x72331)+E(f775(f775(f43(x72331),f775(f775(f242(x72331),x72332),x72333)),f775(f775(f242(x72331),x72334),x72333)),f775(f775(f242(x72331),f775(f775(f43(x72331),x72332),x72334)),x72333))+~P1(f775(f775(f279(x72331),x72334),x72332)) % 186.05/186.63 [7488]~P66(x74881)+E(f775(f775(f82(x74881),f775(x74882,x74883)),f775(f775(f8(a850,x74881),x74882),f775(f294(a850,f775(a114,x74883)),x74884))),f775(f775(f8(a850,x74881),x74882),f775(f294(a850,x74883),x74884)))+~P1(f775(f775(f233(a850),x74883),x74884)) % 186.05/186.63 [7516]~P100(x75161)+P1(f775(f775(f233(x75161),x75162),x75163))+~P1(f775(f775(f233(x75161),f775(f775(f179(x75161),x75164),x75162)),x75163)) % 186.05/186.63 [7517]~P100(x75171)+P1(f775(f775(f233(x75171),x75172),x75173))+~P1(f775(f775(f233(x75171),f775(f775(f179(x75171),x75172),x75174)),x75173)) % 186.05/186.63 [7519]~P100(x75191)+P1(f775(f775(f232(x75191),x75192),x75193))+~P1(f775(f775(f232(x75191),f775(f775(f179(x75191),x75194),x75192)),x75193)) % 186.05/186.63 [7521]~P100(x75211)+P1(f775(f775(f232(x75211),x75212),x75213))+~P1(f775(f775(f232(x75211),f775(f775(f179(x75211),x75212),x75214)),x75213)) % 186.05/186.63 [7523]~P92(x75231)+P1(f775(f775(f232(x75231),x75232),x75233))+~P1(f775(f775(f232(x75231),f775(f775(f103(x75231),x75234),x75232)),x75233)) % 186.05/186.63 [7525]~P92(x75251)+P1(f775(f775(f232(x75251),x75252),x75253))+~P1(f775(f775(f232(x75251),f775(f775(f103(x75251),x75252),x75254)),x75253)) % 186.05/186.63 [7526]~P85(x75261)+P1(f775(f775(f279(x75261),x75262),x75263))+~P1(f775(f775(f279(x75261),f775(f775(f83(x75261),x75264),x75262)),x75263)) % 186.05/186.63 [7527]~P85(x75271)+P1(f775(f775(f279(x75271),x75272),x75273))+~P1(f775(f775(f279(x75271),f775(f775(f83(x75271),x75272),x75274)),x75273)) % 186.05/186.63 [7605]~P1(f775(f775(f334(x76051),x76052),x76054))+P1(f775(f775(f334(x76051),x76052),x76053))+P1(f775(f775(f334(x76051),x76052),f775(f775(f3(f857(x76051,a844)),x76054),x76053))) % 186.05/186.63 [7685]P1(f775(x76851,x76852))+P1(f775(x76853,x76852))+~P1(f775(f775(f775(f103(f857(x76854,a844)),x76853),x76851),x76852)) % 186.05/186.63 [7695]~P1(f775(f775(f334(x76951),x76952),x76954))+~P1(f775(f775(f334(x76951),x76952),x76953))+P1(f775(f775(f334(x76951),x76952),f775(f775(f104(f857(x76951,a844)),x76953),x76954))) % 186.05/186.63 [7751]~P100(x77511)+~P1(f775(f63(x77511),x77514))+E(f775(f775(f66(x77511,x77511,f236(x77511)),x77512),f775(f775(f302(x77511),x77513),x77514)),f775(f775(f236(x77511),x77513),f775(f775(f66(x77511,x77511,f236(x77511)),x77512),x77514))) % 186.05/186.63 [7752]~P100(x77521)+~P1(f775(f63(x77521),x77524))+E(f775(f775(f66(x77521,x77521,f179(x77521)),x77522),f775(f775(f302(x77521),x77523),x77524)),f775(f775(f179(x77521),x77523),f775(f775(f66(x77521,x77521,f179(x77521)),x77522),x77524))) % 186.05/186.63 [7753]~P92(x77531)+~P1(f775(f63(x77531),x77534))+E(f775(f775(f66(x77531,x77531,f103(x77531)),x77532),f775(f775(f302(x77531),x77533),x77534)),f775(f775(f103(x77531),x77533),f775(f775(f66(x77531,x77531,f103(x77531)),x77532),x77534))) % 186.05/186.63 [7754]~P98(x77541)+~P1(f775(f63(x77541),x77544))+E(f775(f775(f66(x77541,x77541,f104(x77541)),x77542),f775(f775(f302(x77541),x77543),x77544)),f775(f775(f104(x77541),x77543),f775(f775(f66(x77541,x77541,f104(x77541)),x77542),x77544))) % 186.05/186.63 [7756]~P135(x77561)+~P89(x77561)+E(f775(f775(f82(x77561),f775(f775(f83(x77561),f775(f106(x77561),x77562)),x77563)),f775(f775(f83(x77561),f775(f106(x77561),x77562)),x77564)),f775(f775(f83(x77561),f775(f106(x77561),x77562)),f775(f775(f82(x77561),x77563),x77564))) % 186.05/186.63 [7757]~P121(x77571)+~P89(x77571)+E(f775(f775(f3(x77571),f775(f775(f83(x77571),f775(f106(x77571),x77572)),x77573)),f775(f775(f83(x77571),f775(f106(x77571),x77572)),x77574)),f775(f775(f83(x77571),f775(f106(x77571),x77572)),f775(f775(f3(x77571),x77573),x77574))) % 186.05/186.63 [7870]E(x78701,x78702)+P1(f775(f775(f334(x78703),x78701),f775(f158(x78703),x78704)))+~P1(f775(f775(f334(x78703),x78701),f775(f158(x78703),f775(f775(f140(x78703),x78702),x78704)))) % 186.05/186.63 [8041]P53(x80411,x80412,x80413)+~P53(x80411,x80412,x80414)+~P1(f775(f775(f232(f857(f856(x80411,x80412),a844)),x80413),x80414)) % 186.05/186.63 [8084]P1(f775(f775(f334(x80841),x80842),x80843))+P1(f775(f775(f334(x80841),x80842),x80844))+~P1(f775(f775(f334(x80841),x80842),f775(f775(f103(f857(x80841,a844)),x80844),x80843))) % 186.05/186.63 [8095]~P47(x80951,x80954,x80953)+~P1(f775(f775(f334(x80951),x80952),x80954))+P1(f775(f775(f334(f856(x80951,x80951)),f775(f775(f241(x80951,x80951),x80952),x80952)),x80953)) % 186.05/186.63 [8107]~P1(f775(f63(x81072),x81074))+~P1(f775(f63(x81071),x81073))+P1(f775(f63(f856(x81071,x81072)),f775(f775(f248(x81071,x81072),x81073),f775(f18(f857(x81072,a844),x81071),x81074)))) % 186.05/186.63 [8108]~P1(f775(f775(f334(x81081),x81082),x81084))+~P1(f775(f775(f232(f857(x81081,a844)),x81083),x81084))+P1(f775(f775(f232(f857(x81081,a844)),f775(f775(f302(x81081),x81082),x81083)),x81084)) % 186.05/186.63 [8116]~P2(x81162)+~P70(x81162)+E(f775(f775(f11(x81161,x81162),f775(f775(f10(a850,x81162,x81161),f102(x81162)),x81163)),x81164),f775(f102(x81162),f775(f775(f11(x81161,a850),x81163),x81164))) % 186.05/186.63 [8117]~P70(x81172)+~P133(x81172)+E(f775(f775(f11(x81171,x81172),f775(f775(f10(a1,x81172,x81171),f105(x81172)),x81173)),x81174),f775(f105(x81172),f775(f775(f11(x81171,a1),x81173),x81174))) % 186.05/186.63 [8143]E(f775(f775(f3(f857(x81431,a844)),x81432),f775(f775(f3(f857(x81431,a844)),x81433),x81434)),x81434)+~P1(f775(f775(f232(f857(x81431,a844)),x81432),x81433))+~P1(f775(f775(f232(f857(x81431,a844)),x81434),x81432)) % 186.05/186.63 [8235]~P1(f775(f63(x82351),x82354))+E(f775(f775(f3(a850),f775(f775(f8(x82351,a850),x82352),x82353)),f775(f775(f8(x82351,a850),x82352),x82354)),f775(f775(f8(x82351,a850),x82352),f775(f775(f3(f857(x82351,a844)),x82353),x82354)))+~P1(f775(f775(f232(f857(x82351,a844)),x82354),x82353)) % 186.05/186.63 [8392]~P12(x83921,x83924,x83923)+~P1(f775(f775(f334(x83921),x83922),x83924))+P1(f775(f775(f334(x83921),x83922),f775(f277(x83921,x83921,x83923),f775(f775(f302(x83921),x83922),f180(f857(x83921,a844)))))) % 186.05/186.63 [8455]~P1(f775(f775(f232(f857(x84551,a844)),x84552),x84553))+~P1(f775(f775(f232(f857(x84551,a844)),x84552),x84554))+P1(f775(f775(f232(f857(x84551,a844)),x84552),f775(f775(f104(f857(x84551,a844)),x84553),x84554))) % 186.05/186.63 [8547]E(x85471,f180(f857(x85472,a844)))+P1(f775(f63(x85473),x85474))+~P1(f775(f63(f856(x85473,x85472)),f775(f775(f248(x85473,x85472),x85474),f775(f18(f857(x85472,a844),x85473),x85471)))) % 186.05/186.63 [8548]E(x85481,f180(f857(x85482,a844)))+P1(f775(f63(x85483),x85484))+~P1(f775(f63(f856(x85482,x85483)),f775(f775(f248(x85482,x85483),x85481),f775(f18(f857(x85483,a844),x85482),x85484)))) % 186.05/186.63 [8606]P1(f775(f775(f334(x86061),x86062),f322(x86061,x86063)))+~P1(f775(f775(f334(x86061),x86064),f322(x86061,x86063)))+~P1(f775(f775(f334(f856(x86061,x86061)),f775(f775(f241(x86061,x86061),x86062),x86064)),x86063)) % 186.05/186.63 [8658]~P36(x86581,x86584)+P1(f775(f775(f334(f856(x86581,x86581)),f775(f775(f241(x86581,x86581),x86583),x86582)),f300(x86581,x86584)))+P36(x86581,f775(f775(f302(f856(x86581,x86581)),f775(f775(f241(x86581,x86581),x86582),x86583)),x86584)) % 186.05/186.63 [8659]~P56(x86591,x86594)+P1(f775(f775(f334(f856(x86591,x86591)),f775(f775(f241(x86591,x86591),x86593),x86592)),f300(x86591,x86594)))+P56(x86591,f775(f775(f302(f856(x86591,x86591)),f775(f775(f241(x86591,x86591),x86592),x86593)),x86594)) % 186.05/186.63 [8730]~E(x87302,x87303)+~P1(f775(f775(f334(x87301),x87302),f775(f158(x87301),x87304)))+P1(f775(f775(f334(f856(x87301,x87301)),f775(f775(f241(x87301,x87301),x87302),x87303)),f775(f158(f856(x87301,x87301)),f775(f775(f167(x87301,x87301),x87304),x87304)))) % 186.05/186.63 [8802]~E(x88023,x88024)+P1(f775(f775(f251(x88021,x88021,a844),a330),x88022))+~P1(f775(f775(f334(f856(x88021,x88021)),x88022),f775(f158(f856(x88021,x88021)),f775(f775(f167(x88021,x88021),x88023),x88024)))) % 186.05/186.63 [8838]P1(f775(f775(f334(f856(f851(x88381),f851(x88381))),f775(f775(f241(f851(x88381),f851(x88381)),x88382),x88383)),f137(x88381,x88384)))+~E(f775(f775(f159(x88381),f775(f181(f851(x88381)),x88382)),x88383),x88382)+~P1(f775(f775(f233(a850),f775(f181(f851(x88381)),x88382)),f775(f181(f851(x88381)),x88383))) % 186.05/186.63 [8932]~P1(f775(f63(x89321),x89324))+P1(f775(f775(f334(x89321),f412(x89322,x89323,x89324,x89321)),x89324))+P1(f775(f63(x89323),f775(f775(f46(x89321,f857(x89323,a844)),x89324),x89322))) % 186.05/186.63 [8933]~P1(f775(f63(x89331),x89334))+P1(f775(f775(f334(x89331),f609(x89332,x89333,x89334,x89331)),x89334))+P1(f775(f63(x89333),f775(f775(f46(x89331,f857(x89333,a844)),x89334),x89332))) % 186.05/186.63 [9013]P1(f775(f775(f334(f856(x90131,x90131)),x90132),f775(f775(f281(x90131,x90131,x90131),x90133),f300(x90131,x90133))))+~P1(f775(f775(f233(a850),f2(a850)),x90134))+~P1(f775(f775(f334(f856(x90131,x90131)),x90132),f775(f775(f173(f856(x90131,x90131),a844),x90134),x90133))) % 186.05/186.63 [9021]~P36(x90211,x90212)+~P1(f775(f775(f334(f856(x90211,x90211)),f775(f775(f241(x90211,x90211),x90214),x90213)),x90212))+~P1(f775(f775(f334(f856(x90211,x90211)),f775(f775(f241(x90211,x90211),x90213),x90214)),x90212)) % 186.05/186.63 [9137]~P1(f775(f63(x91371),x91374))+E(f775(f775(f8(x91371,a850),f775(f775(f10(f857(x91372,a844),a850,x91371),f42(x91372)),x91373)),x91374),f775(f42(f856(x91371,x91372)),f775(f775(f248(x91371,x91372),x91374),x91373)))+P1(f775(f775(f334(x91371),f562(x91373,x91372,x91374,x91371)),x91374)) % 186.05/186.63 [9139]~P1(f775(f127(x91391),x91392))+P1(f775(f127(x91391),f775(f775(f148(x91391,x91392),x91393),x91394)))+P1(f775(f775(f334(x91391),x91394),f775(f775(f3(f857(x91391,a844)),f775(f158(x91391),x91392)),f775(f775(f302(x91391),f775(f775(f153(x91391),x91392),x91393)),f180(f857(x91391,a844)))))) % 186.05/186.63 [9148]~P1(f775(f63(x91482),x91483))+~P1(f775(f63(x91481),f775(x91484,f412(x91484,x91481,x91483,x91482))))+P1(f775(f63(x91481),f775(f775(f46(x91482,f857(x91481,a844)),x91483),x91484))) % 186.05/186.63 [9149]~P1(f775(f63(x91492),x91493))+~P1(f775(f63(x91491),f775(x91494,f609(x91494,x91491,x91493,x91492))))+P1(f775(f63(x91491),f775(f775(f46(x91492,f857(x91491,a844)),x91493),x91494))) % 186.05/186.63 [9214]~P1(f775(f775(f334(f856(x92141,x92141)),x92142),f775(f775(f281(x92141,x92141,x92141),x92144),f300(x92141,x92144))))+P1(f775(f775(f334(f856(x92141,x92141)),x92142),f775(f775(f281(x92141,x92141,x92141),x92143),f300(x92141,x92143))))+~P1(f775(f775(f232(f857(f856(x92141,x92141),a844)),x92144),x92143)) % 186.05/186.63 [9222]E(f775(f775(f159(x92221),f740(x92224,x92223,x92222,x92221)),x92223),f775(f775(f159(x92221),f740(x92224,x92223,x92222,x92221)),x92222))+~P1(f775(f775(f334(f856(f851(x92221),f851(x92221))),f775(f775(f241(f851(x92221),f851(x92221)),x92222),x92223)),f137(x92221,x92224)))+E(f775(f775(f159(x92221),f775(f181(f851(x92221)),x92222)),x92223),x92222) % 186.05/186.63 [9238]~P1(f775(f63(x92381),x92384))+E(f775(f775(f8(x92381,a850),f775(f775(f10(f857(x92382,a844),a850,x92381),f42(x92382)),x92383)),x92384),f775(f42(f856(x92381,x92382)),f775(f775(f248(x92381,x92382),x92384),x92383)))+~P1(f775(f63(x92382),f775(x92383,f562(x92383,x92382,x92384,x92381)))) % 186.05/186.63 [9243]~E(f775(f181(f851(x92431)),x92433),f775(f181(f851(x92431)),x92432))+P1(f775(f775(f334(f856(f851(x92431),f851(x92431))),f775(f775(f241(f851(x92431),f851(x92431)),x92432),x92433)),f147(x92431,x92434)))+P1(f775(f775(f334(f856(x92431,x92431)),f717(x92434,x92433,x92432,x92431)),f775(f158(f856(x92431,x92431)),f775(f775(f167(x92431,x92431),x92432),x92433)))) % 186.05/186.63 [9325]~P1(f775(f775(f334(f856(f851(x93251),f851(x93251))),f775(f775(f241(f851(x93251),f851(x93251)),x93252),x93253)),f137(x93251,x93254)))+E(f775(f775(f159(x93251),f775(f181(f851(x93251)),x93252)),x93253),x93252)+P1(f775(f775(f233(a850),f740(x93254,x93253,x93252,x93251)),f775(f775(f236(a850),f775(f181(f851(x93251)),x93252)),f775(f181(f851(x93251)),x93253)))) % 186.05/186.63 [9344]~P1(f775(f775(f334(f856(f851(x93441),f851(x93441))),f775(f775(f241(f851(x93441),f851(x93441)),x93442),x93443)),f137(x93441,x93444)))+P1(f775(f775(f233(a850),f775(f181(f851(x93441)),x93442)),f775(f181(f851(x93441)),x93443)))+P1(f775(f775(f233(a850),f740(x93444,x93443,x93442,x93441)),f775(f775(f236(a850),f775(f181(f851(x93441)),x93442)),f775(f181(f851(x93441)),x93443)))) % 186.05/186.63 [9620]~P1(f775(f775(f775(x96201,f708(x96201,x96204,x96203,x96202)),f711(x96201,x96204,x96203,x96202)),f712(x96201,x96204,x96203,x96202)))+P1(f775(f775(f775(x96201,x96202),x96203),x96204))+~P1(f775(f321(f856(f857(a1,f854(f851(a842))),f856(a1,a1)),a311),f775(f775(f241(f857(a1,f854(f851(a842))),f856(a1,a1)),x96202),f775(f775(f241(a1,a1),x96203),x96204)))) % 186.05/186.63 [9681]P1(f775(f775(f775(x96811,x96812),x96813),x96814))+P1(f775(f321(f856(f857(a1,f854(f851(a842))),f856(a1,a1)),a311),f775(f775(f241(f857(a1,f854(f851(a842))),f856(a1,a1)),f708(x96811,x96814,x96813,x96812)),f775(f775(f241(a1,a1),f711(x96811,x96814,x96813,x96812)),f712(x96811,x96814,x96813,x96812)))))+~P1(f775(f321(f856(f857(a1,f854(f851(a842))),f856(a1,a1)),a311),f775(f775(f241(f857(a1,f854(f851(a842))),f856(a1,a1)),x96812),f775(f775(f241(a1,a1),x96813),x96814)))) % 186.05/186.63 [9719]~P1(f775(f775(f334(f856(f851(x97191),f851(x97191))),f775(f775(f241(f851(x97191),f851(x97191)),x97192),x97193)),f137(x97191,x97194)))+E(f775(f775(f159(x97191),f775(f181(f851(x97191)),x97192)),x97193),x97192)+P1(f775(f775(f334(f856(x97191,x97191)),f775(f775(f241(x97191,x97191),f775(f775(f153(x97191),x97192),f740(x97194,x97193,x97192,x97191))),f775(f775(f153(x97191),x97193),f740(x97194,x97193,x97192,x97191)))),x97194)) % 186.05/186.63 [9722]~P1(f775(f775(f334(f856(f851(x97221),f851(x97221))),f775(f775(f241(f851(x97221),f851(x97221)),x97222),x97223)),f137(x97221,x97224)))+P1(f775(f775(f233(a850),f775(f181(f851(x97221)),x97222)),f775(f181(f851(x97221)),x97223)))+P1(f775(f775(f334(f856(x97221,x97221)),f775(f775(f241(x97221,x97221),f775(f775(f153(x97221),x97222),f740(x97224,x97223,x97222,x97221))),f775(f775(f153(x97221),x97223),f740(x97224,x97223,x97222,x97221)))),x97224)) % 186.05/186.63 [9792]~E(f775(f181(f851(x97921)),x97922),f775(f181(f851(x97921)),x97923))+P1(f775(f775(f334(f856(f851(x97921),f851(x97921))),f775(f775(f241(f851(x97921),f851(x97921)),x97922),x97923)),f147(x97921,x97924)))+~P1(f775(f775(f334(f856(x97921,x97921)),f775(f775(f241(x97921,x97921),f775(f775(f153(x97921),x97922),f733(x97924,x97923,x97922,x97921))),f775(f775(f153(x97921),x97923),f733(x97924,x97923,x97922,x97921)))),x97924)) % 186.05/186.63 [9932]~P66(x99321)+~P1(f775(f63(x99322),x99324))+E(f775(f155(x99321),f775(f775(f143(x99322,x99321),x99323),f92(f851(x99322),f775(f775(f20(f851(x99322),a844,a844),f775(f775(f10(a844,f857(a844,a844),f851(x99322)),a331),f775(f775(f9(f851(x99322),f857(x99322,a844),a844),f775(f775(f10(f857(x99322,a844),f857(f857(x99322,a844),a844),f851(x99322)),a330),f158(x99322))),x99324))),f127(x99322))))),f225(x99322,x99321,x99323,x99324)) % 186.05/186.63 [7324]~P60(x73242)+E(x73241,f2(x73242))+E(f775(f775(f283(x73242),f775(f775(f82(x73242),x73243),f775(f775(f83(x73242),x73244),x73241))),x73241),f775(f775(f82(x73242),x73244),f775(f775(f283(x73242),x73243),x73241))) % 186.05/186.63 [7325]~P7(x73252)+E(x73251,f2(x73252))+E(f775(f775(f43(x73252),f775(f775(f82(x73252),x73253),f775(f775(f83(x73252),x73254),x73251))),x73251),f775(f775(f82(x73252),x73254),f775(f775(f43(x73252),x73253),x73251))) % 186.05/186.63 [7326]~P7(x73262)+E(x73261,f2(x73262))+E(f775(f775(f43(x73262),f775(f775(f82(x73262),x73263),f775(f775(f83(x73262),x73261),x73264))),x73261),f775(f775(f82(x73262),x73264),f775(f775(f43(x73262),x73263),x73261))) % 186.05/186.63 [7567]~P60(x75672)+E(x75671,f2(x75672))+E(f775(f775(f283(x75672),f775(f775(f82(x75672),x75673),f775(f775(f83(x75672),x75674),x75671))),x75671),f775(f775(f82(x75672),f775(f775(f283(x75672),x75673),x75671)),x75674)) % 186.05/186.63 [7568]~P61(x75682)+E(x75681,f2(x75682))+E(f775(f775(f283(x75682),f775(f775(f82(x75682),x75683),f775(f775(f83(x75682),x75681),x75684))),x75681),f775(f775(f82(x75682),f775(f775(f283(x75682),x75683),x75681)),x75684)) % 186.05/186.63 [7569]~P61(x75692)+E(x75691,f2(x75692))+E(f775(f775(f283(x75692),f775(f775(f3(x75692),x75693),f775(f775(f83(x75692),x75691),x75694))),x75691),f775(f775(f3(x75692),f775(f775(f283(x75692),x75693),x75691)),x75694)) % 186.05/186.63 [8620]~E(f775(f775(f281(x86201,x86201,x86201),x86202),x86204),f180(f857(f856(x86201,x86201),a844)))+~E(f775(f775(f281(x86201,x86201,x86201),x86202),x86203),f180(f857(f856(x86201,x86201),a844)))+E(f775(f775(f281(x86201,x86201,x86201),x86202),f775(f775(f103(f857(f856(x86201,x86201),a844)),x86203),x86204)),f180(f857(f856(x86201,x86201),a844))) % 186.05/186.63 [8731]~P1(f775(f775(f232(f857(x87311,a844)),x87313),x87314))+~P1(f775(f775(f232(f857(x87311,a844)),x87312),x87314))+P1(f775(f775(f232(f857(x87311,a844)),f775(f775(f103(f857(x87311,a844)),x87312),x87313)),x87314)) % 186.05/186.63 [9071]~P1(f775(f63(x90711),x90714))+~P1(f775(f63(x90711),x90713))+E(f775(f775(f3(a850),f775(f775(f82(a850),f775(f775(f8(x90711,a850),x90712),x90713)),f775(f775(f8(x90711,a850),x90712),x90714))),f775(f775(f8(x90711,a850),x90712),f775(f775(f104(f857(x90711,a844)),x90713),x90714))),f775(f775(f8(x90711,a850),x90712),f775(f775(f103(f857(x90711,a844)),x90713),x90714))) % 186.05/186.63 [9146]~P1(f775(f775(f334(x91461),x91463),x91462))+~P1(f775(f775(f232(f857(x91461,a844)),x91462),f775(f775(f302(x91461),x91463),x91464)))+P1(f775(f775(f232(f857(x91461,a844)),f775(f775(f3(f857(x91461,a844)),x91462),f775(f775(f302(x91461),x91463),f180(f857(x91461,a844))))),x91464)) % 186.05/186.63 [9297]~P1(f775(f775(f334(x92971),x92973),x92972))+P1(f775(f775(f232(f857(x92971,a844)),x92972),f775(f775(f302(x92971),x92973),x92974)))+~P1(f775(f775(f232(f857(x92971,a844)),f775(f775(f3(f857(x92971,a844)),x92972),f775(f775(f302(x92971),x92973),f180(f857(x92971,a844))))),x92974)) % 186.05/186.63 [9382]~P1(f775(f775(f233(a850),x93822),x93824))+~P1(f775(f775(f232(a850),x93821),x93823))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x93821),x93822)),f775(f775(f241(a850,a850),x93823),x93824))),a40)) % 186.05/186.63 [9383]~P1(f775(f775(f232(a850),x93832),x93834))+~P1(f775(f775(f232(a850),x93831),x93833))+P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),f775(f775(f241(a850,a850),x93831),x93832)),f775(f775(f241(a850,a850),x93833),x93834))),a72)) % 186.05/186.63 [9757]~P29(x97571,f857(f857(x97571,a844),a844),f775(f775(f9(x97571,f857(f856(x97571,x97571),a844),f857(f857(x97571,a844),a844)),f775(f775(f10(f857(x97571,a844),f857(f857(f856(x97571,x97571),a844),f857(f857(x97571,a844),a844)),x97571),f61(x97571)),f775(f775(f9(x97571,f857(x97571,a844),f857(x97571,a844)),f302(x97571)),f180(f857(x97571,a844))))),x97573),x97572)+~P1(f775(f775(f334(x97571),x97574),x97572))+E(f775(f775(f3(f857(f857(x97571,a844),a844)),f775(f775(f61(x97571),x97572),x97573)),f775(f775(f61(x97571),f775(f775(f302(x97571),x97574),f180(f857(x97571,a844)))),x97573)),f775(f775(f61(x97571),f775(f775(f3(f857(x97571,a844)),x97572),f775(f775(f302(x97571),x97574),f180(f857(x97571,a844))))),x97573)) % 186.05/186.63 [9896]~P47(x98961,x98962,x98964)+~P1(f775(f775(f334(f856(x98961,x98961)),x98963),x98964))+P1(f775(f775(f251(x98961,x98961,a844),f775(f775(f9(x98961,f857(x98961,a844),f857(x98961,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x98961,a844),f857(x98961,a844)),x98961),f10(a844,a844,x98961)),f775(f775(f10(a844,f857(a844,a844),x98961),a331),f775(f775(f9(x98961,f857(x98961,a844),a844),f334(x98961)),x98962)))),f775(f775(f9(x98961,f857(x98961,a844),a844),f334(x98961)),x98962))),x98963)) % 186.05/186.63 [9906]P1(f775(f63(x99061),x99062))+~P1(f775(f63(x99063),f775(f303(x99061,x99063,x99064),x99062)))+~P1(f775(f63(x99061),f775(f256(x99061),f775(f775(f20(x99061,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99061),a331),f775(f775(f9(x99061,f857(x99061,a844),a844),f334(x99061)),x99062))),f775(f775(f9(x99061,x99063,a844),f775(f775(f10(x99063,f857(x99063,a844),x99061),a330),x99064)),f775(x99064,f599(x99064,x99063,x99062,x99061))))))) % 186.05/186.63 [8024]~P61(x80242)+E(x80241,f2(x80242))+E(f775(f775(f283(x80242),f775(f775(f82(x80242),f775(f775(f83(x80242),x80241),x80243)),x80244)),x80241),f775(f775(f82(x80242),x80243),f775(f775(f283(x80242),x80244),x80241))) % 186.05/186.63 [8025]~P61(x80252)+E(x80251,f2(x80252))+E(f775(f775(f283(x80252),f775(f775(f3(x80252),f775(f775(f83(x80252),x80251),x80253)),x80254)),x80251),f775(f775(f3(x80252),x80253),f775(f775(f283(x80252),x80254),x80251))) % 186.05/186.63 [8865]~E(f775(f775(f281(x88651,x88651,x88651),x88653),x88654),f180(f857(f856(x88651,x88651),a844)))+~E(f775(f775(f281(x88651,x88651,x88651),x88652),x88654),f180(f857(f856(x88651,x88651),a844)))+E(f775(f775(f281(x88651,x88651,x88651),f775(f775(f103(f857(f856(x88651,x88651),a844)),x88652),x88653)),x88654),f180(f857(f856(x88651,x88651),a844))) % 186.05/186.63 [9840]~P139(x98401)+~P139(x98402)+E(f775(f775(f310(x98401),f775(f775(f9(x98401,a101,f854(f851(a842))),f775(f775(f10(f857(x98402,f854(f851(a842))),f857(a101,f854(f851(a842))),x98401),f310(x98402)),f775(f775(f10(f857(x98402,f856(x98401,x98402)),f857(x98402,f854(f851(a842))),x98401),f775(f10(f856(x98401,x98402),f854(f851(a842)),x98402),x98403)),f241(x98401,x98402)))),x98404)),x98404),f775(f775(f310(f856(x98401,x98402)),x98403),x98404)) % 186.05/186.63 [9832]P1(f775(x98321,f585(x98322,x98323,x98321,x98324)))+~P1(f775(f63(x98324),f775(f256(x98324),x98321)))+P1(f775(f63(x98323),f775(f256(x98323),f775(f775(f10(f857(x98324,a844),a844,x98323),f89(x98324)),f775(f775(f10(f857(x98324,a844),f857(x98324,a844),x98323),f775(f20(x98324,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98324),a331),x98321))),x98322))))) % 186.05/186.63 [9853]~P1(f775(f63(x98532),f775(f256(x98532),x98533)))+~P1(f775(f63(x98531),f775(f256(x98531),f775(f775(f9(x98531,x98532,a844),x98534),f585(x98534,x98531,x98533,x98532)))))+P1(f775(f63(x98531),f775(f256(x98531),f775(f775(f10(f857(x98532,a844),a844,x98531),f89(x98532)),f775(f775(f10(f857(x98532,a844),f857(x98532,a844),x98531),f775(f20(x98532,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98532),a331),x98533))),x98534))))) % 186.05/186.63 [5707]~E(x57075,x57072)+P39(f35(x57071,x57073),x57072,x57074,x57075)+P1(f775(x57071,x57072)) % 186.05/186.63 [6275]E(x62751,x62752)+~P39(f35(x62753,x62754),x62751,x62755,x62752)+P1(f775(x62753,x62751)) % 186.05/186.63 [7830]~P39(x78302,x78303,x78304,x78305)+~P39(f35(x78301,x78302),x78305,x78304,x78303)+P39(f35(x78301,x78302),x78303,x78304,x78303) % 186.05/186.63 [8987]E(x89871,x89872)+~P39(f35(x89875,x89873),x89871,x89874,x89872)+P39(x89873,x89871,x89874,f674(x89872,x89874,x89871,x89873,x89875)) % 186.05/186.63 [8988]E(x89881,x89882)+~P39(f35(x89885,x89883),x89881,x89884,x89882)+P39(x89883,x89881,x89884,f823(x89882,x89884,x89881,x89883,x89885)) % 186.05/186.63 [8990]E(x89901,x89902)+P39(f35(x89903,x89904),f674(x89901,x89905,x89902,x89904,x89903),x89905,x89901)+~P39(f35(x89903,x89904),x89902,x89905,x89901) % 186.05/186.63 [8991]E(x89911,x89912)+P39(f35(x89913,x89914),f823(x89911,x89915,x89912,x89914,x89913),x89915,x89911)+~P39(f35(x89913,x89914),x89912,x89915,x89911) % 186.05/186.63 [8993]~P39(f35(x89935,x89931),x89932,x89933,x89934)+P39(x89931,x89932,x89933,f674(x89934,x89933,x89932,x89931,x89935))+~P1(f775(x89935,x89932)) % 186.05/186.63 [8994]~P39(f35(x89945,x89941),x89942,x89943,x89944)+P39(x89941,x89942,x89943,f823(x89944,x89943,x89942,x89941,x89945))+~P1(f775(x89945,x89942)) % 186.05/186.63 [8998]~P39(f35(x89981,x89982),x89985,x89984,x89983)+P39(f35(x89981,x89982),f674(x89983,x89984,x89985,x89982,x89981),x89984,x89983)+~P1(f775(x89981,x89985)) % 186.05/186.63 [8999]~P39(f35(x89991,x89992),x89995,x89994,x89993)+P39(f35(x89991,x89992),f823(x89993,x89994,x89995,x89992,x89991),x89994,x89993)+~P1(f775(x89991,x89995)) % 186.05/186.63 [6425]E(x64251,x64252)+~E(f775(x64253,x64251),f775(x64253,x64252))+~P29(x64254,x64255,x64253,f239(f857(x64254,a844))) % 186.05/186.63 [6590]~E(f775(x65903,x65905),f183(x65902))+~E(f775(x65904,x65905),f183(x65902))+E(f775(f170(x65901,x65902,x65903,x65904),x65905),f183(x65902)) % 186.05/186.63 [7365]E(x73651,x73652)+~P29(x73653,x73654,x73655,f239(f857(x73653,a844)))+~E(f775(f303(x73653,x73654,x73655),x73651),f775(f303(x73653,x73654,x73655),x73652)) % 186.05/186.63 [7623]P29(x76232,x76233,f522(x76234,x76233,x76232,x76231),x76231)+~E(f775(f303(x76233,x76232,x76235),x76234),x76231)+E(x76231,f180(f857(x76232,a844))) % 186.05/186.63 [8154]~P1(f775(f775(x81543,x81542),x81545))+~P1(f775(f775(x81543,x81544),x81542))+P1(f775(f775(f334(x81541),x81542),f282(x81541,x81543,x81544,x81545))) % 186.05/186.63 [8155]~P1(f775(f775(x81553,x81552),x81555))+~P1(f775(f775(x81553,x81554),x81552))+P1(f775(f775(f334(x81551),x81552),f291(x81551,x81553,x81554,x81555))) % 186.05/186.63 [8693]~P29(x86931,x86933,x86935,f239(f857(x86931,a844)))+~P29(x86933,x86932,x86934,f239(f857(x86933,a844)))+P29(x86931,x86932,f775(f75(x86933,x86932,x86931,x86934),x86935),f239(f857(x86931,a844))) % 186.05/186.63 [9192]P1(f775(f775(f334(f856(x91921,x91921)),f775(f775(f241(x91921,x91921),x91922),x91923)),f300(x91921,x91924)))+~P1(f775(f775(f334(f856(x91921,x91921)),f775(f775(f241(x91921,x91921),x91922),x91925)),f300(x91921,x91924)))+~P1(f775(f775(f334(f856(x91921,x91921)),f775(f775(f241(x91921,x91921),x91925),x91923)),f300(x91921,x91924))) % 186.05/186.63 [9229]~P100(x92292)+~P1(f775(f127(x92291),x92295))+P1(f775(f127(x92291),f139(x92291,x92292,x92293,x92294,x92295))) % 186.05/186.63 [5239]~E(x52392,f115(x52391))+E(f775(f775(f125(x52391),x52392),x52393),f775(f775(f140(x52391),x52394),x52395))+~E(x52393,f775(f775(f140(x52391),x52394),x52395)) % 186.05/186.63 [5240]~E(x52402,f115(x52401))+E(f775(f775(f125(x52401),x52402),x52403),f775(f775(f140(x52401),x52404),x52405))+~E(f775(f775(f140(x52401),x52404),x52405),x52403) % 186.05/186.63 [6381]~E(f775(f181(f851(x63811)),x63815),f775(f181(f851(x63812)),x63814))+E(f775(f775(f143(f856(x63811,x63812),x63812),f250(x63811,x63812)),x63813),x63814)+~E(f775(f775(f167(x63811,x63812),x63815),x63814),x63813) % 186.05/186.63 [6382]~E(f775(f181(f851(x63821)),x63824),f775(f181(f851(x63822)),x63825))+E(f775(f775(f143(f856(x63821,x63822),x63821),f240(x63821,x63822)),x63823),x63824)+~E(f775(f775(f167(x63821,x63822),x63824),x63825),x63823) % 186.05/186.63 [6880]~P100(x68801)+~P18(x68801,f775(f775(f143(x68802,x68801),x68803),x68805))+P18(x68801,f775(f775(f143(x68802,x68801),x68803),f775(f126(x68802,x68804),x68805))) % 186.05/186.63 [6926]~P1(f775(x69263,x69265))+~P1(f775(f775(x69262,x69264),x69265))+P1(f775(f775(f94(x69261,x69262,x69263),x69264),x69265)) % 186.05/186.63 [7023]~P100(x70231)+P18(x70231,f775(f775(f143(x70232,x70231),x70233),f151(x70232,x70234,x70235)))+~P18(x70231,f775(f775(f143(x70232,x70231),x70233),x70235)) % 186.05/186.63 [7046]~P53(x70463,x70462,x70465)+~P53(x70461,x70463,x70464)+P53(x70461,x70462,f775(f775(f281(x70461,x70463,x70462),x70464),x70465)) % 186.05/186.63 [7137]E(x71371,x71372)+~P29(x71373,x71374,x71375,f239(f857(x71373,a844)))+~E(f775(f775(f143(x71373,x71374),x71375),x71371),f775(f775(f143(x71373,x71374),x71375),x71372)) % 186.05/186.63 [7220]P39(x72201,x72202,x72203,x72204)+~P39(x72201,x72202,x72205,x72204)+~P1(f775(f775(f232(a850),x72205),x72203)) % 186.05/186.63 [7310]~P1(f775(f775(f233(a850),x73101),f775(x73103,x73105)))+P1(f775(f775(f233(a850),x73101),f144(x73102,x73103,x73104)))+~P1(f775(f775(f334(x73102),x73105),f775(f158(x73102),x73104))) % 186.05/186.63 [7311]~P1(f775(f775(f232(a850),x73111),f775(x73113,x73115)))+P1(f775(f775(f232(a850),x73111),f144(x73112,x73113,x73114)))+~P1(f775(f775(f334(x73112),x73115),f775(f158(x73112),x73114))) % 186.05/186.63 [7722]~P99(x77221)+P1(f775(f775(f232(f857(x77221,a844)),f295(x77221,x77222,x77223)),f295(x77221,x77224,x77225)))+P1(f775(f775(f232(x77221),x77222),x77223)) % 186.05/186.63 [7749]~P9(x77491)+P1(f775(f775(f232(x77491),f775(f775(f47(x77492,x77491),x77493),x77494)),f775(x77494,x77495)))+~P1(f775(f775(f334(x77492),x77495),x77493)) % 186.05/186.63 [7817]~P29(x78171,x78172,x78174,x78173)+E(f775(f79(x78171,x78172,x78173,x78174),f775(x78174,x78175)),x78175)+~P1(f775(f775(f334(x78171),x78175),x78173)) % 186.05/186.63 [8013]~P1(f775(x80131,x80135))+P1(f775(x80131,f378(x80131,x80132,x80133,x80134)))+~P1(f775(f775(f334(x80134),x80135),x80133)) % 186.05/186.63 [8014]~P1(f775(x80141,x80145))+P1(f775(x80141,f378(x80141,x80142,x80143,x80144)))+~P1(f775(f775(f334(x80144),x80145),x80142)) % 186.05/186.63 [8105]P1(f775(f63(x81051),x81052))+~P1(f775(f63(x81053),x81054))+~P1(f775(f775(f232(f857(x81051,a844)),x81052),f775(f303(x81053,x81051,x81055),x81054))) % 186.05/186.63 [8266]E(x82661,x82662)+~P29(x82663,x82664,x82665,f775(f775(f103(f857(x82663,a844)),f775(f158(x82663),x82661)),f775(f158(x82663),x82662)))+~E(f775(f775(f143(x82663,x82664),x82665),x82661),f775(f775(f143(x82663,x82664),x82665),x82662)) % 186.05/186.63 [8323]~P99(x83231)+~P1(f775(f775(f233(f857(x83231,a844)),f295(x83231,x83234,x83235)),f295(x83231,x83232,x83233)))+P1(f775(f775(f232(x83231),x83232),x83233)) % 186.05/186.63 [8391]~P29(x83911,x83914,x83915,f239(f857(x83911,a844)))+~P1(f775(f775(f334(x83914),f775(x83915,x83912)),f775(f303(x83911,x83914,x83915),x83913)))+P1(f775(f775(f334(x83911),x83912),x83913)) % 186.05/186.63 [8471]P1(f775(x84711,x84712))+~P1(f775(x84711,f382(x84711,x84713,x84714,x84715)))+~P1(f775(f775(f334(x84715),x84712),x84714)) % 186.05/186.63 [8472]P1(f775(x84721,x84722))+~P1(f775(x84721,f382(x84721,x84723,x84724,x84725)))+~P1(f775(f775(f334(x84725),x84722),x84723)) % 186.05/186.63 [8728]~P29(x87282,x87283,x87281,x87284)+E(f775(x87281,f775(f79(x87282,x87283,x87284,x87281),x87285)),x87285)+~P1(f775(f775(f334(x87283),x87285),f775(f303(x87282,x87283,x87281),x87284))) % 186.05/186.63 [8812]E(x88121,f115(x88122))+E(f775(f775(f140(x88122),x88123),f732(x88124,x88123,x88125,x88121,x88122)),x88121)+~E(f775(f775(f125(x88122),x88121),x88125),f775(f775(f140(x88122),x88123),x88124)) % 186.05/186.63 [8813]E(x88131,f115(x88132))+E(f775(f775(f140(x88132),x88133),f734(x88134,x88131,x88135,x88133,x88132)),x88131)+~E(f775(f775(f125(x88132),x88131),x88134),f775(f775(f140(x88132),x88133),x88135)) % 186.05/186.63 [8828]E(f775(f775(f140(x88282),x88283),f732(x88284,x88283,x88281,x88285,x88282)),x88285)+~E(f775(f775(f125(x88282),x88285),x88281),f775(f775(f140(x88282),x88283),x88284))+E(x88281,f775(f775(f140(x88282),x88283),x88284)) % 186.05/186.63 [8829]E(f775(f775(f140(x88291),x88292),f734(x88294,x88295,x88293,x88292,x88291)),x88295)+~E(f775(f775(f125(x88291),x88295),x88294),f775(f775(f140(x88291),x88292),x88293))+E(f775(f775(f140(x88291),x88292),x88293),x88294) % 186.05/186.63 [8905]~E(f775(f303(x89053,x89052,x89054),f239(f857(x89053,a844))),f239(f857(x89052,a844)))+~E(f775(f303(x89051,x89053,x89055),f239(f857(x89051,a844))),f239(f857(x89053,a844)))+E(f775(f303(x89051,x89052,f775(f75(x89053,x89052,x89051,x89054),x89055)),f239(f857(x89051,a844))),f239(f857(x89052,a844))) % 186.05/186.63 [9235]E(x92351,f115(x92352))+~E(f775(f775(f125(x92352),x92351),x92353),f775(f775(f140(x92352),x92355),x92354))+E(f775(f775(f125(x92352),f734(x92353,x92351,x92354,x92355,x92352)),x92353),x92354) % 186.05/186.63 [9236]E(x92361,f115(x92362))+~E(f775(f775(f125(x92362),x92361),x92365),f775(f775(f140(x92362),x92364),x92363))+E(f775(f775(f125(x92362),f732(x92363,x92364,x92365,x92361,x92362)),x92365),x92363) % 186.05/186.63 [9244]E(f775(f775(f125(x92442),f732(x92444,x92443,x92441,x92445,x92442)),x92441),x92444)+~E(f775(f775(f125(x92442),x92445),x92441),f775(f775(f140(x92442),x92443),x92444))+E(x92441,f775(f775(f140(x92442),x92443),x92444)) % 186.05/186.63 [9245]~E(f775(f775(f125(x92451),x92455),x92454),f775(f775(f140(x92451),x92452),x92453))+E(f775(f775(f125(x92451),f734(x92454,x92455,x92453,x92452,x92451)),x92454),x92453)+E(f775(f775(f140(x92451),x92452),x92453),x92454) % 186.05/186.63 [9246]E(f775(f775(f125(x92461),x92465),f736(x92463,x92462,x92464,x92465,x92461)),x92462)+E(f775(f775(f125(x92461),x92462),f735(x92463,x92462,x92464,x92465,x92461)),x92465)+~E(f775(f775(f125(x92461),x92465),x92464),f775(f775(f125(x92461),x92462),x92463)) % 186.05/186.63 [9277]~P100(x92771)+P18(x92771,f775(f775(f143(x92772,x92771),x92773),f139(x92772,x92771,x92773,x92774,x92775)))+~P18(x92771,f775(f775(f143(x92772,x92771),x92773),x92775)) % 186.05/186.63 [9293]~P57(x92935,x92931,x92934,x92933)+P1(f775(f775(x92931,x92932),f538(x92933,x92934,x92931,x92935,x92932)))+~P1(f775(f775(f334(x92935),x92932),x92934)) % 186.05/186.63 [9391]~P1(f775(f775(f334(f856(x93911,x93911)),f775(f775(f241(x93911,x93911),x93915),x93913)),f300(x93911,x93914)))+P1(f775(f775(f334(f856(x93911,x93911)),f775(f775(f241(x93911,x93911),x93912),x93913)),f775(f775(f281(x93911,x93911,x93911),x93914),f300(x93911,x93914))))+~P1(f775(f775(f334(f856(x93911,x93911)),f775(f775(f241(x93911,x93911),x93912),x93915)),f775(f775(f281(x93911,x93911,x93911),x93914),f300(x93911,x93914)))) % 186.05/186.63 [9392]~P1(f775(f775(f334(f856(x93921,x93921)),f775(f775(f241(x93921,x93921),x93922),x93925)),f300(x93921,x93924)))+P1(f775(f775(f334(f856(x93921,x93921)),f775(f775(f241(x93921,x93921),x93922),x93923)),f775(f775(f281(x93921,x93921,x93921),x93924),f300(x93921,x93924))))+~P1(f775(f775(f334(f856(x93921,x93921)),f775(f775(f241(x93921,x93921),x93925),x93923)),f775(f775(f281(x93921,x93921,x93921),x93924),f300(x93921,x93924)))) % 186.05/186.63 [9394]P1(f775(f775(f334(f856(f851(x93941),f851(x93941))),f775(f775(f241(f851(x93941),f851(x93941)),x93942),x93943)),f147(x93941,f300(x93941,x93944))))+~P1(f775(f775(f334(f856(f851(x93941),f851(x93941))),f775(f775(f241(f851(x93941),f851(x93941)),x93942),x93945)),f147(x93941,f300(x93941,x93944))))+~P1(f775(f775(f334(f856(f851(x93941),f851(x93941))),f775(f775(f241(f851(x93941),f851(x93941)),x93945),x93943)),f147(x93941,f300(x93941,x93944)))) % 186.05/186.63 [9398]E(f775(f775(f125(x93981),x93982),f735(x93983,x93982,x93984,x93985,x93981)),x93985)+E(f775(f775(f125(x93981),f736(x93983,x93982,x93984,x93985,x93981)),x93983),x93984)+~E(f775(f775(f125(x93981),x93982),x93983),f775(f775(f125(x93981),x93985),x93984)) % 186.05/186.63 [9399]E(f775(f775(f125(x93991),x93992),f736(x93993,x93994,x93995,x93992,x93991)),x93994)+E(f775(f775(f125(x93991),f735(x93993,x93994,x93995,x93992,x93991)),x93995),x93993)+~E(f775(f775(f125(x93991),x93992),x93995),f775(f775(f125(x93991),x93994),x93993)) % 186.05/186.63 [9456]P1(f775(f775(f334(f856(x94561,x94561)),f775(f775(f241(x94561,x94561),x94562),x94563)),f775(f775(f281(x94561,x94561,x94561),x94564),f300(x94561,x94564))))+~P1(f775(f775(f334(f856(x94561,x94561)),f775(f775(f241(x94561,x94561),x94562),x94565)),f775(f775(f281(x94561,x94561,x94561),x94564),f300(x94561,x94564))))+~P1(f775(f775(f334(f856(x94561,x94561)),f775(f775(f241(x94561,x94561),x94565),x94563)),f775(f775(f281(x94561,x94561,x94561),x94564),f300(x94561,x94564)))) % 186.05/186.63 [9489]E(f775(f775(f125(x94891),f735(x94892,x94893,x94894,x94895,x94891)),x94894),x94892)+~E(f775(f775(f125(x94891),x94893),x94892),f775(f775(f125(x94891),x94895),x94894))+E(f775(f775(f125(x94891),f736(x94892,x94893,x94894,x94895,x94891)),x94892),x94894) % 186.05/186.63 [9504]~P57(x95041,x95044,x95043,x95042)+~P1(f775(f775(f334(x95041),x95045),x95043))+P1(f775(f775(f334(x95041),f538(x95042,x95043,x95044,x95041,x95045)),x95042)) % 186.05/186.63 [9612]~P1(f775(f775(f334(f856(f857(x96121,a844),f857(x96121,a844))),f775(f775(f241(f857(x96121,a844),f857(x96121,a844)),x96124),x96123)),f324(x96121,x96122)))+~P1(f775(f775(f334(x96121),x96125),x96124))+P1(f775(f775(f334(x96121),f625(x96122,x96123,x96124,x96121,x96125)),x96123)) % 186.05/186.63 [6457]~P21(x64572,x64575,x64571)+~P1(f775(f63(x64572),x64574))+E(f775(x64571,f775(f775(f302(x64572),x64573),x64574)),f775(f775(f66(x64572,x64572,x64575),x64573),x64574)) % 186.05/186.63 [6458]~E(x64583,x64584)+~E(x64582,x64585)+E(f775(f775(f302(x64581),x64582),f775(f775(f302(x64581),x64583),f180(f857(x64581,a844)))),f775(f775(f302(x64581),x64584),f775(f775(f302(x64581),x64585),f180(f857(x64581,a844))))) % 186.05/186.63 [6470]P1(f775(x64702,x64705))+E(f162(x64701,x64702,f775(f775(f125(x64701),x64703),x64704)),f162(x64701,x64702,x64703))+~P1(f775(f775(f334(x64701),x64705),f775(f158(x64701),x64703))) % 186.05/186.63 [6507]E(f775(x65071,x65072),f239(f857(x65073,a844)))+~E(f775(f775(f47(x65074,f857(x65073,a844)),x65075),x65071),f239(f857(x65073,a844)))+~P1(f775(f775(f334(x65074),x65072),x65075)) % 186.05/186.63 [6508]E(f775(x65081,x65082),f180(f857(x65083,a844)))+~E(f775(f775(f46(x65084,f857(x65083,a844)),x65085),x65081),f180(f857(x65083,a844)))+~P1(f775(f775(f334(x65084),x65082),x65085)) % 186.05/186.63 [6829]~P1(f775(f775(f187(x68291),x68293),x68295))+~P1(f775(f775(f187(x68292),x68295),x68294))+P1(f775(f775(f187(f36(x68291,x68292)),x68293),x68294)) % 186.05/186.63 [7033]~E(x70332,x70334)+~P137(x70331)+E(f775(f775(f82(x70331),f775(f775(f83(x70331),x70332),x70333)),f775(f775(f83(x70331),x70334),x70335)),f775(f775(f82(x70331),f775(f775(f83(x70331),x70332),x70335)),f775(f775(f83(x70331),x70334),x70333))) % 186.05/186.63 [7093]~P9(x70931)+~P1(f775(f775(f334(x70934),x70933),x70935))+P1(f775(f775(f232(x70931),f775(x70932,x70933)),f775(f775(f46(x70934,x70931),x70935),x70932))) % 186.05/186.63 [7142]~P102(x71421)+P1(f775(f775(f232(x71421),f775(x71422,x71423)),f775(x71424,x71423)))+~P1(f775(f775(f232(f857(x71425,x71421)),x71422),x71424)) % 186.05/186.63 [7278]E(x72781,x72782)+E(x72783,x72781)+~E(f775(f775(f302(x72784),x72781),f775(f775(f302(x72784),x72785),f180(f857(x72784,a844)))),f775(f775(f302(x72784),x72782),f775(f775(f302(x72784),x72783),f180(f857(x72784,a844))))) % 186.05/186.63 [7279]E(x72791,x72792)+E(x72793,x72791)+~E(f775(f775(f302(x72794),x72793),f775(f775(f302(x72794),x72792),f180(f857(x72794,a844)))),f775(f775(f302(x72794),x72795),f775(f775(f302(x72794),x72791),f180(f857(x72794,a844))))) % 186.05/186.63 [7280]E(x72801,x72802)+E(x72801,x72803)+~E(f775(f775(f302(x72804),x72803),f775(f775(f302(x72804),x72802),f180(f857(x72804,a844)))),f775(f775(f302(x72804),x72805),f775(f775(f302(x72804),x72801),f180(f857(x72804,a844))))) % 186.05/186.63 [7281]E(x72811,x72812)+E(x72811,x72813)+~E(f775(f775(f302(x72814),x72811),f775(f775(f302(x72814),x72815),f180(f857(x72814,a844)))),f775(f775(f302(x72814),x72812),f775(f775(f302(x72814),x72813),f180(f857(x72814,a844))))) % 186.05/186.63 [7827]P29(x78271,x78272,x78273,x78274)+~P29(x78271,x78272,x78273,x78275)+~P1(f775(f775(f232(f857(x78271,a844)),x78274),x78275)) % 186.05/186.63 [7930]P1(f775(x79301,x79302))+~P1(f775(f775(f187(x79304),x79302),x79305))+P1(f775(f775(f187(f33(x79301,x79303,x79304)),x79302),x79305)) % 186.05/186.63 [7958]~P1(f775(x79581,x79584))+~P1(f775(f775(f187(x79582),x79584),x79585))+P1(f775(f775(f187(f33(x79581,x79582,x79583)),x79584),x79585)) % 186.05/186.63 [8003]E(x80031,x80032)+~E(f775(f303(x80033,x80034,x80035),x80031),f775(f303(x80033,x80034,x80035),x80032))+~P29(x80033,x80034,x80035,f775(f775(f103(f857(x80033,a844)),x80031),x80032)) % 186.05/186.63 [8103]~P29(x81031,x81032,x81033,x81035)+~P29(x81031,x81032,x81033,x81034)+P29(x81031,x81032,x81033,f775(f775(f104(f857(x81031,a844)),x81034),x81035)) % 186.05/186.63 [8208]~P66(x82081)+E(f775(f775(f82(x82081),f775(x82082,x82083)),f775(f155(x82081),f775(f775(f143(x82084,x82081),x82082),f151(x82084,x82083,x82085)))),f775(f155(x82081),f775(f775(f143(x82084,x82081),x82082),x82085)))+~P1(f775(f775(f334(x82084),x82083),f775(f158(x82084),x82085))) % 186.05/186.63 [8295]~P100(x82951)+~P18(x82951,f775(f775(f143(x82952,x82951),x82953),x82955))+P18(x82951,f775(f775(f143(x82952,x82951),x82953),f775(f775(f138(x82952,x82951,x82953),x82954),x82955))) % 186.05/186.63 [8376]P1(f775(x83761,x83762))+P1(f775(f775(f187(x83763),x83762),x83764))+~P1(f775(f775(f187(f33(x83761,x83765,x83763)),x83762),x83764)) % 186.05/186.63 [8387]~P9(x83871)+P1(f775(f775(f232(x83871),f775(f775(f46(x83872,x83871),x83873),x83874)),f775(f775(f46(x83872,x83871),x83875),x83874)))+~P1(f775(f775(f232(f857(x83872,a844)),x83873),x83875)) % 186.05/186.63 [8388]~P9(x83881)+P1(f775(f775(f232(x83881),f775(f775(f47(x83882,x83881),x83883),x83884)),f775(f775(f47(x83882,x83881),x83885),x83884)))+~P1(f775(f775(f232(f857(x83882,a844)),x83885),x83883)) % 186.05/186.63 [8397]~P1(f775(x83974,x83972))+P1(f775(f775(f187(x83971),x83972),x83973))+~P1(f775(f775(f187(f33(x83974,x83971,x83975)),x83972),x83973)) % 186.05/186.63 [8421]~P100(x84213)+P1(f775(f127(x84211),x84212))+~P1(f775(f127(x84211),f775(f775(f138(x84211,x84213,x84214),x84215),x84212))) % 186.05/186.63 [8431]P1(f775(f775(f187(x84311),x84312),x84313))+P1(f775(f775(f187(x84314),x84312),x84313))+~P1(f775(f775(f187(f33(x84315,x84311,x84314)),x84312),x84313)) % 186.05/186.63 [8555]~P100(x85551)+~P1(f775(f775(f334(x85552),x85553),f775(f158(x85552),x85554)))+~P1(f775(f127(x85552),f775(f775(f138(x85552,x85551,x85555),x85553),x85554))) % 186.05/186.63 [8630]~P100(x86301)+P18(x86301,f775(f775(f143(x86302,x86301),x86303),x86304))+~P18(x86301,f775(f775(f143(x86302,x86301),x86303),f775(f775(f138(x86302,x86301,x86303),x86305),x86304))) % 186.05/186.63 [8715]~P100(x87152)+E(f775(f775(f138(x87151,x87152,x87153),x87154),x87155),f139(x87151,x87152,x87153,x87154,x87155))+P1(f775(f775(f334(x87152),f775(x87153,x87154)),f775(f303(x87151,x87152,x87153),f775(f158(x87151),x87155)))) % 186.05/186.63 [8782]~P100(x87822)+E(f139(x87821,x87822,x87823,x87824,x87825),x87825)+~P1(f775(f775(f334(x87822),f775(x87823,x87824)),f775(f303(x87821,x87822,x87823),f775(f158(x87821),x87825)))) % 186.05/186.63 [8796]~P29(x87962,x87961,x87963,x87965)+P1(f775(f775(f233(f857(x87961,a844)),f775(f303(x87962,x87961,x87963),x87964)),f775(f303(x87962,x87961,x87963),x87965)))+~P1(f775(f775(f233(f857(x87962,a844)),x87964),x87965)) % 186.05/186.63 [8943]~P29(x89431,x89432,x89433,f239(f857(x89431,a844)))+~P1(f775(f775(f232(f857(x89432,a844)),x89434),f775(f303(x89431,x89432,x89433),x89435)))+P1(f775(f775(f232(f857(x89431,a844)),f775(f305(x89431,x89432,x89433),x89434)),x89435)) % 186.05/186.63 [8962]~E(f775(f303(x89623,x89621,x89624),f239(f857(x89623,a844))),f239(f857(x89621,a844)))+P1(f775(f775(f232(f857(x89621,a844)),x89622),f775(f303(x89623,x89621,x89624),x89625)))+~P1(f775(f775(f232(f857(x89623,a844)),f775(f305(x89623,x89621,x89624),x89622)),x89625)) % 186.05/186.63 [9000]~E(f775(f227(x90002),x90004),f775(f166(x90001,x90002,x90005),x90003))+~P1(f775(f127(x90001),f775(f775(f143(f856(x90001,x90002),x90001),f240(x90001,x90002)),x90005)))+P1(f775(f775(f334(f856(x90001,x90002)),f775(f775(f241(x90001,x90002),x90003),x90004)),f775(f158(f856(x90001,x90002)),x90005))) % 186.05/186.63 [9064]~P29(x90641,x90644,x90645,f239(f857(x90641,a844)))+~P1(f775(f775(f232(f857(x90644,a844)),f775(f303(x90641,x90644,x90645),x90642)),f775(f303(x90641,x90644,x90645),x90643)))+P1(f775(f775(f232(f857(x90641,a844)),x90642),x90643)) % 186.05/186.63 [9130]E(f775(f227(x91301),x91302),f775(f166(x91303,x91301,x91304),x91305))+~P1(f775(f127(x91303),f775(f775(f143(f856(x91303,x91301),x91303),f240(x91303,x91301)),x91304)))+~P1(f775(f775(f334(f856(x91303,x91301)),f775(f775(f241(x91303,x91301),x91305),x91302)),f775(f158(f856(x91303,x91301)),x91304))) % 186.05/186.63 [9132]E(f775(f166(x91321,x91322,x91323),x91324),f775(f227(x91322),x91325))+~P1(f775(f127(x91321),f775(f775(f143(f856(x91321,x91322),x91321),f240(x91321,x91322)),x91323)))+~P1(f775(f775(f334(f856(x91321,x91322)),f775(f775(f241(x91321,x91322),x91324),x91325)),f775(f158(f856(x91321,x91322)),x91323))) % 186.05/186.63 [9339]~P20(x93391,x93392,x93393)+~P1(f775(f63(x93391),x93395))+P1(f775(f68(x93391,x93392,x93393,x93394,x93395),f775(f775(f66(x93391,x93392,x93393),x93394),x93395))) % 186.05/186.63 [9413]P1(f775(x94131,f700(x94132,x94131,x94133,x94134,x94135)))+~P1(f775(f775(f232(f857(x94135,a844)),x94134),x94133))+P1(f775(f775(f232(f857(x94135,a844)),f775(f775(f104(f857(x94135,a844)),x94134),f775(f256(x94135),x94131))),f775(f775(f104(f857(x94135,a844)),x94133),f775(f256(x94135),x94132)))) % 186.05/186.63 [9502]~P9(x95025)+P1(f775(f775(f334(x95021),f665(x95022,x95023,x95021,x95024,x95025)),x95023))+P1(f775(f775(f232(x95025),x95024),f775(f775(f47(x95021,x95025),x95023),x95022))) % 186.05/186.63 [9514]~P1(f775(x95145,f700(x95145,x95143,x95144,x95142,x95141)))+~P1(f775(f775(f232(f857(x95141,a844)),x95142),x95144))+P1(f775(f775(f232(f857(x95141,a844)),f775(f775(f104(f857(x95141,a844)),x95142),f775(f256(x95141),x95143))),f775(f775(f104(f857(x95141,a844)),x95144),f775(f256(x95141),x95145)))) % 186.05/186.63 [9577]P1(f775(f775(f334(x95771),f700(x95772,x95773,x95774,x95775,x95771)),x95775))+~P1(f775(f775(f232(f857(x95771,a844)),x95775),x95774))+P1(f775(f775(f232(f857(x95771,a844)),f775(f775(f104(f857(x95771,a844)),x95775),f775(f256(x95771),x95773))),f775(f775(f104(f857(x95771,a844)),x95774),f775(f256(x95771),x95772)))) % 186.05/186.63 [9623]~P9(x96231)+~P1(f775(f775(f232(x96231),x96232),f775(x96235,f665(x96235,x96234,x96233,x96232,x96231))))+P1(f775(f775(f232(x96231),x96232),f775(f775(f47(x96233,x96231),x96234),x96235))) % 186.05/186.63 [9653]~P70(x96531)+~P1(f775(f63(x96532),x96535))+E(f775(f775(f775(f67(x96531,x96532,f83(x96531)),f775(f775(f20(x96532,x96531,x96531),f775(f775(f10(x96531,f857(x96531,x96531),x96532),f83(x96531)),x96533)),x96534)),f80(x96531)),x96535),f775(f775(f83(x96531),f775(f775(f775(f67(x96531,x96532,f83(x96531)),x96533),f80(x96531)),x96535)),f775(f775(f775(f67(x96531,x96532,f83(x96531)),x96534),f80(x96531)),x96535))) % 186.05/186.63 [9702]~P1(f775(f775(f334(f856(f857(x97021,a844),f857(x97021,a844))),f775(f775(f241(f857(x97021,a844),f857(x97021,a844)),x97025),x97024)),f324(x97021,x97023)))+~P1(f775(f775(f334(x97021),x97022),x97025))+P1(f775(f775(f334(f856(x97021,x97021)),f775(f775(f241(x97021,x97021),x97022),f625(x97023,x97024,x97025,x97021,x97022))),x97023)) % 186.05/186.63 [9850]~P1(f775(f775(f334(f856(f851(x98501),f851(x98501))),f775(f775(f241(f851(x98501),f851(x98501)),f775(f775(f125(x98501),x98505),x98502)),f775(f775(f125(x98501),x98505),x98503))),f137(x98501,x98504)))+P1(f775(f775(f334(f856(f851(x98501),f851(x98501))),f775(f775(f241(f851(x98501),f851(x98501)),x98502),x98503)),f137(x98501,x98504)))+P1(f775(f775(f334(f856(x98501,x98501)),f775(f775(f241(x98501,x98501),f741(x98504,x98503,x98502,x98505,x98501)),f741(x98504,x98503,x98502,x98505,x98501))),x98504)) % 186.05/186.63 [7145]~E(x71453,x71455)+E(f775(f775(f153(x71451),f775(f775(f148(x71451,x71452),x71453),x71454)),x71455),x71454)+~P1(f775(f775(f233(a850),x71453),f775(f181(f851(x71451)),x71452))) % 186.05/186.63 [7154]~E(f775(f181(f851(x71541)),x71543),f775(f181(f851(x71542)),x71544))+E(f775(f166(x71541,x71542,f775(f775(f167(x71541,x71542),x71543),x71544)),x71545),f183(x71542))+P1(f775(f775(f334(x71541),x71545),f775(f158(x71541),x71543))) % 186.05/186.63 [7274]~E(f775(f775(f125(x72741),x72742),x72744),f775(f775(f125(x72741),x72743),x72745))+E(f775(f775(f159(x72741),f775(f181(f851(x72741)),x72742)),x72743),x72742)+P1(f775(f775(f232(a850),f775(f181(f851(x72741)),x72743)),f775(f181(f851(x72741)),x72742))) % 186.05/186.63 [7788]~E(f775(f775(f125(x77881),x77882),x77884),f775(f775(f125(x77881),x77883),x77885))+E(f775(f775(f159(x77881),f775(f181(f851(x77881)),x77882)),x77883),x77882)+~P1(f775(f775(f232(a850),f775(f181(f851(x77881)),x77882)),f775(f181(f851(x77881)),x77883))) % 186.05/186.63 [7812]~P1(f775(f63(x78121),f775(x78124,x78125)))+~P1(f775(f775(f334(x78122),x78125),x78123))+P1(f775(f63(x78121),f775(f775(f47(x78122,f857(x78121,a844)),x78123),x78124))) % 186.05/186.63 [7924]~E(f775(f181(f851(x79241)),x79242),f775(f181(f851(x79243)),x79244))+~E(f775(f166(x79241,x79243,f775(f775(f167(x79241,x79243),x79242),x79244)),x79245),f183(x79243))+~P1(f775(f775(f334(x79241),x79245),f775(f158(x79241),x79242))) % 186.05/186.63 [7990]~P47(x79901,x79903,x79905)+~P47(x79901,x79902,x79904)+P47(x79901,f775(f775(f103(f857(x79901,a844)),x79902),x79903),f775(f775(f103(f857(f856(x79901,x79901),a844)),x79904),x79905)) % 186.05/186.63 [7991]~P47(x79911,x79913,x79915)+~P47(x79911,x79912,x79914)+P47(x79911,f775(f775(f104(f857(x79911,a844)),x79912),x79913),f775(f775(f104(f857(f856(x79911,x79911),a844)),x79914),x79915)) % 186.05/186.63 [8339]E(f775(f775(f241(x83391,x83392),f775(f775(f153(x83391),x83393),x83394)),f775(f775(f153(x83392),x83395),x83394)),f775(f775(f153(f856(x83391,x83392)),f775(f775(f167(x83391,x83392),x83393),x83395)),x83394))+~P1(f775(f775(f233(a850),x83394),f775(f181(f851(x83391)),x83393)))+~P1(f775(f775(f233(a850),x83394),f775(f181(f851(x83392)),x83395))) % 186.05/186.63 [8499]~P47(x84991,x84993,x84994)+P1(f775(f775(f334(x84991),x84992),x84993))+~P1(f775(f775(f334(f856(x84991,x84991)),f775(f775(f241(x84991,x84991),x84995),x84992)),x84994)) % 186.05/186.63 [8500]~P47(x85001,x85003,x85004)+P1(f775(f775(f334(x85001),x85002),x85003))+~P1(f775(f775(f334(f856(x85001,x85001)),f775(f775(f241(x85001,x85001),x85002),x85005)),x85004)) % 186.05/186.63 [8501]~P12(x85011,x85013,x85014)+P1(f775(f775(f334(x85011),x85012),x85013))+~P1(f775(f775(f334(f856(x85011,x85011)),f775(f775(f241(x85011,x85011),x85015),x85012)),x85014)) % 186.05/186.63 [8502]~P12(x85021,x85023,x85024)+P1(f775(f775(f334(x85021),x85022),x85023))+~P1(f775(f775(f334(f856(x85021,x85021)),f775(f775(f241(x85021,x85021),x85022),x85025)),x85024)) % 186.05/186.63 [8738]~P12(x87381,x87385,x87382)+E(f775(f277(x87381,x87381,x87382),f775(f775(f302(x87381),x87383),f180(f857(x87381,a844)))),f775(f277(x87381,x87381,x87382),f775(f775(f302(x87381),x87384),f180(f857(x87381,a844)))))+~P1(f775(f775(f334(f856(x87381,x87381)),f775(f775(f241(x87381,x87381),x87383),x87384)),x87382)) % 186.05/186.63 [8902]P1(f775(x89021,x89022))+~P1(f775(f775(f334(x89023),x89022),x89025))+P1(f775(f775(f334(x89023),f382(x89021,x89024,x89025,x89023)),f775(f775(f103(f857(x89023,a844)),x89025),x89024))) % 186.05/186.63 [8903]P1(f775(x89031,x89032))+~P1(f775(f775(f334(x89033),x89032),x89034))+P1(f775(f775(f334(x89033),f382(x89031,x89034,x89035,x89033)),f775(f775(f103(f857(x89033,a844)),x89035),x89034))) % 186.05/186.63 [8911]~P1(f775(x89112,x89115))+~P1(f775(f775(f334(x89111),x89115),x89114))+P1(f775(f775(f334(x89111),f378(x89112,x89113,x89114,x89111)),f775(f775(f103(f857(x89111,a844)),x89114),x89113))) % 186.05/186.63 [8912]~P1(f775(x89122,x89125))+~P1(f775(f775(f334(x89121),x89125),x89123))+P1(f775(f775(f334(x89121),f378(x89122,x89123,x89124,x89121)),f775(f775(f103(f857(x89121,a844)),x89124),x89123))) % 186.05/186.63 [8925]~P1(f775(f775(f232(f857(x89251,a844)),x89255),x89253))+~P1(f775(f775(f232(f857(x89251,a844)),x89252),x89254))+P1(f775(f775(f232(f857(x89251,a844)),f775(f775(f3(f857(x89251,a844)),x89252),x89253)),f775(f775(f3(f857(x89251,a844)),x89254),x89255))) % 186.05/186.63 [8926]~P1(f775(f775(f232(f857(x89261,a844)),x89263),x89265))+~P1(f775(f775(f232(f857(x89261,a844)),x89262),x89264))+P1(f775(f775(f232(f857(x89261,a844)),f775(f775(f103(f857(x89261,a844)),x89262),x89263)),f775(f775(f103(f857(x89261,a844)),x89264),x89265))) % 186.05/186.63 [8927]~P1(f775(f775(f232(f857(x89271,a844)),x89273),x89275))+~P1(f775(f775(f232(f857(x89271,a844)),x89272),x89274))+P1(f775(f775(f232(f857(x89271,a844)),f775(f775(f104(f857(x89271,a844)),x89272),x89273)),f775(f775(f104(f857(x89271,a844)),x89274),x89275))) % 186.05/186.63 [9016]P1(f775(f775(f334(f856(x90161,x90161)),f775(f775(f241(x90161,x90161),x90162),x90163)),f327(x90161,x90164,x90165)))+~P1(f775(f775(f232(a850),f775(x90164,x90162)),f775(x90164,x90163)))+~P1(f775(f775(f334(f856(x90161,x90161)),f775(f775(f241(x90161,x90161),x90162),x90163)),x90165)) % 186.05/186.63 [9023]~E(f775(f181(f851(x90231)),x90233),f775(f181(f851(x90232)),x90234))+E(f775(f166(x90231,x90232,f775(f775(f167(x90231,x90232),x90233),x90234)),x90235),f775(f227(x90232),f716(x90235,x90234,x90232,x90233,x90231)))+~P1(f775(f775(f334(x90231),x90235),f775(f158(x90231),x90233))) % 186.05/186.63 [9172]P1(f775(f775(f334(f856(x91721,x91721)),f775(f775(f241(x91721,x91721),x91722),x91723)),f300(x91721,x91724)))+~P1(f775(f775(f334(f856(x91721,x91721)),f775(f775(f241(x91721,x91721),x91722),x91725)),f300(x91721,x91724)))+~P1(f775(f775(f334(f856(x91721,x91721)),f775(f775(f241(x91721,x91721),x91725),x91723)),x91724)) % 186.05/186.63 [9173]P1(f775(f775(f334(f856(x91731,x91731)),f775(f775(f241(x91731,x91731),x91732),x91733)),f300(x91731,x91734)))+~P1(f775(f775(f334(f856(x91731,x91731)),f775(f775(f241(x91731,x91731),x91735),x91733)),f300(x91731,x91734)))+~P1(f775(f775(f334(f856(x91731,x91731)),f775(f775(f241(x91731,x91731),x91732),x91735)),x91734)) % 186.05/186.63 [9267]E(x92671,x92672)+E(f775(a114,f643(x92673,x92674,x92671,x92672,x92675)),x92674)+~P1(f775(f775(f334(f856(x92675,x92675)),f775(f775(f241(x92675,x92675),x92672),x92671)),f775(f775(f173(f856(x92675,x92675),a844),x92674),x92673))) % 186.05/186.63 [9268]E(x92681,x92682)+E(f775(a114,f645(x92683,x92684,x92681,x92682,x92685)),x92684)+~P1(f775(f775(f334(f856(x92685,x92685)),f775(f775(f241(x92685,x92685),x92682),x92681)),f775(f775(f173(f856(x92685,x92685),a844),x92684),x92683))) % 186.05/186.63 [9269]E(x92691,f2(a850))+E(f775(a114,f643(x92692,x92691,x92693,x92694,x92695)),x92691)+~P1(f775(f775(f334(f856(x92695,x92695)),f775(f775(f241(x92695,x92695),x92694),x92693)),f775(f775(f173(f856(x92695,x92695),a844),x92691),x92692))) % 186.05/186.63 [9270]E(x92701,f2(a850))+E(f775(a114,f645(x92702,x92701,x92703,x92704,x92705)),x92701)+~P1(f775(f775(f334(f856(x92705,x92705)),f775(f775(f241(x92705,x92705),x92704),x92703)),f775(f775(f173(f856(x92705,x92705),a844),x92701),x92702))) % 186.05/186.63 [9289]P1(f775(f775(f334(f856(x92891,x92891)),f775(f775(f241(x92891,x92891),x92892),x92893)),f775(f775(f281(x92891,x92891,x92891),x92894),f300(x92891,x92894))))+~P1(f775(f775(f334(f856(x92891,x92891)),f775(f775(f241(x92891,x92891),x92892),x92895)),x92894))+~P1(f775(f775(f334(f856(x92891,x92891)),f775(f775(f241(x92891,x92891),x92895),x92893)),x92894)) % 186.05/186.63 [9298]~P1(f775(f775(f334(f856(x92981,x92981)),f775(f775(f241(x92981,x92981),x92982),x92985)),f300(x92981,x92984)))+P1(f775(f775(f334(f856(x92981,x92981)),f775(f775(f241(x92981,x92981),x92982),x92983)),f775(f775(f281(x92981,x92981,x92981),x92984),f300(x92981,x92984))))+~P1(f775(f775(f334(f856(x92981,x92981)),f775(f775(f241(x92981,x92981),x92985),x92983)),x92984)) % 186.05/186.63 [9335]~P12(x93351,x93355,x93352)+~P1(f775(f775(f334(f856(x93351,x93351)),f775(f775(f241(x93351,x93351),x93353),x93354)),x93352))+P1(f775(f775(f232(f857(x93351,a844)),f775(f277(x93351,x93351,x93352),f775(f775(f302(x93351),x93353),f180(f857(x93351,a844))))),f775(f277(x93351,x93351,x93352),f775(f775(f302(x93351),x93354),f180(f857(x93351,a844)))))) % 186.05/186.63 [9387]P1(f775(f775(f334(f856(x93871,x93871)),f775(f775(f241(x93871,x93871),x93872),x93873)),f775(f775(f281(x93871,x93871,x93871),x93874),f300(x93871,x93874))))+~P1(f775(f775(f334(f856(x93871,x93871)),f775(f775(f241(x93871,x93871),x93872),x93875)),f775(f775(f281(x93871,x93871,x93871),x93874),f300(x93871,x93874))))+~P1(f775(f775(f334(f856(x93871,x93871)),f775(f775(f241(x93871,x93871),x93875),x93873)),x93874)) % 186.05/186.63 [9388]P1(f775(f775(f334(f856(x93881,x93881)),f775(f775(f241(x93881,x93881),x93882),x93883)),f775(f775(f281(x93881,x93881,x93881),x93884),f300(x93881,x93884))))+~P1(f775(f775(f334(f856(x93881,x93881)),f775(f775(f241(x93881,x93881),x93885),x93883)),f775(f775(f281(x93881,x93881,x93881),x93884),f300(x93881,x93884))))+~P1(f775(f775(f334(f856(x93881,x93881)),f775(f775(f241(x93881,x93881),x93882),x93885)),x93884)) % 186.05/186.63 [9435]~P1(f775(f68(x94351,x94351,x94354,x94352,x94353),x94355))+P1(f775(f775(f334(x94351),x94352),x94353))+P1(f775(f64(x94351,x94354,f775(f775(f302(x94351),x94352),x94353)),x94355)) % 186.05/186.63 [9478]~E(f775(f303(x94783,x94782,x94785),x94784),x94781)+E(x94781,f180(f857(x94782,a844)))+P1(f775(f775(f232(f857(x94783,a844)),f775(f303(x94782,x94783,f522(x94784,x94783,x94782,x94781)),x94781)),x94784)) % 186.05/186.63 [9517]~P9(x95175)+P1(f775(f775(f334(x95171),f391(x95172,x95173,x95174,x95171,x95175)),x95174))+P1(f775(f775(f232(x95175),f775(f775(f46(x95171,x95175),x95174),x95173)),x95172)) % 186.05/186.63 [9679]E(x96791,x96792)+P1(f775(f775(f334(f856(x96793,x96793)),f775(f775(f241(x96793,x96793),x96791),f644(x96794,x96795,x96792,x96791,x96793))),x96794))+~P1(f775(f775(f334(f856(x96793,x96793)),f775(f775(f241(x96793,x96793),x96791),x96792)),f775(f775(f173(f856(x96793,x96793),a844),x96795),x96794))) % 186.05/186.63 [9680]E(x96801,f2(a850))+P1(f775(f775(f334(f856(x96802,x96802)),f775(f775(f241(x96802,x96802),x96803),f644(x96804,x96801,x96805,x96803,x96802))),x96804))+~P1(f775(f775(f334(f856(x96802,x96802)),f775(f775(f241(x96802,x96802),x96803),x96805)),f775(f775(f173(f856(x96802,x96802),a844),x96801),x96804))) % 186.05/186.63 [9724]~P9(x97241)+~P1(f775(f775(f232(x97241),f775(x97244,f391(x97245,x97244,x97243,x97242,x97241))),x97245))+P1(f775(f775(f232(x97241),f775(f775(f46(x97242,x97241),x97243),x97244)),x97245)) % 186.05/186.63 [9779]E(x97791,x97792)+P1(f775(f775(f334(f856(x97793,x97793)),f775(f775(f241(x97793,x97793),f646(x97794,x97795,x97791,x97792,x97793)),x97791)),x97794))+~P1(f775(f775(f334(f856(x97793,x97793)),f775(f775(f241(x97793,x97793),x97792),x97791)),f775(f775(f173(f856(x97793,x97793),a844),x97795),x97794))) % 186.05/186.63 [9780]E(x97801,f2(a850))+P1(f775(f775(f334(f856(x97802,x97802)),f775(f775(f241(x97802,x97802),f646(x97803,x97801,x97804,x97805,x97802)),x97804)),x97803))+~P1(f775(f775(f334(f856(x97802,x97802)),f775(f775(f241(x97802,x97802),x97805),x97804)),f775(f775(f173(f856(x97802,x97802),a844),x97801),x97803))) % 186.05/186.63 [9784]E(x97841,x97842)+P1(f775(f775(f334(f856(x97843,x97843)),f775(f775(f241(x97843,x97843),x97841),f646(x97844,x97845,x97842,x97841,x97843))),f775(f775(f173(f856(x97843,x97843),a844),f645(x97844,x97845,x97842,x97841,x97843)),x97844)))+~P1(f775(f775(f334(f856(x97843,x97843)),f775(f775(f241(x97843,x97843),x97841),x97842)),f775(f775(f173(f856(x97843,x97843),a844),x97845),x97844))) % 186.05/186.63 [9785]E(x97851,f2(a850))+P1(f775(f775(f334(f856(x97852,x97852)),f775(f775(f241(x97852,x97852),x97853),f646(x97854,x97851,x97855,x97853,x97852))),f775(f775(f173(f856(x97852,x97852),a844),f645(x97854,x97851,x97855,x97853,x97852)),x97854)))+~P1(f775(f775(f334(f856(x97852,x97852)),f775(f775(f241(x97852,x97852),x97853),x97855)),f775(f775(f173(f856(x97852,x97852),a844),x97851),x97854))) % 186.05/186.63 [9841]E(x98411,x98412)+P1(f775(f775(f334(f856(x98413,x98413)),f775(f775(f241(x98413,x98413),f644(x98414,x98415,x98411,x98412,x98413)),x98411)),f775(f775(f173(f856(x98413,x98413),a844),f643(x98414,x98415,x98411,x98412,x98413)),x98414)))+~P1(f775(f775(f334(f856(x98413,x98413)),f775(f775(f241(x98413,x98413),x98412),x98411)),f775(f775(f173(f856(x98413,x98413),a844),x98415),x98414))) % 186.05/186.63 [9842]E(x98421,f2(a850))+P1(f775(f775(f334(f856(x98422,x98422)),f775(f775(f241(x98422,x98422),f644(x98423,x98421,x98424,x98425,x98422)),x98424)),f775(f775(f173(f856(x98422,x98422),a844),f643(x98423,x98421,x98424,x98425,x98422)),x98423)))+~P1(f775(f775(f334(f856(x98422,x98422)),f775(f775(f241(x98422,x98422),x98425),x98424)),f775(f775(f173(f856(x98422,x98422),a844),x98421),x98423))) % 186.05/186.63 [9875]~P66(x98752)+~P1(f775(f63(x98751),x98755))+E(f775(f775(f8(x98751,x98752),f775(f775(f9(x98751,x98752,x98752),f775(f775(f20(x98751,x98752,f857(x98752,x98752)),f775(f775(f10(a844,f857(x98752,f857(x98752,x98752)),x98751),f98(x98752)),f775(f775(f9(x98751,f857(x98751,a844),a844),f334(x98751)),x98753))),x98754)),f2(x98752))),x98755),f775(f775(f8(x98751,x98752),x98754),f775(f775(f104(f857(x98751,a844)),x98755),x98753))) % 186.05/186.63 [8553]~P66(x85531)+~P1(f775(f63(x85534),x85535))+E(f775(f775(f82(x85531),f775(x85532,x85533)),f775(f775(f8(x85534,x85531),x85532),f775(f775(f3(f857(x85534,a844)),x85535),f775(f775(f302(x85534),x85533),f180(f857(x85534,a844)))))),f775(f775(f8(x85534,x85531),x85532),f775(f775(f302(x85534),x85533),x85535))) % 186.05/186.63 [8554]~P70(x85541)+~P1(f775(f63(x85544),x85545))+E(f775(f775(f83(x85541),f775(x85542,x85543)),f775(f775(f11(x85544,x85541),x85542),f775(f775(f3(f857(x85544,a844)),x85545),f775(f775(f302(x85544),x85543),f180(f857(x85544,a844)))))),f775(f775(f11(x85544,x85541),x85542),f775(f775(f302(x85544),x85543),x85545))) % 186.05/186.63 [8834]~P100(x88342)+~P18(x88342,f775(f142(x88342),f775(f775(f143(x88341,x88342),x88344),x88345)))+E(f775(f126(x88341,f775(f775(f10(x88342,a844,x88341),f775(f233(x88342),x88343)),x88344)),x88345),f162(x88341,f775(f775(f10(x88342,a844,x88341),f775(f233(x88342),x88343)),x88344),x88345)) % 186.05/186.63 [8855]~P66(x88551)+E(f775(f775(f82(x88551),f775(f775(f8(a850,x88551),x88552),f295(a850,x88553,x88554))),f775(f775(f8(a850,x88551),x88552),f295(a850,f775(f775(f82(a850),x88554),f80(a850)),f775(f775(f82(a850),x88554),x88555)))),f775(f775(f8(a850,x88551),x88552),f295(a850,x88553,f775(f775(f82(a850),x88554),x88555))))+~P1(f775(f775(f232(a850),x88553),f775(f775(f82(a850),x88554),f80(a850)))) % 186.05/186.63 [8856]~P1(f775(f775(f334(x88561),x88564),x88565))+~P1(f775(f775(f232(f857(x88561,a844)),f775(f158(x88561),x88562)),x88565))+P1(f775(f775(f232(f857(x88561,a844)),f775(f158(x88561),f775(f775(f148(x88561,x88562),x88563),x88564))),x88565)) % 186.05/186.63 [9073]~P9(x90732)+~P1(f775(f63(x90731),x90735))+E(f775(f775(f66(x90731,x90732,f775(f775(f10(x90732,f857(x90732,x90732),x90731),f103(x90732)),x90733)),x90734),x90735),f775(f775(f103(x90732),x90734),f775(f775(f46(x90731,x90732),x90735),x90733))) % 186.05/186.63 [9074]~P9(x90742)+~P1(f775(f63(x90741),x90745))+E(f775(f775(f66(x90741,x90742,f775(f775(f10(x90742,f857(x90742,x90742),x90741),f104(x90742)),x90743)),x90744),x90745),f775(f775(f104(x90742),x90744),f775(f775(f47(x90741,x90742),x90745),x90743))) % 186.05/186.63 [9159]~P29(x91591,x91592,x91593,x91595)+P29(x91591,x91592,x91593,f775(f775(f302(x91591),x91594),x91595))+P1(f775(f775(f334(x91592),f775(x91593,x91594)),f775(f303(x91591,x91592,x91593),f775(f775(f3(f857(x91591,a844)),x91595),f775(f775(f302(x91591),x91594),f180(f857(x91591,a844))))))) % 186.05/186.63 [9361]~P1(f775(f775(f334(f856(f851(x93611),f851(x93611))),f775(f775(f241(f851(x93611),f851(x93611)),x93612),x93614)),f147(x93611,x93615)))+~P1(f775(f775(f233(a850),x93613),f775(f181(f851(x93611)),x93612)))+P1(f775(f775(f334(f856(x93611,x93611)),f775(f775(f241(x93611,x93611),f775(f775(f153(x93611),x93612),x93613)),f775(f775(f153(x93611),x93614),x93613))),x93615)) % 186.05/186.63 [9587]E(x95871,f2(a1))+~P1(f775(f56(x95873,x95871),f775(f775(f241(a1,a1),x95874),x95875)))+P1(f775(f56(f775(f775(f83(a1),x95872),x95873),x95871),f775(f775(f241(a1,a1),f775(f775(f82(a1),f775(f775(f83(a1),x95872),x95874)),f775(f775(f43(a1),f775(f775(f83(a1),x95872),x95875)),x95871))),f52(a1,f775(f775(f83(a1),x95872),x95875),x95871)))) % 186.05/186.63 [9592]~P1(f775(f775(f233(a850),f2(a850)),x95923))+~P1(f775(f55(x95922,x95923),f775(f775(f241(a850,a850),x95924),x95925)))+P1(f775(f55(f775(f775(f83(a850),x95921),x95922),x95923),f775(f775(f241(a850,a850),f775(f775(f82(a850),f775(f775(f83(a850),x95921),x95924)),f775(f775(f43(a850),f775(f775(f83(a850),x95921),x95925)),x95923))),f52(a850,f775(f775(f83(a850),x95921),x95925),x95923)))) % 186.05/186.63 [9897]~P66(x98972)+~P1(f775(f63(x98971),x98974))+E(f775(f775(f8(x98971,x98972),x98973),f775(f256(x98971),f775(f775(f20(x98971,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98971),a331),f775(f775(f9(x98971,f857(x98971,a844),a844),f334(x98971)),x98974))),f775(f775(f9(x98971,f857(x98971,a844),a844),f334(x98971)),x98975)))),f775(f775(f8(x98971,x98972),f775(f775(f9(x98971,x98972,x98972),f775(f775(f20(x98971,x98972,f857(x98972,x98972)),f775(f775(f10(a844,f857(x98972,f857(x98972,x98972)),x98971),f98(x98972)),f775(f775(f9(x98971,f857(x98971,a844),a844),f334(x98971)),x98975))),x98973)),f2(x98972))),x98974)) % 186.05/186.63 [8191]~E(f775(f775(f125(x81911),x81912),x81915),f775(f775(f125(x81911),x81913),x81914))+E(f775(f775(f125(x81911),f775(f775(f128(x81911),f775(f181(f851(x81911)),x81912)),x81913)),x81914),x81915)+P1(f775(f775(f232(a850),f775(f181(f851(x81911)),x81913)),f775(f181(f851(x81911)),x81912))) % 186.05/186.63 [8390]~E(f775(f775(f125(x83902),x83903),x83901),f775(f775(f125(x83902),x83904),x83905))+E(x83901,f775(f775(f125(x83902),f775(f775(f128(x83902),f775(f181(f851(x83902)),x83903)),x83904)),x83905))+~P1(f775(f775(f232(a850),f775(f181(f851(x83902)),x83903)),f775(f181(f851(x83902)),x83904))) % 186.05/186.63 [8482]~E(f775(f775(f82(a850),f775(f775(f83(a850),x84823),x84824)),x84821),f775(f775(f82(a850),f775(f775(f83(a850),x84822),x84824)),x84825))+~P1(f775(f775(f232(a850),x84823),x84822))+E(x84821,f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x84822),x84823)),x84824)),x84825)) % 186.05/186.63 [8483]~E(f775(f775(f82(a850),f775(f775(f83(a850),x84831),x84833)),x84834),f775(f775(f82(a850),f775(f775(f83(a850),x84832),x84833)),x84835))+~P1(f775(f775(f232(a850),x84832),x84831))+E(f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x84831),x84832)),x84833)),x84834),x84835) % 186.05/186.63 [8623]E(f775(f775(f82(a850),f775(f775(f83(a850),x86231),x86232)),x86233),f775(f775(f82(a850),f775(f775(f83(a850),x86234),x86232)),x86235))+~P1(f775(f775(f232(a850),x86234),x86231))+~E(x86235,f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x86231),x86234)),x86232)),x86233)) % 186.05/186.63 [8624]E(f775(f775(f82(a850),f775(f775(f83(a850),x86241),x86242)),x86243),f775(f775(f82(a850),f775(f775(f83(a850),x86244),x86242)),x86245))+~P1(f775(f775(f232(a850),x86244),x86241))+~E(f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x86241),x86244)),x86242)),x86243),x86245) % 186.05/186.63 [8958]~P1(f775(f775(f279(a1),x89581),x89584))+~P1(f775(f775(f279(a1),x89581),f775(f775(f82(a1),x89582),x89585)))+P1(f775(f775(f279(a1),x89581),f775(f775(f82(a1),f775(f775(f82(a1),x89582),f775(f775(f83(a1),x89583),x89584))),x89585))) % 186.05/186.63 [9160]~P1(f775(f775(f279(a1),x91601),x91604))+P1(f775(f775(f279(a1),x91601),f775(f775(f82(a1),x91602),x91603)))+~P1(f775(f775(f279(a1),x91601),f775(f775(f82(a1),f775(f775(f82(a1),x91602),f775(f775(f83(a1),x91605),x91604))),x91603))) % 186.05/186.63 [9411]~P60(x94112)+~P1(f775(f63(x94111),x94115))+E(f775(f775(f11(x94111,x94112),f775(f775(f20(x94111,x94112,x94112),f775(f775(f10(x94112,f857(x94112,x94112),x94111),f283(x94112)),x94113)),x94114)),x94115),f775(f775(f283(x94112),f775(f775(f11(x94111,x94112),x94113),x94115)),f775(f775(f11(x94111,x94112),x94114),x94115))) % 186.05/186.63 [9531]~E(f648(x95315,x95314,x95313,x95312,x95311),f649(x95315,x95314,x95313,x95312,x95311))+P1(f775(f775(f334(f856(x95311,x95311)),f775(f775(f241(x95311,x95311),x95312),x95313)),f300(x95311,x95314)))+~P1(f775(f775(f334(f856(x95311,x95311)),f775(f775(f241(x95311,x95311),x95312),x95313)),f300(x95311,f775(f775(f103(f857(f856(x95311,x95311),a844)),x95314),x95315)))) % 186.05/186.63 [9532]~E(f657(x95325,x95324,x95323,x95322,x95321),f658(x95325,x95324,x95323,x95322,x95321))+P1(f775(f775(f334(f856(x95321,x95321)),f775(f775(f241(x95321,x95321),x95322),x95323)),f300(x95321,x95324)))+~P1(f775(f775(f334(f856(x95321,x95321)),f775(f775(f241(x95321,x95321),x95322),x95323)),f300(x95321,f775(f775(f103(f857(f856(x95321,x95321),a844)),x95324),x95325)))) % 186.05/186.63 [9712]P1(f775(f775(f334(f856(x97121,x97121)),f775(f775(f241(x97121,x97121),x97122),f658(x97125,x97124,x97123,x97122,x97121))),f300(x97121,x97124)))+P1(f775(f775(f334(f856(x97121,x97121)),f775(f775(f241(x97121,x97121),x97122),x97123)),f300(x97121,x97124)))+~P1(f775(f775(f334(f856(x97121,x97121)),f775(f775(f241(x97121,x97121),x97122),x97123)),f300(x97121,f775(f775(f103(f857(f856(x97121,x97121),a844)),x97124),x97125)))) % 186.05/186.63 [9806]P1(f775(f775(f334(f856(x98061,x98061)),f775(f775(f241(x98061,x98061),f649(x98065,x98064,x98063,x98062,x98061)),x98063)),f300(x98061,x98064)))+P1(f775(f775(f334(f856(x98061,x98061)),f775(f775(f241(x98061,x98061),x98062),x98063)),f300(x98061,x98064)))+~P1(f775(f775(f334(f856(x98061,x98061)),f775(f775(f241(x98061,x98061),x98062),x98063)),f300(x98061,f775(f775(f103(f857(f856(x98061,x98061),a844)),x98064),x98065)))) % 186.05/186.63 [9848]P1(f775(f775(f334(f856(x98481,x98481)),f775(f775(f241(x98481,x98481),x98482),x98483)),f300(x98481,x98484)))+P1(f775(f775(f334(f856(x98481,x98481)),f775(f775(f241(x98481,x98481),f648(x98485,x98484,x98483,x98482,x98481)),f649(x98485,x98484,x98483,x98482,x98481))),x98485))+~P1(f775(f775(f334(f856(x98481,x98481)),f775(f775(f241(x98481,x98481),x98482),x98483)),f300(x98481,f775(f775(f103(f857(f856(x98481,x98481),a844)),x98484),x98485)))) % 186.05/186.63 [9849]P1(f775(f775(f334(f856(x98491,x98491)),f775(f775(f241(x98491,x98491),x98492),x98493)),f300(x98491,x98494)))+P1(f775(f775(f334(f856(x98491,x98491)),f775(f775(f241(x98491,x98491),f658(x98495,x98494,x98493,x98492,x98491)),f657(x98495,x98494,x98493,x98492,x98491))),x98495))+~P1(f775(f775(f334(f856(x98491,x98491)),f775(f775(f241(x98491,x98491),x98492),x98493)),f300(x98491,f775(f775(f103(f857(f856(x98491,x98491),a844)),x98494),x98495)))) % 186.05/186.63 [9974]~P1(f775(f775(f334(f856(f851(x99741),f851(x99741))),f775(f775(f241(f851(x99741),f851(x99741)),x99744),x99745)),f147(x99741,x99742)))+~P1(f775(f775(f334(f856(x99741,x99741)),x99743),f775(f158(f856(x99741,x99741)),f775(f775(f167(x99741,x99741),x99744),x99745))))+P1(f775(f775(f251(x99741,x99741,a844),f775(f775(f9(x99741,f857(f856(x99741,x99741),a844),f857(x99741,a844)),f775(f775(f10(f857(x99741,f857(f857(f856(x99741,x99741),a844),a844)),f857(f857(f856(x99741,x99741),a844),f857(x99741,a844)),x99741),f9(x99741,f857(f856(x99741,x99741),a844),a844)),f775(f775(f10(f857(x99741,f856(x99741,x99741)),f857(x99741,f857(f857(f856(x99741,x99741),a844),a844)),x99741),f775(f10(f856(x99741,x99741),f857(f857(f856(x99741,x99741),a844),a844),x99741),f334(f856(x99741,x99741)))),f241(x99741,x99741)))),x99742)),x99743)) % 186.05/186.63 [9439]~P1(f775(f775(f232(a850),x94393),x94392))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),x94393),x94394)),x94391)),f775(f775(f82(a850),f775(f775(f83(a850),x94392),x94394)),x94395)))+P1(f775(f775(f233(a850),x94391),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x94392),x94393)),x94394)),x94395))) % 186.05/186.63 [9440]~P1(f775(f775(f232(a850),x94403),x94402))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),x94403),x94404)),x94401)),f775(f775(f82(a850),f775(f775(f83(a850),x94402),x94404)),x94405)))+P1(f775(f775(f232(a850),x94401),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x94402),x94403)),x94404)),x94405))) % 186.05/186.63 [9460]~P1(f775(f775(f232(a850),x94601),x94604))+P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),x94601),x94602)),x94603)),f775(f775(f82(a850),f775(f775(f83(a850),x94604),x94602)),x94605)))+~P1(f775(f775(f233(a850),x94603),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x94604),x94601)),x94602)),x94605))) % 186.05/186.63 [9461]~P1(f775(f775(f232(a850),x94611),x94614))+P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),x94611),x94612)),x94613)),f775(f775(f82(a850),f775(f775(f83(a850),x94614),x94612)),x94615)))+~P1(f775(f775(f232(a850),x94613),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x94614),x94611)),x94612)),x94615))) % 186.05/186.63 [9567]~P1(f775(f775(f232(a850),x95672),x95671))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),x95671),x95673)),x95674)),f775(f775(f82(a850),f775(f775(f83(a850),x95672),x95673)),x95675)))+P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x95671),x95672)),x95673)),x95674)),x95675)) % 186.05/186.63 [9568]~P1(f775(f775(f232(a850),x95682),x95681))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),x95681),x95683)),x95684)),f775(f775(f82(a850),f775(f775(f83(a850),x95682),x95683)),x95685)))+P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x95681),x95682)),x95683)),x95684)),x95685)) % 186.05/186.63 [9609]~P1(f775(f775(f232(a850),x96094),x96091))+P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),x96091),x96092)),x96093)),f775(f775(f82(a850),f775(f775(f83(a850),x96094),x96092)),x96095)))+~P1(f775(f775(f233(a850),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x96091),x96094)),x96092)),x96093)),x96095)) % 186.05/186.63 [9610]~P1(f775(f775(f232(a850),x96104),x96101))+P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),x96101),x96102)),x96103)),f775(f775(f82(a850),f775(f775(f83(a850),x96104),x96102)),x96105)))+~P1(f775(f775(f232(a850),f775(f775(f82(a850),f775(f775(f83(a850),f775(f775(f3(a850),x96101),x96104)),x96102)),x96103)),x96105)) % 186.05/186.63 [9833]~P16(x98331,x98332,x98335,x98333)+~P1(f775(f775(f334(f856(x98331,x98331)),x98334),x98335))+P1(f775(f775(f251(x98331,x98331,a844),f775(f775(f9(x98331,f857(x98331,x98332),f857(x98331,a844)),f775(f775(f10(f857(x98332,a844),f857(f857(x98331,x98332),f857(x98331,a844)),x98331),f10(x98332,a844,x98331)),f775(f775(f10(x98332,f857(x98332,a844),x98331),a330),x98333))),x98333)),x98334)) % 186.05/186.63 [7160]~P39(x71604,x71602,x71605,x71606)+P39(f33(x71601,x71603,x71604),x71602,x71605,x71606)+P1(f775(x71601,x71602)) % 186.05/186.63 [7240]~P39(x72402,x72404,x72405,x72406)+P39(f33(x72401,x72402,x72403),x72404,x72405,x72406)+~P1(f775(x72401,x72404)) % 186.05/186.63 [7331]P39(x73313,x73312,x73314,x73315)+~P39(f33(x73311,x73316,x73313),x73312,x73314,x73315)+P1(f775(x73311,x73312)) % 186.05/186.63 [7364]P39(x73641,x73642,x73643,x73644)+~P39(f33(x73645,x73641,x73646),x73642,x73643,x73644)+~P1(f775(x73645,x73642)) % 186.05/186.63 [7736]~P39(x77361,x77363,x77364,x77366)+~P39(x77362,x77366,x77364,x77365)+P39(f36(x77361,x77362),x77363,x77364,x77365) % 186.05/186.63 [7739]P39(x77391,x77392,x77393,x77394)+P39(x77395,x77392,x77393,x77394)+~P39(f33(x77396,x77391,x77395),x77392,x77393,x77394) % 186.05/186.63 [6710]~E(f775(x67104,x67105),f183(x67102))+E(f775(f170(x67101,x67102,x67103,x67104),x67105),f775(f227(x67102),x67106))+~E(f775(x67103,x67105),f775(f227(x67102),x67106)) % 186.05/186.63 [6817]~E(f775(x68173,x68176),f183(x68171))+E(f775(f229(f854(x68171),x68172,f183(x68171),x68173),f775(x68174,x68175)),f183(x68171))+~E(f775(x68174,x68175),f775(f227(x68172),x68176)) % 186.05/186.63 [7422]E(f775(x74221,x74222),f183(x74223))+~E(f775(f170(x74225,x74223,x74226,x74221),x74222),f775(f227(x74223),x74224))+E(f775(x74221,x74222),f775(f227(x74223),x74224)) % 186.05/186.63 [7460]~E(f775(f170(x74606,x74603,x74605,x74601),x74602),f775(f227(x74603),x74604))+E(f775(x74601,x74602),f775(f227(x74603),x74604))+E(f775(x74605,x74602),f775(f227(x74603),x74604)) % 186.05/186.63 [8351]~P23(x83516,x83511,x83512,x83514)+E(f775(f75(x83511,x83511,x83511,f775(x83512,x83513)),f775(x83514,x83515)),f775(f75(x83511,x83511,x83511,f775(x83514,x83515)),f775(x83512,x83513)))+~P1(f775(f63(x83516),x83515)) % 186.05/186.63 [8748]~P29(x87481,x87483,x87485,x87486)+~P29(x87483,x87482,x87484,f775(f303(x87481,x87483,x87485),x87486))+P29(x87481,x87482,f775(f75(x87483,x87482,x87481,x87484),x87485),x87486) % 186.05/186.63 [9252]~P1(f775(f775(x92523,x92522),x92526))+~P1(f775(f775(x92524,x92525),x92522))+P1(f775(f775(f334(x92521),x92522),f292(x92521,x92523,x92524,x92525,x92526))) % 186.05/186.63 [9253]~P1(f775(f775(x92534,x92532),x92536))+~P1(f775(f775(x92533,x92535),x92532))+P1(f775(f775(f334(x92531),x92532),f289(x92531,x92533,x92534,x92535,x92536))) % 186.05/186.63 [9362]E(x93621,x93622)+E(x93623,x93624)+~P1(f775(f775(f334(f856(f851(x93625),f851(x93625))),f775(f775(f241(f851(x93625),f851(x93625)),f775(f775(f140(x93625),x93623),x93621)),f775(f775(f140(x93625),x93624),x93622))),f146(x93625,x93626))) % 186.05/186.63 [9371]~E(x93712,x93714)+P1(f775(f775(f334(f856(f851(x93711),f851(x93711))),f775(f775(f241(f851(x93711),f851(x93711)),f775(f775(f140(x93711),x93712),x93713)),f775(f775(f140(x93711),x93714),x93715))),f135(x93711,x93716)))+~P1(f775(f775(f334(f856(f851(x93711),f851(x93711))),f775(f775(f241(f851(x93711),f851(x93711)),x93713),x93715)),f135(x93711,x93716))) % 186.05/186.63 [9372]~E(x93722,x93724)+P1(f775(f775(f334(f856(f851(x93721),f851(x93721))),f775(f775(f241(f851(x93721),f851(x93721)),f775(f775(f140(x93721),x93722),x93723)),f775(f775(f140(x93721),x93724),x93725))),f137(x93721,x93726)))+~P1(f775(f775(f334(f856(f851(x93721),f851(x93721))),f775(f775(f241(f851(x93721),f851(x93721)),x93723),x93725)),f137(x93721,x93726))) % 186.05/186.63 [9373]~E(x93732,x93734)+P1(f775(f775(f334(f856(f851(x93731),f851(x93731))),f775(f775(f241(f851(x93731),f851(x93731)),f775(f775(f140(x93731),x93732),x93733)),f775(f775(f140(x93731),x93734),x93735))),f146(x93731,x93736)))+~P1(f775(f775(f334(f856(f851(x93731),f851(x93731))),f775(f775(f241(f851(x93731),f851(x93731)),x93733),x93735)),f146(x93731,x93736))) % 186.05/186.63 [9374]~E(x93742,x93744)+P1(f775(f775(f334(f856(f851(x93741),f851(x93741))),f775(f775(f241(f851(x93741),f851(x93741)),f775(f775(f125(x93741),x93742),x93743)),f775(f775(f125(x93741),x93744),x93745))),f146(x93741,x93746)))+~P1(f775(f775(f334(f856(f851(x93741),f851(x93741))),f775(f775(f241(f851(x93741),f851(x93741)),x93743),x93745)),f146(x93741,x93746))) % 186.05/186.63 [9375]~E(x93753,x93755)+P1(f775(f775(f334(f856(f851(x93751),f851(x93751))),f775(f775(f241(f851(x93751),f851(x93751)),f775(f775(f125(x93751),x93752),x93753)),f775(f775(f125(x93751),x93754),x93755))),f146(x93751,x93756)))+~P1(f775(f775(f334(f856(f851(x93751),f851(x93751))),f775(f775(f241(f851(x93751),f851(x93751)),x93752),x93754)),f146(x93751,x93756))) % 186.05/186.63 [9428]E(x94281,x94282)+P1(f775(f775(f334(f856(f851(x94283),f851(x94283))),f775(f775(f241(f851(x94283),f851(x94283)),x94281),x94282)),f146(x94283,x94284)))+~P1(f775(f775(f334(f856(f851(x94283),f851(x94283))),f775(f775(f241(f851(x94283),f851(x94283)),f775(f775(f140(x94283),x94285),x94281)),f775(f775(f140(x94283),x94286),x94282))),f146(x94283,x94284))) % 186.05/186.63 [9569]~E(x95693,x95695)+P1(f775(f775(f334(f856(f851(x95691),f851(x95691))),f775(f775(f241(f851(x95691),f851(x95691)),f775(f775(f125(x95691),x95692),f775(f775(f140(x95691),x95693),f115(x95691)))),f775(f775(f125(x95691),x95694),f775(f775(f140(x95691),x95695),f115(x95691))))),f146(x95691,x95696)))+~P1(f775(f775(f334(f856(f851(x95691),f851(x95691))),f775(f775(f241(f851(x95691),f851(x95691)),x95692),x95694)),f146(x95691,x95696))) % 186.05/186.63 [9580]E(f775(x95801,x95802),f183(x95803))+~E(f775(f229(f854(x95806),x95803,f183(x95806),x95804),f775(x95801,x95802)),f183(x95806))+E(f775(x95804,f707(x95802,x95801,x95804,x95805,x95806,x95803)),f183(x95806)) % 186.05/186.63 [9581]E(f775(x95811,x95812),f183(x95813))+~E(f775(f229(f854(x95816),x95813,f183(x95816),x95814),f775(x95811,x95812)),f183(x95816))+E(f775(f227(x95813),f707(x95812,x95811,x95814,x95815,x95816,x95813)),f775(x95811,x95812)) % 186.05/186.63 [9613]E(x96131,x96132)+E(x96133,x96134)+~P1(f775(f775(f334(f856(f851(x96135),f851(x96135))),f775(f775(f241(f851(x96135),f851(x96135)),f775(f775(f125(x96135),x96133),f775(f775(f140(x96135),x96131),f115(x96135)))),f775(f775(f125(x96135),x96134),f775(f775(f140(x96135),x96132),f115(x96135))))),f146(x96135,x96136))) % 186.05/186.63 [9635]E(x96351,x96352)+~P1(f775(f775(f334(f856(f851(x96353),f851(x96353))),f775(f775(f241(f851(x96353),f851(x96353)),f775(f775(f125(x96353),x96351),f775(f775(f140(x96353),x96355),f115(x96353)))),f775(f775(f125(x96353),x96352),f775(f775(f140(x96353),x96356),f115(x96353))))),f146(x96353,x96354)))+P1(f775(f775(f334(f856(f851(x96353),f851(x96353))),f775(f775(f241(f851(x96353),f851(x96353)),x96351),x96352)),f146(x96353,x96354))) % 186.05/186.63 [9664]~P1(f775(f775(f334(f856(f857(x96641,a844),f857(x96641,a844))),f775(f775(f241(f857(x96641,a844),f857(x96641,a844)),x96642),x96644)),f324(x96641,x96646)))+~P1(f775(f775(f334(f856(f857(x96641,a844),f857(x96641,a844))),f775(f775(f241(f857(x96641,a844),f857(x96641,a844)),x96643),x96645)),f324(x96641,x96646)))+P1(f775(f775(f334(f856(f857(x96641,a844),f857(x96641,a844))),f775(f775(f241(f857(x96641,a844),f857(x96641,a844)),f775(f775(f103(f857(x96641,a844)),x96642),x96643)),f775(f775(f103(f857(x96641,a844)),x96644),x96645))),f324(x96641,x96646))) % 186.05/186.63 [5132]~E(f775(x51323,x51326),x51325)+~E(x51324,f775(f227(x51321),x51326))+E(f775(f775(f196(x51321,x51322),x51323),x51324),f775(f227(x51322),x51325)) % 186.05/186.63 [5530]~E(f775(f775(f125(x55301),x55306),x55303),x55305)+E(f775(f775(f125(x55301),x55302),x55303),f775(f775(f140(x55301),x55304),x55305))+~E(x55302,f775(f775(f140(x55301),x55304),x55306)) % 186.05/186.63 [5531]~E(f775(f775(f125(x55311),x55316),x55313),x55315)+E(f775(f775(f125(x55311),x55312),x55313),f775(f775(f125(x55311),x55314),x55315))+~E(x55312,f775(f775(f125(x55311),x55314),x55316)) % 186.05/186.63 [5533]E(f775(f775(f125(x55331),x55332),x55333),f775(f775(f140(x55331),x55334),x55335))+~E(f775(f775(f140(x55331),x55334),x55336),x55332)+~E(x55335,f775(f775(f125(x55331),x55336),x55333)) % 186.05/186.63 [5535]~E(f775(f775(f125(x55351),x55352),x55356),x55354)+E(f775(f775(f125(x55351),x55352),x55353),f775(f775(f125(x55351),x55354),x55355))+~E(x55353,f775(f775(f125(x55351),x55356),x55355)) % 186.05/186.63 [6703]E(f775(x67031,x67032),f775(x67033,x67032))+~E(f775(f775(f143(x67034,x67035),x67031),x67036),f775(f775(f143(x67034,x67035),x67033),x67036))+~P1(f775(f775(f334(x67034),x67032),f775(f158(x67034),x67036))) % 186.05/186.63 [7096]~P23(x70964,x70965,x70966,x70961)+E(f775(f775(x70961,x70962),x70963),f775(f775(f66(x70964,x70965,x70966),x70963),x70962))+~P1(f775(f63(x70964),x70962)) % 186.05/186.63 [7165]~E(x71652,f775(x71654,x71656))+~P1(f775(f775(f334(x71653),x71656),x71655))+P1(f775(f775(f334(x71651),x71652),f775(f303(x71653,x71651,x71654),x71655))) % 186.05/186.63 [7166]~E(f775(x71664,x71662),x71666)+~P1(f775(f775(f334(x71663),x71666),x71665))+P1(f775(f775(f334(x71661),x71662),f775(f305(x71661,x71663,x71664),x71665))) % 186.05/186.63 [7642]~P34(x76421,x76422,x76424,x76426)+P34(x76421,x76422,f775(f775(f140(x76421),x76423),x76424),f775(f775(f140(x76421),x76425),x76426))+~P1(f775(f775(x76422,x76423),x76425)) % 186.05/186.63 [8631]~P55(x86314,x86315,x86311,x86312,x86316)+E(f775(x86311,f775(x86312,x86313)),x86313)+~P1(f775(f775(f334(x86315),x86313),x86316)) % 186.05/186.63 [9364]E(x93641,x93642)+E(f775(f181(f851(x93643)),x93644),f775(f181(f851(x93643)),x93645))+~P1(f775(f775(f334(f856(f851(x93643),f851(x93643))),f775(f775(f241(f851(x93643),f851(x93643)),f775(f775(f140(x93643),x93641),x93644)),f775(f775(f140(x93643),x93642),x93645))),f135(x93643,x93646))) % 186.05/186.63 [9425]~P20(x94251,x94252,x94253)+E(f775(f775(f66(x94251,x94252,x94253),x94254),x94255),x94256)+~P1(f775(f68(x94251,x94252,x94253,x94254,x94255),x94256)) % 186.05/186.63 [9431]E(f775(f181(f851(x94311)),x94312),f775(f181(f851(x94311)),x94313))+P1(f775(f775(f334(f856(f851(x94311),f851(x94311))),f775(f775(f241(f851(x94311),f851(x94311)),x94312),x94313)),f135(x94311,x94314)))+~P1(f775(f775(f334(f856(f851(x94311),f851(x94311))),f775(f775(f241(f851(x94311),f851(x94311)),f775(f775(f140(x94311),x94315),x94312)),f775(f775(f140(x94311),x94316),x94313))),f135(x94311,x94314))) % 186.05/186.63 [9452]~P1(f775(f775(f334(f856(x94521,x94521)),f775(f775(f241(x94521,x94521),x94522),x94524)),f300(x94521,x94526)))+P1(f775(f775(f334(f856(f851(x94521),f851(x94521))),f775(f775(f241(f851(x94521),f851(x94521)),f775(f775(f140(x94521),x94522),x94523)),f775(f775(f140(x94521),x94524),x94525))),f300(f851(x94521),f146(x94521,x94526))))+~P1(f775(f775(f334(f856(f851(x94521),f851(x94521))),f775(f775(f241(f851(x94521),f851(x94521)),x94523),x94525)),f300(f851(x94521),f146(x94521,x94526)))) % 186.05/186.63 [9925]~P66(x99252)+E(f775(f775(f8(x99251,x99252),f775(f775(f10(f857(x99253,a844),x99252,x99251),f775(f8(x99253,x99252),x99254)),f775(f775(f10(f857(x99253,a844),f857(x99253,a844),x99251),f256(x99253)),f775(f775(f10(f857(x99253,a844),f857(x99253,a844),x99251),f775(f20(x99253,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99253),a331),f775(f775(f9(x99253,f857(x99253,a844),a844),f334(x99253)),x99255)))),f775(f9(x99253,x99251,a844),f775(f775(f10(x99251,f857(x99251,a844),x99253),a330),x99256)))))),f775(f303(x99253,x99251,x99256),x99255)),f775(f775(f8(x99253,x99252),x99254),x99255))+~P1(f775(f63(x99253),x99255)) % 186.05/186.63 [6764]~P100(x67643)+P1(f775(x67642,x67645))+E(f775(f126(x67641,x67642),f775(f775(f138(x67641,x67643,x67644),x67645),x67646)),f775(f126(x67641,x67642),x67646)) % 186.05/186.63 [6766]P1(f775(x67661,x67662))+~E(f156(x67663,x67661,x67664),f775(f775(f241(f851(x67663),f851(x67663)),x67665),x67666))+~P1(f775(f775(f334(x67663),x67662),f775(f158(x67663),x67665))) % 186.05/186.63 [6814]~P1(f775(x68142,x68146))+~E(f156(x68141,x68142,x68143),f775(f775(f241(f851(x68141),f851(x68141)),x68144),x68145))+~P1(f775(f775(f334(x68141),x68146),f775(f158(x68141),x68145))) % 186.05/186.63 [7505]~P19(x75051,x75052,x75053)+~P1(f775(f63(x75051),x75056))+E(f775(f775(f66(x75051,x75052,x75053),x75054),f775(f775(f302(x75051),x75055),x75056)),f775(f775(f66(x75051,x75052,x75053),f775(f775(x75053,x75055),x75054)),x75056)) % 186.05/186.63 [7557]~P100(x75572)+~P1(f775(f775(f232(x75572),f775(x75573,x75574)),f775(x75573,x75575)))+E(f775(f775(f138(x75571,x75572,x75573),x75574),f775(f775(f140(x75571),x75575),x75576)),f775(f775(f140(x75571),x75574),f775(f775(f140(x75571),x75575),x75576))) % 186.05/186.63 [7673]E(x76731,x76732)+~E(f775(f775(f248(x76733,x76734),x76731),f775(f18(f857(x76734,a844),x76733),x76735)),f775(f775(f248(x76733,x76734),x76732),f775(f18(f857(x76734,a844),x76733),x76735)))+~P1(f775(f775(f334(x76734),x76736),x76735)) % 186.05/186.63 [7741]~P19(x77411,x77412,x77413)+~P1(f775(f63(x77411),x77416))+E(f775(f775(f66(x77411,x77412,x77413),x77414),f775(f775(f302(x77411),x77415),x77416)),f775(f775(x77413,x77415),f775(f775(f66(x77411,x77412,x77413),x77414),x77416))) % 186.05/186.63 [7857]~P20(x78571,x78572,x78573)+~P1(f775(f63(x78571),x78576))+E(f775(f775(f66(x78571,x78572,x78573),f775(f775(x78573,x78574),x78575)),x78576),f775(f775(x78573,x78574),f775(f775(f66(x78571,x78572,x78573),x78575),x78576))) % 186.05/186.63 [7925]~P24(x79252,x79255,x79256,x79251)+~P1(f775(f63(x79252),x79254))+E(f775(x79251,f775(f775(f302(x79252),x79253),x79254)),f775(f75(x79255,x79255,x79255,f775(x79251,x79254)),f775(x79256,x79253))) % 186.05/186.63 [7963]~P100(x79632)+P1(f775(f775(f232(x79632),f775(x79633,x79634)),f775(x79633,x79635)))+E(f775(f775(f138(x79631,x79632,x79633),x79634),f775(f775(f140(x79631),x79635),x79636)),f775(f775(f140(x79631),x79635),f775(f775(f138(x79631,x79632,x79633),x79634),x79636))) % 186.05/186.63 [8096]~E(f775(f181(f851(x80961)),x80965),f775(f181(f851(x80962)),x80966))+~E(f775(f181(f851(x80961)),x80963),f775(f181(f851(x80962)),x80964))+E(f775(f775(f125(f856(x80961,x80962)),f775(f775(f167(x80961,x80962),x80963),x80964)),f775(f775(f167(x80961,x80962),x80965),x80966)),f775(f775(f167(x80961,x80962),f775(f775(f125(x80961),x80963),x80965)),f775(f775(f125(x80962),x80964),x80966))) % 186.05/186.63 [8205]~E(x82052,f775(f303(x82053,x82051,x82054),x82056))+P1(f775(f775(f232(f857(x82051,a844)),x82052),f775(f303(x82053,x82051,x82054),x82055)))+~P1(f775(f775(f232(f857(x82053,a844)),x82056),x82055)) % 186.05/186.63 [8307]~P100(x83075)+E(f775(x83071,x83072),f775(x83071,x83073))+E(f775(f775(f138(x83074,x83075,x83071),x83072),f775(f775(f138(x83074,x83075,x83071),x83073),x83076)),f775(f775(f138(x83074,x83075,x83071),x83073),f775(f775(f138(x83074,x83075,x83071),x83072),x83076))) % 186.05/186.63 [8344]~P29(x83443,x83441,x83444,x83445)+P29(x83443,x83441,f775(f775(f775(f74(x83443,x83441),x83444),x83446),x83442),x83445)+P1(f775(f775(f334(x83441),x83442),f775(f303(x83443,x83441,x83444),x83445))) % 186.05/186.63 [8491]~P1(f775(f775(f334(x84912),x84914),f775(x84916,x84913)))+~P1(f775(f775(f334(x84911),x84913),x84915))+P1(f775(f775(f334(f856(x84911,x84912)),f775(f775(f241(x84911,x84912),x84913),x84914)),f775(f775(f248(x84911,x84912),x84915),x84916))) % 186.05/186.63 [8900]~P66(x89002)+~P29(x89004,x89001,x89005,x89006)+E(f775(f775(f8(x89001,x89002),x89003),f775(f303(x89004,x89001,x89005),x89006)),f775(f775(f8(x89004,x89002),f775(f75(x89001,x89002,x89004,x89003),x89005)),x89006)) % 186.05/186.63 [8901]~P70(x89012)+~P29(x89014,x89011,x89015,x89016)+E(f775(f775(f11(x89011,x89012),x89013),f775(f303(x89014,x89011,x89015),x89016)),f775(f775(f11(x89014,x89012),f775(f75(x89011,x89012,x89014,x89013),x89015)),x89016)) % 186.05/186.63 [9140]~P23(x91403,x91401,x91406,x91402)+~P1(f775(f63(x91403),x91404))+E(f775(f75(x91401,x91401,x91401,f775(x91402,f775(f775(f3(f857(x91403,a844)),x91404),f775(f775(f302(x91403),x91405),f180(f857(x91403,a844)))))),f775(x91406,x91405)),f775(x91402,f775(f775(f302(x91403),x91405),x91404))) % 186.05/186.63 [9693]~E(f775(f303(x96932,x96934,x96936),f239(f857(x96932,a844))),f239(f857(x96934,a844)))+~E(f775(f303(x96931,x96933,x96935),f239(f857(x96931,a844))),f239(f857(x96933,a844)))+E(f775(f303(f856(x96931,x96932),f856(x96933,x96934),f252(x96931,x96933,x96932,x96934,x96935,x96936)),f239(f857(f856(x96931,x96932),a844))),f239(f857(f856(x96933,x96934),a844))) % 186.05/186.63 [9755]~P29(x97553,x97554,x97555,f775(x97556,f691(x97556,x97555,x97554,x97553,x97552,x97551)))+P29(x97553,x97554,x97555,f775(f775(f47(x97552,f857(x97553,a844)),x97551),x97556))+E(x97551,f180(f857(x97552,a844))) % 186.05/186.63 [9812]P29(x98126,x98125,x98124,f775(f775(f47(x98122,f857(x98126,a844)),x98121),x98123))+E(x98121,f180(f857(x98122,a844)))+P1(f775(f775(f334(x98122),f691(x98123,x98124,x98125,x98126,x98122,x98121)),x98121)) % 186.05/186.63 [9819]P1(f775(f775(f334(x98191),f621(x98192,x98193,x98194,x98195,x98196,x98191)),x98196))+P1(f775(f775(f232(f857(f856(x98191,x98194),a844)),f775(f775(f248(x98191,x98194),x98196),x98193)),f775(f775(f248(x98191,x98194),x98195),x98192)))+~P1(f775(f775(f232(f857(x98191,a844)),x98196),x98195)) % 186.05/186.63 [9862]P28(x98626,x98625,f775(f775(f302(f849(x98626)),f775(f775(f775(f93(x98626),x98624),x98623),x98622)),f180(f857(f849(x98626),a844))))+~P28(x98626,x98625,f775(f775(f302(f849(x98626)),f775(f775(f775(f93(x98626),x98624),x98623),x98621)),f180(f857(f849(x98626),a844))))+P1(f775(f775(x98621,f541(x98622,x98621,x98623,x98624,x98625,x98626)),f542(x98622,x98621,x98623,x98624,x98625,x98626))) % 186.05/186.63 [9863]P28(x98636,x98635,f775(f775(f302(f849(x98636)),f775(f775(f775(f93(x98636),x98631),x98633),x98632)),f180(f857(f849(x98636),a844))))+~P28(x98636,x98635,f775(f775(f302(f849(x98636)),f775(f775(f775(f93(x98636),x98634),x98633),x98632)),f180(f857(f849(x98636),a844))))+P1(f775(f775(x98631,f543(x98631,x98632,x98633,x98634,x98635,x98636)),f544(x98631,x98632,x98633,x98634,x98635,x98636))) % 186.05/186.63 [9900]~P28(x99001,x99002,f775(f775(f302(f849(x99001)),f775(f775(f775(f93(x99001),x99003),x99004),x99006)),f180(f857(f849(x99001),a844))))+P28(x99001,x99002,f775(f775(f302(f849(x99001)),f775(f775(f775(f93(x99001),x99003),x99004),x99005)),f180(f857(f849(x99001),a844))))+~P1(f775(f775(x99005,f541(x99005,x99006,x99004,x99003,x99002,x99001)),f542(x99005,x99006,x99004,x99003,x99002,x99001))) % 186.05/186.63 [9901]~P28(x99011,x99012,f775(f775(f302(f849(x99011)),f775(f775(f775(f93(x99011),x99016),x99014),x99015)),f180(f857(f849(x99011),a844))))+P28(x99011,x99012,f775(f775(f302(f849(x99011)),f775(f775(f775(f93(x99011),x99013),x99014),x99015)),f180(f857(f849(x99011),a844))))+~P1(f775(f775(x99016,f543(x99013,x99015,x99014,x99016,x99012,x99011)),f544(x99013,x99015,x99014,x99016,x99012,x99011))) % 186.05/186.63 [9942]~P1(f775(f775(f232(f857(x99422,a844)),f775(x99424,f621(x99426,x99424,x99422,x99425,x99423,x99421))),f775(x99426,f621(x99426,x99424,x99422,x99425,x99423,x99421))))+~P1(f775(f775(f232(f857(x99421,a844)),x99423),x99425))+P1(f775(f775(f232(f857(f856(x99421,x99422),a844)),f775(f775(f248(x99421,x99422),x99423),x99424)),f775(f775(f248(x99421,x99422),x99425),x99426))) % 186.05/186.63 [7690]~P1(f775(x76901,x76905))+~P1(f775(x76906,x76904))+P1(f775(x76901,f775(f250(x76902,x76903),f775(f775(f241(x76902,x76903),x76904),x76905)))) % 186.05/186.63 [7691]~P1(f775(x76911,x76914))+~P1(f775(x76916,x76915))+P1(f775(x76911,f775(f240(x76912,x76913),f775(f775(f241(x76912,x76913),x76914),x76915)))) % 186.05/186.63 [7746]~P1(f775(f775(x77464,x77466),x77465))+~P1(f775(f775(f334(x77461),x77466),x77463))+P1(f775(f775(f775(f46(x77461,f857(x77462,a844)),x77463),x77464),x77465)) % 186.05/186.63 [7779]~E(f775(f181(f851(x77791)),x77793),f775(f181(f851(x77794)),x77795))+~E(f775(f166(x77791,x77794,f775(f775(f167(x77791,x77794),x77793),x77795)),x77792),f775(f227(x77794),x77796))+P1(f775(f775(f334(x77791),x77792),f775(f158(x77791),x77793))) % 186.05/186.63 [8049]~P1(f775(f775(f334(x80491),x80492),f775(x80495,x80496)))+~P1(f775(f775(f334(x80493),x80496),x80494))+P1(f775(f775(f334(x80491),x80492),f775(f775(f46(x80493,f857(x80491,a844)),x80494),x80495))) % 186.05/186.63 [8089]P1(f775(f775(x80891,x80892),x80893))+~P1(f775(f775(x80894,x80892),x80893))+~P1(f775(f775(f232(f857(x80895,f857(x80896,a844))),x80894),x80891)) % 186.05/186.63 [8229]P1(f775(f775(x82291,x82292),x82293))+~P1(f775(f775(f334(x82294),x82292),x82295))+~P1(f775(f775(f775(f47(x82294,f857(x82296,a844)),x82295),x82291),x82293)) % 186.05/186.63 [8367]P1(f775(f775(f334(x83671),x83672),f775(x83673,x83674)))+~P1(f775(f775(f334(x83675),x83674),x83676))+~P1(f775(f775(f334(x83671),x83672),f775(f775(f47(x83675,f857(x83671,a844)),x83676),x83673))) % 186.05/186.63 [8613]~P16(x86134,x86135,x86136,x86131)+E(f775(x86131,x86132),f775(x86131,x86133))+~P1(f775(f775(f334(f856(x86134,x86134)),f775(f775(f241(x86134,x86134),x86132),x86133)),x86136)) % 186.05/186.63 [8644]P1(f775(f775(f232(f857(x86441,a844)),x86442),f775(x86443,x86444)))+~P1(f775(f775(f334(x86445),x86444),x86446))+~P1(f775(f775(f232(f857(x86441,a844)),x86442),f775(f775(f47(x86445,f857(x86441,a844)),x86446),x86443))) % 186.05/186.63 [8669]~P53(x86693,x86694,f775(f278(x86694,x86693),x86695))+E(x86691,f180(f857(x86692,a844)))+E(f775(f775(f47(x86692,f857(x86693,a844)),x86691),f775(f775(f10(f857(x86694,a844),f857(x86693,a844),x86692),f277(x86694,x86693,x86695)),x86696)),f775(f277(x86694,x86693,x86695),f775(f775(f47(x86692,f857(x86694,a844)),x86691),x86696))) % 186.05/186.63 [8741]P1(f775(f775(f334(x87411),x87412),f775(f277(x87413,x87411,x87414),x87415)))+~P1(f775(f775(f334(x87413),x87416),x87415))+~P1(f775(f775(f334(f856(x87413,x87411)),f775(f775(f241(x87413,x87411),x87416),x87412)),x87414)) % 186.05/186.63 [9018]P1(f775(f775(f232(f857(x90181,a844)),f775(f277(x90182,x90181,x90183),x90184)),f775(f277(x90182,x90181,x90185),x90186)))+~P1(f775(f775(f232(f857(x90182,a844)),x90184),x90186))+~P1(f775(f775(f232(f857(f856(x90182,x90181),a844)),x90183),x90185)) % 186.05/186.63 [9174]~P1(f775(f775(f334(x91742),x91746),x91744))+~P1(f775(f775(f232(f857(x91741,a844)),x91743),x91745))+P1(f775(f775(f232(f857(f856(x91741,x91742),a844)),f775(f775(f248(x91741,x91742),x91743),f775(f18(f857(x91742,a844),x91741),x91744))),f775(f775(f248(x91741,x91742),x91745),f775(f18(f857(x91742,a844),x91741),x91744)))) % 186.05/186.63 [9322]~E(x93223,x93225)+P1(f775(f775(f334(f856(f851(x93221),f851(x93221))),f775(f775(f241(f851(x93221),f851(x93221)),f775(f775(f140(x93221),x93222),x93223)),f775(f775(f140(x93221),x93224),x93225))),f146(x93221,x93226)))+~P1(f775(f775(f334(f856(x93221,x93221)),f775(f775(f241(x93221,x93221),x93222),x93224)),x93226)) % 186.05/186.63 [9328]~E(f775(f181(f851(x93281)),x93283),f775(f181(f851(x93281)),x93285))+P1(f775(f775(f334(f856(f851(x93281),f851(x93281))),f775(f775(f241(f851(x93281),f851(x93281)),f775(f775(f140(x93281),x93282),x93283)),f775(f775(f140(x93281),x93284),x93285))),f135(x93281,x93286)))+~P1(f775(f775(f334(f856(x93281,x93281)),f775(f775(f241(x93281,x93281),x93282),x93284)),x93286)) % 186.05/186.63 [9356]P1(f775(f775(f334(f856(x93561,x93561)),f775(f775(f241(x93561,x93561),x93562),x93563)),f775(f775(f173(f856(x93561,x93561),a844),f775(a114,x93564)),x93565)))+~P1(f775(f775(f334(f856(x93561,x93561)),f775(f775(f241(x93561,x93561),x93566),x93563)),x93565))+~P1(f775(f775(f334(f856(x93561,x93561)),f775(f775(f241(x93561,x93561),x93562),x93566)),f775(f775(f173(f856(x93561,x93561),a844),x93564),x93565))) % 186.05/186.63 [9357]P1(f775(f775(f334(f856(x93571,x93571)),f775(f775(f241(x93571,x93571),x93572),x93573)),f775(f775(f173(f856(x93571,x93571),a844),f775(a114,x93574)),x93575)))+~P1(f775(f775(f334(f856(x93571,x93571)),f775(f775(f241(x93571,x93571),x93572),x93576)),x93575))+~P1(f775(f775(f334(f856(x93571,x93571)),f775(f775(f241(x93571,x93571),x93576),x93573)),f775(f775(f173(f856(x93571,x93571),a844),x93574),x93575))) % 186.05/186.63 [9360]~P1(f775(f775(f334(x93604),x93605),x93606))+P1(f775(f775(f232(f857(x93601,a844)),x93602),x93603))+~P1(f775(f775(f232(f857(f856(x93601,x93604),a844)),f775(f775(f248(x93601,x93604),x93602),f775(f18(f857(x93604,a844),x93601),x93606))),f775(f775(f248(x93601,x93604),x93603),f775(f18(f857(x93604,a844),x93601),x93606)))) % 186.05/186.63 [9400]E(x94001,x94002)+~P1(f775(f775(f334(f856(f851(x94003),f851(x94003))),f775(f775(f241(f851(x94003),f851(x94003)),f775(f775(f140(x94003),x94001),x94005)),f775(f775(f140(x94003),x94002),x94006))),f135(x94003,x94004)))+P1(f775(f775(f334(f856(x94003,x94003)),f775(f775(f241(x94003,x94003),x94001),x94002)),x94004)) % 186.05/186.63 [9401]E(x94011,x94012)+~P1(f775(f775(f334(f856(f851(x94013),f851(x94013))),f775(f775(f241(f851(x94013),f851(x94013)),f775(f775(f140(x94013),x94011),x94015)),f775(f775(f140(x94013),x94012),x94016))),f137(x94013,x94014)))+P1(f775(f775(f334(f856(x94013,x94013)),f775(f775(f241(x94013,x94013),x94011),x94012)),x94014)) % 186.05/186.63 [9402]E(x94021,x94022)+~P1(f775(f775(f334(f856(f851(x94023),f851(x94023))),f775(f775(f241(f851(x94023),f851(x94023)),f775(f775(f140(x94023),x94021),x94025)),f775(f775(f140(x94023),x94022),x94026))),f146(x94023,x94024)))+P1(f775(f775(f334(f856(x94023,x94023)),f775(f775(f241(x94023,x94023),x94021),x94022)),x94024)) % 186.05/186.63 [9438]P1(f775(f775(f334(f856(f851(x94381),f851(x94381))),f775(f775(f241(f851(x94381),f851(x94381)),f775(f775(f140(x94381),x94382),x94383)),f775(f775(f140(x94381),x94384),x94385))),f147(x94381,x94386)))+~P1(f775(f775(f334(f856(f851(x94381),f851(x94381))),f775(f775(f241(f851(x94381),f851(x94381)),x94383),x94385)),f147(x94381,x94386)))+~P1(f775(f775(f334(f856(x94381,x94381)),f775(f775(f241(x94381,x94381),x94382),x94384)),x94386)) % 186.05/186.63 [9458]P1(f775(x94581,x94582))+~P1(f775(x94581,f388(x94581,x94583,x94584,x94585,x94586)))+~P1(f775(f775(f334(x94586),x94582),f775(f775(f46(x94585,f857(x94586,a844)),x94584),x94583))) % 186.05/186.63 [9463]~P1(f775(f775(f334(f856(f851(x94631),f851(x94631))),f775(f775(f241(f851(x94631),f851(x94631)),f775(f775(f140(x94631),x94632),x94635)),f775(f775(f140(x94631),x94633),x94636))),f135(x94631,x94634)))+P1(f775(f775(f334(f856(f851(x94631),f851(x94631))),f775(f775(f241(f851(x94631),f851(x94631)),x94635),x94636)),f135(x94631,x94634)))+P1(f775(f775(f334(f856(x94631,x94631)),f775(f775(f241(x94631,x94631),x94632),x94633)),x94634)) % 186.05/186.63 [9464]~P1(f775(f775(f334(f856(f851(x94641),f851(x94641))),f775(f775(f241(f851(x94641),f851(x94641)),f775(f775(f140(x94641),x94642),x94645)),f775(f775(f140(x94641),x94643),x94646))),f137(x94641,x94644)))+P1(f775(f775(f334(f856(f851(x94641),f851(x94641))),f775(f775(f241(f851(x94641),f851(x94641)),x94645),x94646)),f137(x94641,x94644)))+P1(f775(f775(f334(f856(x94641,x94641)),f775(f775(f241(x94641,x94641),x94642),x94643)),x94644)) % 186.05/186.63 [9465]~P1(f775(f775(f334(f856(f851(x94651),f851(x94651))),f775(f775(f241(f851(x94651),f851(x94651)),f775(f775(f140(x94651),x94652),x94655)),f775(f775(f140(x94651),x94653),x94656))),f146(x94651,x94654)))+P1(f775(f775(f334(f856(f851(x94651),f851(x94651))),f775(f775(f241(f851(x94651),f851(x94651)),x94655),x94656)),f146(x94651,x94654)))+P1(f775(f775(f334(f856(x94651,x94651)),f775(f775(f241(x94651,x94651),x94652),x94653)),x94654)) % 186.05/186.63 [9541]P1(f775(x95411,x95412))+P1(f775(f775(f334(x95413),f389(x95411,x95414,x95415,x95413,x95416)),x95415))+~P1(f775(f775(f334(x95416),x95412),f775(f775(f46(x95413,f857(x95416,a844)),x95415),x95414))) % 186.05/186.63 [9547]~E(x95472,x95474)+P1(f775(f775(f334(f856(f851(x95471),f851(x95471))),f775(f775(f241(f851(x95471),f851(x95471)),f775(f775(f125(x95471),x95472),f775(f775(f140(x95471),x95473),f115(x95471)))),f775(f775(f125(x95471),x95474),f775(f775(f140(x95471),x95475),f115(x95471))))),f146(x95471,x95476)))+~P1(f775(f775(f334(f856(x95471,x95471)),f775(f775(f241(x95471,x95471),x95473),x95475)),x95476)) % 186.05/186.63 [9627]E(x96271,x96272)+~P1(f775(f775(f334(f856(f851(x96273),f851(x96273))),f775(f775(f241(f851(x96273),f851(x96273)),f775(f775(f125(x96273),x96275),f775(f775(f140(x96273),x96271),f115(x96273)))),f775(f775(f125(x96273),x96276),f775(f775(f140(x96273),x96272),f115(x96273))))),f146(x96273,x96274)))+P1(f775(f775(f334(f856(x96273,x96273)),f775(f775(f241(x96273,x96273),x96271),x96272)),x96274)) % 186.05/186.63 [9652]~P1(f775(f775(f334(f856(f851(x96521),f851(x96521))),f775(f775(f241(f851(x96521),f851(x96521)),f775(f775(f125(x96521),x96525),f775(f775(f140(x96521),x96522),f115(x96521)))),f775(f775(f125(x96521),x96526),f775(f775(f140(x96521),x96523),f115(x96521))))),f146(x96521,x96524)))+P1(f775(f775(f334(f856(f851(x96521),f851(x96521))),f775(f775(f241(f851(x96521),f851(x96521)),x96525),x96526)),f146(x96521,x96524)))+P1(f775(f775(f334(f856(x96521,x96521)),f775(f775(f241(x96521,x96521),x96522),x96523)),x96524)) % 186.05/186.63 [9665]P1(f775(x96651,x96652))+P1(f775(f775(f334(x96653),f388(x96651,x96654,x96655,x96656,x96653)),f775(x96654,f389(x96651,x96654,x96655,x96656,x96653))))+~P1(f775(f775(f334(x96653),x96652),f775(f775(f46(x96656,f857(x96653,a844)),x96655),x96654))) % 186.05/186.63 [8754]~P20(x87543,x87544,x87541)+~P1(f775(f63(x87543),x87546))+E(f775(f775(x87541,x87542),f775(f775(f66(x87543,x87544,x87541),x87545),f775(f775(f3(f857(x87543,a844)),x87546),f775(f775(f302(x87543),x87542),f180(f857(x87543,a844)))))),f775(f775(f66(x87543,x87544,x87541),x87545),f775(f775(f302(x87543),x87542),x87546))) % 186.05/186.63 [8851]~E(f775(f166(x88511,x88512,x88514),x88515),f775(f227(x88512),x88516))+~P1(f775(f775(x88513,x88515),x88516))+E(f775(f166(x88511,x88512,f775(f126(f856(x88511,x88512),f775(f251(x88511,x88512,a844),x88513)),x88514)),x88515),f775(f227(x88512),x88516)) % 186.05/186.63 [9024]~P1(f775(f775(f334(x90245),x90243),x90246))+P1(f775(f775(f232(f857(x90241,a844)),f775(x90242,x90243)),x90244))+~P1(f775(f775(f232(f857(x90241,a844)),f775(f775(f46(x90245,f857(x90241,a844)),x90246),x90242)),x90244)) % 186.05/186.63 [9602]~P12(x96021,x96025,x96024)+P1(f775(f775(f334(f856(x96021,x96021)),f775(f775(f241(x96021,x96021),x96022),x96023)),x96024))+~P1(f775(f775(f334(x96021),x96026),f775(f775(f104(f857(x96021,a844)),f775(f277(x96021,x96021,x96024),f775(f775(f302(x96021),x96022),f180(f857(x96021,a844))))),f775(f277(x96021,x96021,x96024),f775(f775(f302(x96021),x96023),f180(f857(x96021,a844))))))) % 186.05/186.63 [8524]~P121(x85242)+~E(f775(f775(f82(x85242),f775(f775(f83(x85242),x85244),x85245)),x85241),f775(f775(f82(x85242),f775(f775(f83(x85242),x85243),x85245)),x85246))+E(x85241,f775(f775(f82(x85242),f775(f775(f83(x85242),f775(f775(f3(x85242),x85243),x85244)),x85245)),x85246)) % 186.05/186.63 [8525]~P121(x85251)+~E(f775(f775(f82(x85251),f775(f775(f83(x85251),x85252),x85254)),x85255),f775(f775(f82(x85251),f775(f775(f83(x85251),x85253),x85254)),x85256))+E(f775(f775(f82(x85251),f775(f775(f83(x85251),f775(f775(f3(x85251),x85252),x85253)),x85254)),x85255),x85256) % 186.05/186.63 [8672]~P121(x86721)+E(f775(f775(f82(x86721),f775(f775(f83(x86721),x86722),x86723)),x86724),f775(f775(f82(x86721),f775(f775(f83(x86721),x86725),x86723)),x86726))+~E(x86726,f775(f775(f82(x86721),f775(f775(f83(x86721),f775(f775(f3(x86721),x86722),x86725)),x86723)),x86724)) % 186.05/186.63 [8673]~P121(x86731)+E(f775(f775(f82(x86731),f775(f775(f83(x86731),x86732),x86733)),x86734),f775(f775(f82(x86731),f775(f775(f83(x86731),x86735),x86733)),x86736))+~E(f775(f775(f82(x86731),f775(f775(f83(x86731),f775(f775(f3(x86731),x86732),x86735)),x86733)),x86734),x86736) % 186.05/186.63 [8964]~P1(f775(f775(x89644,x89645),x89646))+~P1(f775(f775(x89643,x89645),x89646))+P1(f775(f775(f775(f775(f104(f857(x89641,f857(x89642,a844))),x89643),x89644),x89645),x89646)) % 186.05/186.63 [9193]P1(f775(f775(x91931,x91932),x91933))+P1(f775(f775(x91934,x91932),x91933))+~P1(f775(f775(f775(f775(f103(f857(x91935,f857(x91936,a844))),x91934),x91931),x91932),x91933)) % 186.05/186.63 [9352]~E(f775(f181(f851(x93521)),x93525),f775(f181(f851(x93522)),x93526))+E(f170(x93521,x93522,f172(x93521,x93522,x93523,f775(f775(f3(f857(x93521,a844)),x93524),f775(f158(x93521),x93525))),f166(x93521,x93522,f775(f142(f856(x93521,x93522)),f775(f775(f167(x93521,x93522),x93525),x93526)))),f172(x93521,x93522,f170(x93521,x93522,x93523,f166(x93521,x93522,f775(f142(f856(x93521,x93522)),f775(f775(f167(x93521,x93522),x93525),x93526)))),x93524))+~P1(f775(f775(f232(f857(x93521,a844)),f775(f158(x93521),x93525)),x93524)) % 186.05/186.63 [9480]~P129(x94801)+~P1(f775(f775(f233(x94801),f775(f775(f82(x94801),f775(f775(f83(x94801),x94804),x94805)),x94802)),f775(f775(f82(x94801),f775(f775(f83(x94801),x94803),x94805)),x94806)))+P1(f775(f775(f233(x94801),x94802),f775(f775(f82(x94801),f775(f775(f83(x94801),f775(f775(f3(x94801),x94803),x94804)),x94805)),x94806))) % 186.05/186.63 [9481]~P129(x94811)+~P1(f775(f775(f232(x94811),f775(f775(f82(x94811),f775(f775(f83(x94811),x94814),x94815)),x94812)),f775(f775(f82(x94811),f775(f775(f83(x94811),x94813),x94815)),x94816)))+P1(f775(f775(f232(x94811),x94812),f775(f775(f82(x94811),f775(f775(f83(x94811),f775(f775(f3(x94811),x94813),x94814)),x94815)),x94816))) % 186.05/186.63 [9498]~P129(x94981)+P1(f775(f775(f233(x94981),f775(f775(f82(x94981),f775(f775(f83(x94981),x94982),x94983)),x94984)),f775(f775(f82(x94981),f775(f775(f83(x94981),x94985),x94983)),x94986)))+~P1(f775(f775(f233(x94981),x94984),f775(f775(f82(x94981),f775(f775(f83(x94981),f775(f775(f3(x94981),x94985),x94982)),x94983)),x94986))) % 186.05/186.63 [9499]~P129(x94991)+P1(f775(f775(f232(x94991),f775(f775(f82(x94991),f775(f775(f83(x94991),x94992),x94993)),x94994)),f775(f775(f82(x94991),f775(f775(f83(x94991),x94995),x94993)),x94996)))+~P1(f775(f775(f232(x94991),x94994),f775(f775(f82(x94991),f775(f775(f83(x94991),f775(f775(f3(x94991),x94995),x94992)),x94993)),x94996))) % 186.05/186.63 [9595]~P129(x95951)+~P1(f775(f775(f233(x95951),f775(f775(f82(x95951),f775(f775(f83(x95951),x95952),x95954)),x95955)),f775(f775(f82(x95951),f775(f775(f83(x95951),x95953),x95954)),x95956)))+P1(f775(f775(f233(x95951),f775(f775(f82(x95951),f775(f775(f83(x95951),f775(f775(f3(x95951),x95952),x95953)),x95954)),x95955)),x95956)) % 186.05/186.63 [9596]~P129(x95961)+~P1(f775(f775(f232(x95961),f775(f775(f82(x95961),f775(f775(f83(x95961),x95962),x95964)),x95965)),f775(f775(f82(x95961),f775(f775(f83(x95961),x95963),x95964)),x95966)))+P1(f775(f775(f232(x95961),f775(f775(f82(x95961),f775(f775(f83(x95961),f775(f775(f3(x95961),x95962),x95963)),x95964)),x95965)),x95966)) % 186.05/186.63 [9637]~P129(x96371)+P1(f775(f775(f233(x96371),f775(f775(f82(x96371),f775(f775(f83(x96371),x96372),x96373)),x96374)),f775(f775(f82(x96371),f775(f775(f83(x96371),x96375),x96373)),x96376)))+~P1(f775(f775(f233(x96371),f775(f775(f82(x96371),f775(f775(f83(x96371),f775(f775(f3(x96371),x96372),x96375)),x96373)),x96374)),x96376)) % 186.05/186.63 [9638]~P129(x96381)+P1(f775(f775(f232(x96381),f775(f775(f82(x96381),f775(f775(f83(x96381),x96382),x96383)),x96384)),f775(f775(f82(x96381),f775(f775(f83(x96381),x96385),x96383)),x96386)))+~P1(f775(f775(f232(x96381),f775(f775(f82(x96381),f775(f775(f83(x96381),f775(f775(f3(x96381),x96382),x96385)),x96383)),x96384)),x96386)) % 186.05/186.63 [9807]~P66(x98072)+~P1(f775(f63(x98071),x98076))+E(f775(f775(f8(x98071,x98072),f775(f775(f20(x98071,x98072,x98072),f775(f775(f20(x98071,x98072,f857(x98072,x98072)),f775(f775(f10(a844,f857(x98072,f857(x98072,x98072)),x98071),f98(x98072)),x98073)),x98074)),x98075)),x98076),f775(f775(f82(x98072),f775(f775(f8(x98071,x98072),x98074),f775(f775(f104(f857(x98071,a844)),x98076),f775(f256(x98071),x98073)))),f775(f775(f8(x98071,x98072),x98075),f775(f775(f104(f857(x98071,a844)),x98076),f775(f81(f857(x98071,a844)),f775(f256(x98071),x98073)))))) % 186.05/186.63 [9871]P1(f775(f775(f334(x98712),x98714),x98716))+P1(f775(f775(f334(x98712),x98715),x98716))+E(f775(f305(x98711,x98712,f775(f775(f9(x98711,x98712,x98712),f775(f775(f9(x98711,x98712,f857(x98712,x98712)),f775(f775(f10(a844,f857(x98712,f857(x98712,x98712)),x98711),f98(x98712)),f775(f775(f9(x98711,f857(x98711,a844),a844),f334(x98711)),x98713))),x98714)),x98715)),x98716),f180(f857(x98711,a844))) % 186.05/186.63 [9872]P1(f775(f775(f334(x98722),x98725),x98726))+~P1(f775(f775(f334(x98722),x98724),x98726))+E(f775(f305(x98721,x98722,f775(f775(f9(x98721,x98722,x98722),f775(f775(f9(x98721,x98722,f857(x98722,x98722)),f775(f775(f10(a844,f857(x98722,f857(x98722,x98722)),x98721),f98(x98722)),f775(f775(f9(x98721,f857(x98721,a844),a844),f334(x98721)),x98723))),x98724)),x98725)),x98726),x98723) % 186.05/186.63 [9873]P1(f775(f775(f334(x98732),x98734),x98736))+~P1(f775(f775(f334(x98732),x98735),x98736))+E(f775(f305(x98731,x98732,f775(f775(f9(x98731,x98732,x98732),f775(f775(f9(x98731,x98732,f857(x98732,x98732)),f775(f775(f10(a844,f857(x98732,f857(x98732,x98732)),x98731),f98(x98732)),f775(f775(f9(x98731,f857(x98731,a844),a844),f334(x98731)),x98733))),x98734)),x98735)),x98736),f775(f81(f857(x98731,a844)),x98733)) % 186.05/186.63 [9874]~P1(f775(f775(f334(x98742),x98744),x98746))+~P1(f775(f775(f334(x98742),x98745),x98746))+E(f775(f305(x98741,x98742,f775(f775(f9(x98741,x98742,x98742),f775(f775(f9(x98741,x98742,f857(x98742,x98742)),f775(f775(f10(a844,f857(x98742,f857(x98742,x98742)),x98741),f98(x98742)),f775(f775(f9(x98741,f857(x98741,a844),a844),f334(x98741)),x98743))),x98744)),x98745)),x98746),f239(f857(x98741,a844))) % 186.05/186.63 [10006]P28(x100061,x100062,f775(f775(f302(f849(x100061)),f775(f775(f775(f93(x100061),f775(x100063,x100064)),f775(a27,x100064)),f775(x100065,x100064))),f180(f857(f849(x100061),a844))))+~P1(f775(f775(f334(a846),x100064),x100066))+~P28(x100061,f775(f775(f103(f857(f849(x100061),a844)),x100062),f775(f303(a846,f849(x100061),f775(f775(f20(a846,f857(x100061,f857(a847,a844)),f849(x100061)),f775(f775(f20(a846,a845,f857(f857(x100061,f857(a847,a844)),f849(x100061))),f775(f775(f10(f857(x100061,f857(a847,a844)),f857(a845,f857(f857(x100061,f857(a847,a844)),f849(x100061))),a846),f93(x100061)),x100063)),a27)),x100065)),x100066)),f775(f303(a846,f849(x100061),f775(f775(f20(a846,f857(x100061,f857(a847,a844)),f849(x100061)),f775(f775(f20(a846,a845,f857(f857(x100061,f857(a847,a844)),f849(x100061))),f775(f775(f10(f857(x100061,f857(a847,a844)),f857(a845,f857(f857(x100061,f857(a847,a844)),f849(x100061))),a846),f93(x100061)),x100063)),f775(f775(f10(f854(a845),a845,a846),f231(a845)),a30))),x100065)),x100066)) % 186.05/186.63 [8549]E(x85491,x85492)+~P55(x85494,x85495,x85493,x85496,x85497)+~E(f775(x85493,x85491),f775(x85493,x85492)) % 186.05/186.63 [6924]E(f775(f229(f854(x69241),x69242,f183(x69241),x69243),f775(x69244,x69245)),f775(f227(x69241),x69246))+~E(f775(x69244,x69245),f775(f227(x69242),x69247))+~E(f775(x69243,x69247),f775(f227(x69241),x69246)) % 186.05/186.63 [8571]~P15(x85716,x85715,x85717,x85714,x85711)+E(f775(f775(x85711,x85712),x85713),x85714)+P1(f775(f63(x85715),x85713)) % 186.05/186.63 [9347]P41(x93471,x93472,x93473,x93474,x93475,f775(f775(x93473,x93476),x93477))+~E(f775(f775(x93473,x93476),x93477),x93474)+~E(x93475,f180(f857(x93471,a844))) % 186.05/186.63 [9518]~P1(f775(x95186,x95183))+~P1(f775(f775(f334(f856(x95182,x95182)),f775(f775(f241(x95182,x95182),x95184),x95185)),f775(x95187,x95183)))+P1(f775(f775(f334(f856(f856(x95181,x95182),f856(x95181,x95182))),f775(f775(f241(f856(x95181,x95182),f856(x95181,x95182)),f775(f775(f241(x95181,x95182),x95183),x95184)),f775(f775(f241(x95181,x95182),x95183),x95185))),f275(x95181,x95182,x95186,x95187))) % 186.05/186.63 [9691]~P29(x96913,x96911,x96914,f239(f857(x96913,a844)))+E(f775(f166(x96911,x96912,f775(f775(f143(f856(x96913,x96912),f856(x96911,x96912)),f775(f251(x96913,x96912,f856(x96911,x96912)),f775(f775(f10(x96911,f857(x96912,f856(x96911,x96912)),x96913),f241(x96911,x96912)),x96914))),x96915)),f775(x96914,x96916)),f775(f227(x96912),x96917))+~E(f775(f166(x96913,x96912,x96915),x96916),f775(f227(x96912),x96917)) % 186.05/186.63 [9927]~P41(x99272,x99277,x99273,x99276,x99271,f775(f775(x99273,x99275),x99274))+E(f775(f775(x99273,f453(x99274,x99275,x99271,x99276,x99273,x99277,x99272)),f454(x99274,x99275,x99271,x99276,x99273,x99277,x99272)),f775(f775(x99273,x99275),x99274))+E(x99271,f180(f857(x99272,a844))) % 186.05/186.63 [9928]~P41(x99287,x99286,x99281,x99284,x99285,f775(f775(x99281,x99282),x99283))+E(f775(f775(x99281,f453(x99283,x99282,x99285,x99284,x99281,x99286,x99287)),f454(x99283,x99282,x99285,x99284,x99281,x99286,x99287)),f775(f775(x99281,x99282),x99283))+E(f775(f775(x99281,x99282),x99283),x99284) % 186.05/186.63 [9583]~P1(f775(f68(x95831,x95834,x95835,x95836,x95833),x95837))+P1(f775(f68(x95831,x95834,x95835,x95836,f775(f775(f302(x95831),x95832),x95833)),f775(f775(x95835,x95832),x95837)))+P1(f775(f775(f334(x95831),x95832),x95833)) % 186.05/186.63 [9952]~P41(x99522,x99527,x99526,x99525,x99521,f775(f775(x99526,x99524),x99523))+E(x99521,f180(f857(x99522,a844)))+P1(f775(f775(f334(x99522),f453(x99523,x99524,x99521,x99525,x99526,x99527,x99522)),x99521)) % 186.05/186.63 [9953]~P41(x99535,x99537,x99531,x99534,x99536,f775(f775(x99531,x99532),x99533))+E(f775(f775(x99531,x99532),x99533),x99534)+P1(f775(f775(f334(x99535),f453(x99533,x99532,x99536,x99534,x99531,x99537,x99535)),x99536)) % 186.05/186.63 [6702]~E(x67025,x67027)+~E(x67026,x67024)+E(f775(f775(f775(f775(f74(x67021,f854(x67022)),x67023),x67024),f775(f227(x67022),x67025)),x67026),f775(f227(x67022),x67027)) % 186.05/186.63 [6838]E(x68381,x68382)+~E(f775(x68385,x68381),f775(f227(x68384),x68387))+E(f775(f775(f775(f775(f74(x68383,f854(x68384)),x68385),x68382),f775(f227(x68384),x68386)),x68381),f775(f227(x68384),x68387)) % 186.05/186.63 [7583]E(x75831,x75832)+~E(x75833,x75834)+~E(f775(f775(f775(f775(f74(x75835,f854(x75836)),x75837),x75834),f775(f227(x75836),x75831)),x75833),f775(f227(x75836),x75832)) % 186.05/186.63 [7648]E(x76481,x76482)+E(f775(x76483,x76484),f775(f227(x76485),x76481))+~E(f775(f775(f775(f775(f74(x76486,f854(x76485)),x76483),x76487),f775(f227(x76485),x76482)),x76484),f775(f227(x76485),x76481)) % 186.05/186.63 [7649]E(x76491,x76492)+E(f775(x76493,x76491),f775(f227(x76494),x76495))+~E(f775(f775(f775(f775(f74(x76496,f854(x76494)),x76493),x76492),f775(f227(x76494),x76497)),x76491),f775(f227(x76494),x76495)) % 186.05/186.63 [8775]~P25(x87754,x87755,x87756,x87757,x87751)+~P1(f775(f63(x87755),x87753))+E(f775(f775(x87751,x87752),x87753),f775(f775(f775(f67(x87754,x87755,x87756),x87752),x87757),x87753)) % 186.05/186.63 [8776]~P15(x87764,x87765,x87766,x87767,x87761)+~P1(f775(f63(x87765),x87763))+E(f775(f775(x87761,x87762),x87763),f775(f775(f775(f67(x87764,x87765,x87766),x87762),x87767),x87763)) % 186.05/186.63 [9315]~P28(x93151,x93152,f775(f775(f302(f849(x93151)),f775(f775(f775(f93(x93151),x93153),x93154),x93157)),f180(f857(f849(x93151),a844))))+P28(x93151,x93152,f775(f775(f302(f849(x93151)),f775(f775(f775(f93(x93151),x93153),f36(x93154,x93155)),x93156)),f180(f857(f849(x93151),a844))))+~P28(x93151,x93152,f775(f775(f302(f849(x93151)),f775(f775(f775(f93(x93151),x93157),x93155),x93156)),f180(f857(f849(x93151),a844)))) % 186.05/186.63 [9493]~P27(x94933,x94934,x94935,x94937,x94936,x94931)+~P1(f775(f63(x94934),x94932))+E(f775(x94931,x94932),f775(f775(f775(f67(x94933,x94934,x94935),x94936),x94937),x94932)) % 186.05/186.63 [9632]P41(x96321,x96322,x96323,x96324,x96325,f775(f775(x96323,x96326),x96327))+~P41(x96321,x96322,x96323,x96324,f775(f775(f3(f857(x96321,a844)),x96325),f775(f775(f302(x96321),x96326),f180(f857(x96321,a844)))),x96327)+~P1(f775(f775(f334(x96321),x96326),x96325)) % 186.05/186.63 [9902]~P28(x99021,x99022,f775(f775(f302(f849(x99021)),f775(f775(f775(f93(x99021),f94(x99021,x99023,x99024)),x99025),x99027)),f180(f857(f849(x99021),a844))))+P28(x99021,x99022,f775(f775(f302(f849(x99021)),f775(f775(f775(f93(x99021),x99023),f33(x99024,x99025,x99026)),x99027)),f180(f857(f849(x99021),a844))))+~P28(x99021,x99022,f775(f775(f302(f849(x99021)),f775(f775(f775(f93(x99021),f94(x99021,x99023,f775(f75(a844,a844,a847,a328),x99024))),x99026),x99027)),f180(f857(f849(x99021),a844)))) % 186.05/186.63 [9970]P1(f775(f775(x99707,f836(x99704,x99705,x99701,x99706,x99703,x99702,x99707)),f837(x99704,x99705,x99701,x99706,x99703,x99702,x99707)))+~P1(f775(f775(x99707,f775(f250(x99702,x99703),x99706)),f775(f240(x99702,x99703),x99706)))+P1(f775(x99701,f775(f775(f251(x99702,x99703,x99704),x99705),x99706))) % 186.05/186.63 [9979]~P41(x99792,x99793,x99794,x99795,x99791,f775(f775(x99794,x99797),x99796))+P41(x99792,x99793,x99794,x99795,f775(f775(f3(f857(x99792,a844)),x99791),f775(f775(f302(x99792),f453(x99796,x99797,x99791,x99795,x99794,x99793,x99792)),f180(f857(x99792,a844)))),f454(x99796,x99797,x99791,x99795,x99794,x99793,x99792))+E(x99791,f180(f857(x99792,a844))) % 186.05/186.63 [9980]~P41(x99805,x99806,x99801,x99804,x99807,f775(f775(x99801,x99802),x99803))+P41(x99805,x99806,x99801,x99804,f775(f775(f3(f857(x99805,a844)),x99807),f775(f775(f302(x99805),f453(x99803,x99802,x99807,x99804,x99801,x99806,x99805)),f180(f857(x99805,a844)))),f454(x99803,x99802,x99807,x99804,x99801,x99806,x99805))+E(f775(f775(x99801,x99802),x99803),x99804) % 186.05/186.63 [10000]~P1(f775(x100001,f775(f775(x100005,f837(x100004,x100005,x100001,x100006,x100003,x100002,x100007)),f836(x100004,x100005,x100001,x100006,x100003,x100002,x100007))))+~P1(f775(f775(x100007,f775(f250(x100002,x100003),x100006)),f775(f240(x100002,x100003),x100006)))+P1(f775(x100001,f775(f775(f251(x100002,x100003,x100004),x100005),x100006))) % 186.05/186.63 [9336]P1(f775(f775(f232(f857(f856(x93361,x93362),a844)),f775(f775(f281(x93361,x93363,x93362),x93364),x93365)),f775(f775(f281(x93361,x93363,x93362),x93366),x93367)))+~P1(f775(f775(f232(f857(f856(x93363,x93362),a844)),x93365),x93367))+~P1(f775(f775(f232(f857(f856(x93361,x93363),a844)),x93364),x93366)) % 186.05/186.63 [9643]~P1(f775(f775(f334(x96431),x96436),x96435))+P1(f775(f68(x96431,x96432,x96433,x96434,x96435),f775(f775(x96433,x96436),x96437)))+~P1(f775(f68(x96431,x96432,x96433,x96434,f775(f775(f3(f857(x96431,a844)),x96435),f775(f775(f302(x96431),x96436),f180(f857(x96431,a844))))),x96437)) % 186.05/186.63 [9242]E(f170(x92421,x92422,x92423,f166(x92421,x92422,f775(f142(f856(x92421,x92422)),f775(f775(f167(x92421,x92422),x92424),f775(f775(f148(x92422,x92425),x92426),x92427))))),f170(x92421,x92422,x92423,f166(x92421,x92422,f775(f142(f856(x92421,x92422)),f775(f775(f167(x92421,x92422),x92424),x92425)))))+~P1(f775(f775(f233(a850),x92426),f775(f181(f851(x92422)),x92425)))+~P1(f775(f775(f232(a850),f775(f181(f851(x92421)),x92424)),x92426)) % 186.05/186.63 [10030]~P136(x100301)+~P29(f856(x100302,x100303),x100301,f775(f251(x100302,x100303,x100301),f775(f775(f9(x100302,f857(x100303,x100301),f857(x100303,x100301)),f775(f775(f10(f857(x100301,x100301),f857(f857(x100303,x100301),f857(x100303,x100301)),x100302),f10(x100301,x100301,x100303)),f775(f775(f10(x100301,f857(x100301,x100301),x100302),f83(x100301)),x100304))),x100305)),f775(f775(f248(x100302,x100303),x100306),f775(f18(f857(x100303,a844),x100302),x100307)))+E(f775(f775(f8(x100301,x100301),f39(x100301)),f775(f256(x100301),f775(f775(f10(f857(x100302,a844),a844,x100301),f89(x100302)),f775(f775(f10(f857(x100302,f857(x100303,a844)),f857(x100302,a844),x100301),f775(f10(f857(x100303,a844),a844,x100302),f89(x100303))),f775(f775(f9(x100301,f857(x100302,f857(x100303,a844)),f857(x100302,f857(x100303,a844))),f775(f775(f10(f857(x100302,f857(f857(x100303,a844),f857(x100303,a844))),f857(f857(x100302,f857(x100303,a844)),f857(x100302,f857(x100303,a844))),x100301),f20(x100302,f857(x100303,a844),f857(x100303,a844))),f775(f775(f10(f857(x100302,f857(x100303,f857(a844,a844))),f857(x100302,f857(f857(x100303,a844),f857(x100303,a844))),x100301),f775(f10(f857(x100303,f857(a844,a844)),f857(f857(x100303,a844),f857(x100303,a844)),x100302),f20(x100303,a844,a844))),f775(f775(f10(f857(x100302,f857(x100303,a844)),f857(x100302,f857(x100303,f857(a844,a844))),x100301),f775(f10(f857(x100303,a844),f857(x100303,f857(a844,a844)),x100302),f775(f10(a844,f857(a844,a844),x100303),a331))),f775(f775(f9(x100301,f857(x100302,f857(x100303,x100301)),f857(x100302,f857(x100303,a844))),f775(f775(f10(f857(f857(x100303,x100301),f857(x100303,a844)),f857(f857(x100302,f857(x100303,x100301)),f857(x100302,f857(x100303,a844))),x100301),f10(f857(x100303,x100301),f857(x100303,a844),x100302)),f775(f775(f10(f857(x100301,a844),f857(f857(x100303,x100301),f857(x100303,a844)),x100301),f10(x100301,a844,x100303)),a330))),f775(f775(f9(x100302,f857(x100303,x100301),f857(x100303,x100301)),f775(f775(f10(f857(x100301,x100301),f857(f857(x100303,x100301),f857(x100303,x100301)),x100302),f10(x100301,x100301,x100303)),f775(f775(f10(x100301,f857(x100301,x100301),x100302),f83(x100301)),x100304))),x100305)))))),f775(f775(f9(x100302,f857(x100303,a844),f857(x100303,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x100303,a844),f857(x100303,a844)),x100302),f10(a844,a844,x100303)),f775(f775(f10(a844,f857(a844,a844),x100302),a331),f775(f775(f9(x100302,f857(x100302,a844),a844),f334(x100302)),x100306)))),f775(f775(f9(x100303,f857(x100303,a844),a844),f334(x100303)),x100307))))))),f775(f775(f83(x100301),f775(f775(f8(x100302,x100301),x100304),x100306)),f775(f775(f8(x100303,x100301),x100305),x100307))) % 186.05/186.63 [9721]P51(x97211,x97212,x97213,x97214,x97215,x97216,x97217)+~P1(f775(f775(x97214,x97216),x97218))+~P1(f775(f775(x97215,x97218),x97217)) % 186.05/186.63 [9122]~P23(x91228,x91221,x91223,x91225)+~P1(f775(f63(x91228),x91226))+E(f775(f75(x91221,x91221,x91222,f775(x91223,x91224)),f775(f75(x91221,x91221,x91222,f775(x91225,x91226)),x91227)),f775(f75(x91221,x91221,x91222,f775(x91225,x91226)),f775(f75(x91221,x91221,x91222,f775(x91223,x91224)),x91227))) % 186.05/186.63 [9485]~P26(x94857,x94852,x94855,x94858,x94856,x94851)+~P1(f775(f63(x94852),x94854))+E(f775(x94851,f775(f775(f302(x94852),x94853),x94854)),f775(f775(x94855,f775(x94856,x94853)),f775(x94851,x94854))) % 186.05/186.63 [9593]~P29(x95932,x95934,x95936,x95938)+~P29(x95931,x95933,x95935,x95937)+P29(f856(x95931,x95932),f856(x95933,x95934),f252(x95931,x95933,x95932,x95934,x95935,x95936),f775(f775(f248(x95931,x95932),x95937),f775(f18(f857(x95932,a844),x95931),x95938))) % 186.05/186.63 [9278]P1(f775(f775(f334(f856(x92781,x92782)),f775(f775(f241(x92781,x92782),x92783),x92784)),f775(f775(f281(x92781,x92785,x92782),x92786),x92787)))+~P1(f775(f775(f334(f856(x92781,x92785)),f775(f775(f241(x92781,x92785),x92783),x92788)),x92786))+~P1(f775(f775(f334(f856(x92785,x92782)),f775(f775(f241(x92785,x92782),x92788),x92784)),x92787)) % 186.05/186.63 [9468]~P1(f775(f775(f232(f857(f856(x94683,x94682),a844)),x94685),f775(f775(f248(x94683,x94682),x94688),f775(f18(f857(x94682,a844),x94683),x94687))))+~P1(f775(f775(f232(f857(f856(x94681,x94683),a844)),x94684),f775(f775(f248(x94681,x94683),x94686),f775(f18(f857(x94683,a844),x94681),x94688))))+P1(f775(f775(f232(f857(f856(x94681,x94682),a844)),f775(f775(f281(x94681,x94683,x94682),x94684),x94685)),f775(f775(f248(x94681,x94682),x94686),f775(f18(f857(x94682,a844),x94681),x94687)))) % 186.05/186.63 [9513]~E(x95133,x95135)+P1(f775(f775(f334(f856(f856(x95131,x95132),f856(x95131,x95132))),f775(f775(f241(f856(x95131,x95132),f856(x95131,x95132)),f775(f775(f241(x95131,x95132),x95133),x95134)),f775(f775(f241(x95131,x95132),x95135),x95136))),f325(x95131,x95132,x95137,x95138)))+~P1(f775(f775(f334(f856(x95132,x95132)),f775(f775(f241(x95132,x95132),x95134),x95136)),x95138)) % 186.05/186.63 [9611]E(x96111,x96112)+~P1(f775(f775(f334(f856(f856(x96113,x96115),f856(x96113,x96115))),f775(f775(f241(f856(x96113,x96115),f856(x96113,x96115)),f775(f775(f241(x96113,x96115),x96111),x96116)),f775(f775(f241(x96113,x96115),x96112),x96117))),f325(x96113,x96115,x96114,x96118)))+P1(f775(f775(f334(f856(x96113,x96113)),f775(f775(f241(x96113,x96113),x96111),x96112)),x96114)) % 186.05/186.63 [9626]~P1(f775(f775(f334(f856(f856(x96261,x96265),f856(x96261,x96265))),f775(f775(f241(f856(x96261,x96265),f856(x96261,x96265)),f775(f775(f241(x96261,x96265),x96262),x96266)),f775(f775(f241(x96261,x96265),x96263),x96267))),f325(x96261,x96265,x96264,x96268)))+P1(f775(f775(f334(f856(x96261,x96261)),f775(f775(f241(x96261,x96261),x96262),x96263)),x96264))+P1(f775(f775(f334(f856(x96265,x96265)),f775(f775(f241(x96265,x96265),x96266),x96267)),x96268)) % 186.05/186.63 [9542]~P27(x95427,x95425,x95421,x95428,x95422,x95424)+~P1(f775(f63(x95425),x95426))+E(f775(f775(x95421,f775(x95422,x95423)),f775(x95424,f775(f775(f3(f857(x95425,a844)),x95426),f775(f775(f302(x95425),x95423),f180(f857(x95425,a844)))))),f775(x95424,f775(f775(f302(x95425),x95423),x95426))) % 186.05/186.63 [9081]~P1(f775(f775(f775(x90815,x90818),x90816),x90817))+~P1(f775(f775(f334(x90811),x90818),x90814))+P1(f775(f775(f775(f775(f46(x90811,f857(x90812,f857(x90813,a844))),x90814),x90815),x90816),x90817)) % 186.05/186.63 [9266]P1(f775(f775(f775(x92661,x92662),x92663),x92664))+~P1(f775(f775(f334(x92665),x92662),x92666))+~P1(f775(f775(f775(f775(f47(x92665,f857(x92667,f857(x92668,a844))),x92666),x92661),x92663),x92664)) % 186.05/186.63 [9459]~P25(x94593,x94592,x94594,x94598,x94591)+~P1(f775(f63(x94592),x94597))+E(f775(f775(x94591,f775(f775(f20(x94592,x94593,x94593),f775(f775(f10(x94593,f857(x94593,x94593),x94592),x94594),x94595)),x94596)),x94597),f775(f775(x94594,f775(f775(x94591,x94595),x94597)),f775(f775(x94591,x94596),x94597))) % 186.05/186.63 [9699]~E(f775(f303(x96992,x96994,x96996),x96998),x969910)+~E(f775(f303(x96991,x96993,x96995),x96997),x96999)+E(f775(f303(f856(x96991,x96992),f856(x96993,x96994),f252(x96991,x96993,x96992,x96994,x96995,x96996)),f775(f775(f248(x96991,x96992),x96997),f775(f18(f857(x96992,a844),x96991),x96998))),f775(f775(f248(x96993,x96994),x96999),f775(f18(f857(x96994,a844),x96993),x969910))) % 186.05/186.63 [4731]~P100(x47312)+~P18(x47312,x47311)+P18(x47312,f116(x47312,x47311))+E(x47311,f115(x47312)) % 186.05/186.63 [4964]~P9(x49642)+E(f12(x49642,x49641),f45(x49642,x49641))+E(x49641,f180(f857(x49642,a844)))+~P1(f775(f63(x49642),x49641)) % 186.05/186.63 [4965]~P9(x49652)+E(f15(x49652,x49651),f44(x49652,x49651))+E(x49651,f180(f857(x49652,a844)))+~P1(f775(f63(x49652),x49651)) % 186.05/186.63 [5905]~P93(x59052)+E(x59051,f180(f857(x59052,a844)))+P1(f775(f775(f232(x59052),f12(x59052,x59051)),f15(x59052,x59051)))+~P1(f775(f63(x59052),x59051)) % 186.05/186.63 [5919]~P38(x59192)+~P38(x59191)+E(x59191,x59192)+~E(f775(f303(a1,a850,a107),x59191),f775(f303(a1,a850,a107),x59192)) % 186.05/186.63 [8944]~P110(x89441)+~P1(f775(f775(f334(x89441),x89442),f112(x89441)))+P1(f775(f775(f233(x89441),f775(f775(f82(x89441),f775(f775(f82(x89441),f80(x89441)),x89442)),x89442)),f2(x89441)))+~P1(f775(f775(f233(x89441),x89442),f2(x89441))) % 186.05/186.63 [9163]~P110(x91631)+~P1(f775(f775(f334(x91631),x91632),f112(x91631)))+~P1(f775(f775(f233(x91631),f775(f775(f82(x91631),f775(f775(f82(x91631),f80(x91631)),x91632)),x91632)),f2(x91631)))+P1(f775(f775(f233(x91631),x91632),f2(x91631))) % 186.05/186.63 [4784]~P105(x47842)+~P136(x47842)+E(x47841,f2(a850))+E(f775(f775(f242(x47842),f2(x47842)),x47841),f2(x47842)) % 186.05/186.63 [4788]~P105(x47881)+~P136(x47881)+~E(x47882,f2(a850))+E(f775(f775(f242(x47881),f2(x47881)),x47882),f80(x47881)) % 186.05/186.63 [4951]~P120(x49512)+E(x49511,f80(x49512))+E(x49511,f775(f81(x49512),f80(x49512)))+~E(f775(f775(f83(x49512),x49511),x49511),f80(x49512)) % 186.05/186.63 [5195]~P82(x51952)+E(x51951,f2(x51952))+E(f84(x51952,x51951),f775(f81(x51952),f80(x51952)))+P1(f775(f775(f233(x51952),f2(x51952)),x51951)) % 186.05/186.63 [5427]~P82(x54272)+E(f84(x54272,x54271),f80(x54272))+E(x54271,f2(x54272))+~P1(f775(f775(f233(x54272),f2(x54272)),x54271)) % 186.05/186.63 [5436]E(x54361,x54362)+~E(f775(f106(a850),x54361),f775(f106(a850),x54362))+P1(f775(a186,f775(f106(a1),x54362)))+P1(f775(a186,f775(f106(a1),x54361))) % 186.05/186.63 [5483]~P87(x54831)+~E(x54832,f2(x54831))+E(f775(f775(f82(x54831),x54832),x54832),f2(x54831))+~P1(f775(f775(f334(x54831),x54832),f112(x54831))) % 186.05/186.63 [5519]E(x55191,f2(a1))+~E(f775(f775(f43(a1),x55192),x55191),f2(a1))+P1(f775(f775(f233(a1),x55191),x55192))+P1(f775(f775(f233(a1),x55192),x55191)) % 186.05/186.63 [5548]E(x55481,f2(a1))+~E(f775(f775(f43(a1),x55482),x55481),f2(a1))+P1(f775(f775(f232(a1),x55482),f2(a1)))+P1(f775(f775(f233(a1),x55482),x55481)) % 186.05/186.63 [5580]E(x55801,f2(a1))+~E(f775(f775(f43(a1),x55802),x55801),f2(a1))+P1(f775(f775(f232(a1),f2(a1)),x55802))+P1(f775(f775(f233(a1),x55801),x55802)) % 186.05/186.63 [5617]~P87(x56172)+E(x56171,f2(x56172))+~E(f775(f775(f82(x56172),x56171),x56171),f2(x56172))+~P1(f775(f775(f334(x56172),x56171),f112(x56172))) % 186.05/186.63 [5684]E(f775(f106(a850),x56841),f775(f106(a850),x56842))+~E(f775(f106(a1),x56842),f2(a1))+P1(f775(a186,f775(f106(a1),x56842)))+~P1(f775(a186,f775(f106(a1),x56841))) % 186.05/186.63 [5713]~E(f775(f106(a850),x57132),f775(f106(a850),x57131))+E(f775(f106(a1),x57131),f2(a1))+P1(f775(a186,f775(f106(a1),x57131)))+~P1(f775(a186,f775(f106(a1),x57132))) % 186.05/186.63 [5722]~P100(x57222)+E(x57221,f180(f857(x57222,a844)))+~P1(f775(f63(x57222),x57221))+P1(f775(f775(f334(x57222),f16(x57222,x57221)),x57221)) % 186.05/186.63 [5723]~P100(x57232)+E(x57231,f180(f857(x57232,a844)))+~P1(f775(f63(x57232),x57231))+P1(f775(f775(f334(x57232),f17(x57232,x57231)),x57231)) % 186.05/186.63 [5885]~P110(x58851)+~P88(x58851)+P1(f775(f775(f233(x58851),f2(x58851)),f775(f106(x58851),x58852)))+~P1(f775(f775(f233(a1),a85),x58852)) % 186.05/186.63 [5886]~P110(x58861)+~P88(x58861)+P1(f775(f775(f232(x58861),f2(x58861)),f775(f106(x58861),x58862)))+~P1(f775(f775(f232(a1),a85),x58862)) % 186.05/186.63 [5904]~P110(x59041)+~P88(x59041)+E(f775(f77(x59041),f775(f106(x59041),x59042)),f775(f106(x59041),x59042))+P1(f775(f775(f233(x59041),f775(f106(x59041),x59042)),f2(x59041))) % 186.05/186.63 [5946]E(x59461,x59462)+~E(f775(a107,x59461),f775(a107,x59462))+~P1(f775(f775(f232(a1),f2(a1)),x59462))+~P1(f775(f775(f232(a1),f2(a1)),x59461)) % 186.05/186.63 [6143]~P88(x61432)+~P110(x61432)+~P1(f775(f775(f233(x61432),f2(x61432)),f775(f106(x61432),x61431)))+P1(f775(f775(f233(a1),a85),x61431)) % 186.05/186.63 [6144]~P88(x61442)+~P110(x61442)+~P1(f775(f775(f232(x61442),f2(x61442)),f775(f106(x61442),x61441)))+P1(f775(f775(f232(a1),a85),x61441)) % 186.05/186.63 [6149]~P110(x61491)+~P88(x61491)+P1(f775(f775(f233(x61491),f775(f106(x61491),x61492)),f2(x61491)))+~P1(f775(f775(f233(a1),x61492),a85)) % 186.05/186.63 [6150]~P110(x61501)+~P88(x61501)+P1(f775(f775(f232(x61501),f775(f106(x61501),x61502)),f2(x61501)))+~P1(f775(f775(f232(a1),x61502),a85)) % 186.05/186.63 [6481]~P88(x64812)+~P110(x64812)+~P1(f775(f775(f233(x64812),f775(f106(x64812),x64811)),f2(x64812)))+P1(f775(f775(f233(a1),x64811),a85)) % 186.05/186.63 [6482]~P88(x64822)+~P110(x64822)+~P1(f775(f775(f232(x64822),f775(f106(x64822),x64821)),f2(x64822)))+P1(f775(f775(f232(a1),x64821),a85)) % 186.05/186.63 [6573]~P110(x65731)+~P88(x65731)+E(f775(f77(x65731),f775(f106(x65731),x65732)),f775(f81(x65731),f775(f106(x65731),x65732)))+~P1(f775(f775(f233(x65731),f775(f106(x65731),x65732)),f2(x65731))) % 186.05/186.63 [6591]E(f775(f106(a850),x65911),f775(f106(a850),x65912))+~E(f775(f106(a1),x65912),f2(a1))+~P1(f775(f775(f232(a1),f775(f106(a1),x65911)),f2(a1)))+~P1(f775(a186,f775(f106(a1),x65911))) % 186.05/186.63 [7004]P1(f775(f775(f279(a850),f775(a107,x70041)),f775(a107,x70042)))+~P1(f775(f775(f232(a1),f2(a1)),x70042))+~P1(f775(f775(f232(a1),f2(a1)),x70041))+~P1(f775(f775(f279(a1),x70041),x70042)) % 186.05/186.63 [7247]~P1(f775(f775(f279(a850),f775(a107,x72471)),f775(a107,x72472)))+~P1(f775(f775(f232(a1),f2(a1)),x72472))+~P1(f775(f775(f232(a1),f2(a1)),x72471))+P1(f775(f775(f279(a1),x72471),x72472)) % 186.05/186.63 [7511]~P100(x75112)+E(x75111,f180(f857(x75112,a844)))+~P1(f775(f63(x75112),x75111))+P1(f775(f775(f232(x75112),f14(x75112,f236(x75112),x75111)),f13(x75112,f179(x75112),x75111))) % 186.05/186.63 [7836]~P10(x78361)+~P38(x78362)+P1(f775(f775(f334(a1),x78361),x78362))+~P1(f775(f775(f334(a850),f775(a107,x78361)),f775(f303(a1,a850,a107),x78362))) % 186.05/186.63 [5719]~P133(x57192)+E(x57191,f2(a1))+E(f775(f81(x57192),f775(f105(x57192),f775(f81(a1),x57191))),f775(f105(x57192),x57191))+~P1(f775(f775(f233(a1),x57191),f2(a1))) % 186.05/186.63 [5795]~P87(x57951)+~P88(x57951)+~P33(x57951,f775(f106(x57951),x57952))+P33(x57951,f775(f106(x57951),f775(f775(f82(a1),x57952),x57952))) % 186.05/186.63 [6133]~P68(x61332)+E(x61331,f180(f857(x61332,a844)))+E(f17(x61332,f775(f303(x61332,x61332,f81(x61332)),x61331)),f775(f81(x61332),f16(x61332,x61331)))+~P1(f775(f63(x61332),x61331)) % 186.05/186.63 [6134]~P68(x61342)+E(x61341,f180(f857(x61342,a844)))+E(f16(x61342,f775(f303(x61342,x61342,f81(x61342)),x61341)),f775(f81(x61342),f17(x61342,x61341)))+~P1(f775(f63(x61342),x61341)) % 186.05/186.63 [6164]~P87(x61641)+~P88(x61641)+P33(x61641,f775(f106(x61641),x61642))+~P33(x61641,f775(f106(x61641),f775(f775(f82(a1),x61642),x61642))) % 186.05/186.63 [6259]E(x62591,f2(a1))+E(f775(a58,f57(f775(f81(a1),x62591),f775(f81(a1),x62592))),f53(x62591,x62592))+P1(f775(f775(f232(a1),f2(a1)),x62592))+~P1(f775(f775(f232(a1),f2(a1)),x62591)) % 186.05/186.63 [8593]~P38(x85932)+~P38(x85931)+P1(f775(f775(f233(f857(a850,a844)),f775(f303(a1,a850,a107),x85931)),f775(f303(a1,a850,a107),x85932)))+~P1(f775(f775(f233(f857(a1,a844)),x85931),x85932)) % 186.05/186.63 [8868]~P38(x88682)+~P38(x88681)+~P1(f775(f775(f233(f857(a850,a844)),f775(f303(a1,a850,a107),x88681)),f775(f303(a1,a850,a107),x88682)))+P1(f775(f775(f233(f857(a1,a844)),x88681),x88682)) % 186.05/186.63 [8869]~P38(x88692)+~P38(x88691)+~P1(f775(f775(f232(f857(a850,a844)),f775(f303(a1,a850,a107),x88691)),f775(f303(a1,a850,a107),x88692)))+P1(f775(f775(f232(f857(a1,a844)),x88691),x88692)) % 186.05/186.63 [9307]E(x93071,f2(a1))+E(x93072,f2(a1))+E(f775(f775(f88(a1,f856(a1,a1)),f775(f775(a212,x93072),x93071)),f775(f775(f20(a1,a1,f856(a1,a1)),f775(f775(f10(a1,f857(a1,f856(a1,a1)),a1),f241(a1,a1)),f775(f43(a1),x93072))),f775(f43(a1),x93071))),f210(x93072,x93071))+P1(f775(f775(f233(a1),x93071),f2(a1))) % 186.05/186.63 [8158]~P88(x81582)+~P110(x81582)+~P1(f775(f775(f233(x81582),f775(f106(x81582),x81581)),f80(x81582)))+P1(f775(f775(f233(a1),x81581),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))) % 186.05/186.63 [8159]~P88(x81592)+~P110(x81592)+~P1(f775(f775(f232(x81592),f775(f106(x81592),x81591)),f80(x81592)))+P1(f775(f775(f232(a1),x81591),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))) % 186.05/186.63 [8433]~P110(x84331)+~P88(x84331)+P1(f775(f775(f233(x84331),f775(f106(x84331),x84332)),f80(x84331)))+~P1(f775(f775(f233(a1),x84332),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))) % 186.05/186.63 [8434]~P110(x84341)+~P88(x84341)+P1(f775(f775(f232(x84341),f775(f106(x84341),x84342)),f80(x84341)))+~P1(f775(f775(f232(a1),x84342),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))) % 186.05/186.63 [8618]~P88(x86182)+~P110(x86182)+~P1(f775(f775(f233(x86182),f80(x86182)),f775(f106(x86182),x86181)))+P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),x86181)) % 186.05/186.63 [8619]~P88(x86192)+~P110(x86192)+~P1(f775(f775(f232(x86192),f80(x86192)),f775(f106(x86192),x86191)))+P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),x86191)) % 186.05/186.63 [8951]~P110(x89511)+~P88(x89511)+P1(f775(f775(f233(x89511),f80(x89511)),f775(f106(x89511),x89512)))+~P1(f775(f775(f233(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),x89512)) % 186.05/186.63 [8952]~P110(x89521)+~P88(x89521)+P1(f775(f775(f232(x89521),f80(x89521)),f775(f106(x89521),x89522)))+~P1(f775(f775(f232(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),x89522)) % 186.05/186.63 [9430]~P120(x94302)+E(x94301,f80(x94302))+E(x94301,f775(f81(x94302),f80(x94302)))+~E(f775(f775(f242(x94302),x94301),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f80(x94302)) % 186.05/186.63 [9675]~P62(x96751)+~P88(x96751)+~P1(f775(f775(f233(x96751),f2(x96751)),x96752))+P1(f775(f775(f233(x96751),f2(x96751)),f775(f775(f283(x96751),x96752),f775(f106(x96751),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.63 [9730]~P62(x97301)+~P88(x97301)+P1(f775(f775(f233(x97301),f2(x97301)),x97302))+~P1(f775(f775(f233(x97301),f2(x97301)),f775(f775(f283(x97301),x97302),f775(f106(x97301),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.63 [10005]~P133(x100052)+E(x100051,f2(a1))+P1(f775(f775(f233(a1),x100051),f2(a1)))+E(f775(f775(f251(a1,a1,x100052),f775(f775(f9(a1,f857(a1,f857(x100052,x100052)),f857(a1,x100052)),f775(f775(f10(f857(f857(x100052,x100052),x100052),f857(f857(a1,f857(x100052,x100052)),f857(a1,x100052)),a1),f10(f857(x100052,x100052),x100052,a1)),f775(f775(f10(x100052,f857(f857(x100052,x100052),x100052),a1),f88(x100052,x100052)),f105(x100052)))),f775(f775(f9(a1,f857(x100052,x100052),f857(x100052,x100052)),f775(f775(f10(f857(x100052,f857(x100052,x100052)),f857(f857(x100052,x100052),f857(x100052,x100052)),a1),f20(x100052,x100052,x100052)),f775(f775(f9(a1,f857(x100052,x100052),f857(x100052,f857(x100052,x100052))),f775(f775(f10(f857(x100052,f857(x100052,x100052)),f857(f857(x100052,x100052),f857(x100052,f857(x100052,x100052))),a1),f10(x100052,f857(x100052,x100052),x100052)),f775(f775(f10(a844,f857(x100052,f857(x100052,x100052)),a1),f98(x100052)),f775(f775(f9(a1,a1,a844),a330),f2(a1))))),f775(f775(f20(x100052,x100052,x100052),f82(x100052)),f7(x100052))))),f775(f775(f9(x100052,x100052,x100052),f775(f775(f10(x100052,f857(x100052,x100052),x100052),f82(x100052)),f775(f775(f20(x100052,x100052,x100052),f82(x100052)),f7(x100052)))),f80(x100052))))),f53(x100051,f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f105(x100052),x100051)) % 186.05/186.63 [4757]~P87(x47573)+~P88(x47573)+E(x47571,x47572)+~E(f775(f106(x47573),x47571),f775(f106(x47573),x47572)) % 186.05/186.63 [5894]~P1(f775(x58941,x58942))+~P1(f775(x58941,x58943))+~P1(f775(f775(f232(a850),x58943),f792(x58942,x58941)))+P1(f775(x58941,f2(a850))) % 186.05/186.63 [6326]P140(x63262,x63261,x63263)+E(x63261,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f781(x63263,x63261,x63262)))+P1(f775(f775(f233(a1),x63261),f2(a1))) % 186.05/186.63 [6327]P141(x63272,x63271,x63273)+E(x63271,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f786(x63273,x63271,x63272)))+P1(f775(f775(f233(a1),x63271),f2(a1))) % 186.05/186.63 [6459]P140(x64591,x64592,x64593)+~P1(f775(x64591,x64593))+P1(f775(f775(f232(a1),f2(a1)),f781(x64593,x64592,x64591)))+P1(f775(f775(f233(a1),x64592),f2(a1))) % 186.05/186.63 [6484]P141(x64841,x64842,x64843)+P1(f775(f775(f232(a1),f2(a1)),f786(x64843,x64842,x64841)))+~P1(f775(x64841,f2(a1)))+P1(f775(f775(f233(a1),x64842),f2(a1))) % 186.05/186.63 [6516]P140(x65162,x65161,x65163)+E(x65161,f2(a1))+~P1(f775(x65162,f781(x65163,x65161,x65162)))+P1(f775(f775(f233(a1),x65161),f2(a1))) % 186.05/186.63 [6517]P141(x65172,x65171,x65173)+E(x65171,f2(a1))+~P1(f775(x65172,f787(x65173,x65171,x65172)))+P1(f775(f775(f233(a1),x65171),f2(a1))) % 186.05/186.63 [6621]~P100(x66211)+~P9(x66211)+~P1(f775(f775(f233(x66211),x66212),f44(x66211,x66213)))+P1(f775(f775(f233(x66211),x66212),f671(x66213,x66212,x66211))) % 186.05/186.63 [6631]P140(x66311,x66312,x66313)+~P1(f775(x66311,x66313))+~P1(f775(x66311,f781(x66313,x66312,x66311)))+P1(f775(f775(f233(a1),x66312),f2(a1))) % 186.05/186.63 [6664]P141(x66641,x66642,x66643)+~P1(f775(x66641,f787(x66643,x66642,x66641)))+~P1(f775(x66641,f2(a1)))+P1(f775(f775(f233(a1),x66642),f2(a1))) % 186.05/186.63 [6927]P140(x69272,x69271,x69273)+E(x69271,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f781(x69273,x69271,x69272)))+P1(f775(f775(f233(a1),x69271),f780(x69273,x69271,x69272))) % 186.05/186.63 [6928]P141(x69282,x69281,x69283)+E(x69281,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f786(x69283,x69281,x69282)))+P1(f775(f775(f233(a1),x69281),f785(x69283,x69281,x69282))) % 186.05/186.63 [7045]P140(x70451,x70452,x70453)+~P1(f775(x70451,x70453))+P1(f775(f775(f232(a1),f2(a1)),f781(x70453,x70452,x70451)))+P1(f775(f775(f233(a1),x70452),f780(x70453,x70452,x70451))) % 186.05/186.63 [7066]P141(x70661,x70662,x70663)+P1(f775(f775(f232(a1),f2(a1)),f786(x70663,x70662,x70661)))+P1(f775(f775(f233(a1),x70662),f785(x70663,x70662,x70661)))+~P1(f775(x70661,f2(a1))) % 186.05/186.63 [7097]P140(x70972,x70971,x70973)+E(x70971,f2(a1))+~P1(f775(x70972,f781(x70973,x70971,x70972)))+P1(f775(f775(f233(a1),x70971),f780(x70973,x70971,x70972))) % 186.05/186.63 [7098]P141(x70982,x70981,x70983)+E(x70981,f2(a1))+~P1(f775(x70982,f787(x70983,x70981,x70982)))+P1(f775(f775(f233(a1),x70981),f785(x70983,x70981,x70982))) % 186.05/186.63 [7138]P140(x71382,x71381,x71383)+E(x71381,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f781(x71383,x71381,x71382)))+~P1(f775(x71382,f780(x71383,x71381,x71382))) % 186.05/186.63 [7139]P141(x71392,x71391,x71393)+E(x71391,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f786(x71393,x71391,x71392)))+~P1(f775(x71392,f788(x71393,x71391,x71392))) % 186.05/186.63 [7244]P140(x72441,x72442,x72443)+~P1(f775(x72441,x72443))+~P1(f775(x72441,f781(x72443,x72442,x72441)))+P1(f775(f775(f233(a1),x72442),f780(x72443,x72442,x72441))) % 186.05/186.63 [7260]P141(x72601,x72602,x72603)+~P1(f775(x72601,f787(x72603,x72602,x72601)))+P1(f775(f775(f233(a1),x72602),f785(x72603,x72602,x72601)))+~P1(f775(x72601,f2(a1))) % 186.05/186.63 [7266]P140(x72661,x72662,x72663)+~P1(f775(x72661,x72663))+P1(f775(f775(f232(a1),f2(a1)),f781(x72663,x72662,x72661)))+~P1(f775(x72661,f780(x72663,x72662,x72661))) % 186.05/186.63 [7284]P141(x72841,x72842,x72843)+P1(f775(f775(f232(a1),f2(a1)),f786(x72843,x72842,x72841)))+~P1(f775(x72841,f788(x72843,x72842,x72841)))+~P1(f775(x72841,f2(a1))) % 186.05/186.63 [7308]P140(x73082,x73081,x73083)+E(x73081,f2(a1))+~P1(f775(x73082,f781(x73083,x73081,x73082)))+~P1(f775(x73082,f780(x73083,x73081,x73082))) % 186.05/186.63 [7309]P141(x73092,x73091,x73093)+E(x73091,f2(a1))+~P1(f775(x73092,f787(x73093,x73091,x73092)))+~P1(f775(x73092,f788(x73093,x73091,x73092))) % 186.05/186.63 [7405]P140(x74051,x74052,x74053)+~P1(f775(x74051,x74053))+~P1(f775(x74051,f781(x74053,x74052,x74051)))+~P1(f775(x74051,f780(x74053,x74052,x74051))) % 186.05/186.63 [7420]P141(x74201,x74202,x74203)+~P1(f775(x74201,f787(x74203,x74202,x74201)))+~P1(f775(x74201,f788(x74203,x74202,x74201)))+~P1(f775(x74201,f2(a1))) % 186.05/186.63 [7471]P140(x74712,x74711,x74713)+E(x74711,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f781(x74713,x74711,x74712)))+P1(f775(f775(f232(a1),f780(x74713,x74711,x74712)),f2(a1))) % 186.05/186.63 [7472]P141(x74722,x74721,x74723)+E(x74721,f2(a1))+P1(f775(f775(f232(a1),f2(a1)),f786(x74723,x74721,x74722)))+P1(f775(f775(f232(a1),f785(x74723,x74721,x74722)),f2(a1))) % 186.05/186.63 [7473]~P2(x74731)+~P1(f775(f775(f334(x74731),x74733),f176(x74731)))+~P1(f775(f775(f334(x74731),x74732),f176(x74731)))+P1(f775(f775(f334(x74731),f775(f775(f82(x74731),x74732),x74733)),f176(x74731))) % 186.05/186.63 [7474]~P133(x74741)+~P1(f775(f775(f334(x74741),x74743),f112(x74741)))+~P1(f775(f775(f334(x74741),x74742),f112(x74741)))+P1(f775(f775(f334(x74741),f775(f775(f82(x74741),x74742),x74743)),f112(x74741))) % 186.05/186.63 [7475]~P2(x74751)+~P1(f775(f775(f334(x74751),x74753),f176(x74751)))+~P1(f775(f775(f334(x74751),x74752),f176(x74751)))+P1(f775(f775(f334(x74751),f775(f775(f83(x74751),x74752),x74753)),f176(x74751))) % 186.05/186.63 [7476]~P133(x74761)+~P1(f775(f775(f334(x74761),x74763),f112(x74761)))+~P1(f775(f775(f334(x74761),x74762),f112(x74761)))+P1(f775(f775(f334(x74761),f775(f775(f83(x74761),x74762),x74763)),f112(x74761))) % 186.05/186.63 [7477]~P133(x74771)+~P1(f775(f775(f334(x74771),x74773),f112(x74771)))+~P1(f775(f775(f334(x74771),x74772),f112(x74771)))+P1(f775(f775(f334(x74771),f775(f775(f3(x74771),x74772),x74773)),f112(x74771))) % 186.05/186.63 [7478]~P81(x74781)+~P1(f775(f775(f233(x74781),x74783),f2(x74781)))+~P1(f775(f775(f233(x74781),x74782),f2(x74781)))+P1(f775(f775(f233(x74781),f775(f775(f82(x74781),x74782),x74783)),f2(x74781))) % 186.05/186.63 [7479]~P81(x74791)+~P1(f775(f775(f232(x74791),x74792),f2(x74791)))+~P1(f775(f775(f233(x74791),x74793),f2(x74791)))+P1(f775(f775(f233(x74791),f775(f775(f82(x74791),x74792),x74793)),f2(x74791))) % 186.05/186.63 [7480]~P81(x74801)+~P1(f775(f775(f232(x74801),x74803),f2(x74801)))+~P1(f775(f775(f233(x74801),x74802),f2(x74801)))+P1(f775(f775(f233(x74801),f775(f775(f82(x74801),x74802),x74803)),f2(x74801))) % 186.05/186.63 [7481]~P81(x74811)+~P1(f775(f775(f232(x74811),x74813),f2(x74811)))+~P1(f775(f775(f232(x74811),x74812),f2(x74811)))+P1(f775(f775(f232(x74811),f775(f775(f82(x74811),x74812),x74813)),f2(x74811))) % 186.05/186.63 [7507]P140(x75073,x75071,x75072)+E(x75071,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x75071),f782(x75072,x75071,x75073))),f781(x75072,x75071,x75073)),x75072)+P1(f775(f775(f233(a1),x75071),f2(a1))) % 186.05/186.63 [7508]P141(x75083,x75081,x75082)+E(x75081,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x75081),f787(x75082,x75081,x75083))),f786(x75082,x75081,x75083)),x75082)+P1(f775(f775(f233(a1),x75081),f2(a1))) % 186.05/186.63 [7593]P140(x75931,x75932,x75933)+~P1(f775(x75931,x75933))+P1(f775(f775(f232(a1),f2(a1)),f781(x75933,x75932,x75931)))+P1(f775(f775(f232(a1),f780(x75933,x75932,x75931)),f2(a1))) % 186.05/186.63 [7624]P141(x76241,x76242,x76243)+P1(f775(f775(f232(a1),f2(a1)),f786(x76243,x76242,x76241)))+~P1(f775(x76241,f2(a1)))+P1(f775(f775(f232(a1),f785(x76243,x76242,x76241)),f2(a1))) % 186.05/186.63 [7632]P140(x76323,x76321,x76322)+~P1(f775(x76323,x76322))+E(f775(f775(f82(a1),f775(f775(f83(a1),x76321),f782(x76322,x76321,x76323))),f781(x76322,x76321,x76323)),x76322)+P1(f775(f775(f233(a1),x76321),f2(a1))) % 186.05/186.63 [7637]P140(x76372,x76371,x76373)+E(x76371,f2(a1))+~P1(f775(x76372,f781(x76373,x76371,x76372)))+P1(f775(f775(f232(a1),f780(x76373,x76371,x76372)),f2(a1))) % 186.05/186.63 [7638]P141(x76382,x76381,x76383)+E(x76381,f2(a1))+~P1(f775(x76382,f787(x76383,x76381,x76382)))+P1(f775(f775(f232(a1),f785(x76383,x76381,x76382)),f2(a1))) % 186.05/186.63 [7643]P141(x76433,x76431,x76432)+E(f775(f775(f82(a1),f775(f775(f83(a1),x76431),f787(x76432,x76431,x76433))),f786(x76432,x76431,x76433)),x76432)+~P1(f775(x76433,f2(a1)))+P1(f775(f775(f233(a1),x76431),f2(a1))) % 186.05/186.63 [7696]P140(x76961,x76962,x76963)+~P1(f775(x76961,x76963))+~P1(f775(x76961,f781(x76963,x76962,x76961)))+P1(f775(f775(f232(a1),f780(x76963,x76962,x76961)),f2(a1))) % 186.05/186.63 [7701]P141(x77011,x77012,x77013)+~P1(f775(x77011,f787(x77013,x77012,x77011)))+~P1(f775(x77011,f2(a1)))+P1(f775(f775(f232(a1),f785(x77013,x77012,x77011)),f2(a1))) % 186.05/186.63 [7775]~P62(x77751)+~P1(f775(f775(f233(x77751),f775(f775(f283(x77751),x77753),x77752)),f2(x77751)))+P1(f775(f775(f233(x77751),x77752),f2(x77751)))+P1(f775(f775(f233(x77751),x77753),f2(x77751))) % 186.05/186.63 [7776]~P119(x77761)+~P1(f775(f775(f232(x77761),f775(f775(f83(x77761),x77763),x77762)),f2(x77761)))+P1(f775(f775(f232(x77761),x77762),f2(x77761)))+P1(f775(f775(f232(x77761),x77763),f2(x77761))) % 186.05/186.63 [7777]~P62(x77771)+~P1(f775(f775(f232(x77771),f775(f775(f283(x77771),x77773),x77772)),f2(x77771)))+P1(f775(f775(f232(x77771),x77772),f2(x77771)))+P1(f775(f775(f232(x77771),x77773),f2(x77771))) % 186.05/186.63 [7889]P140(x78893,x78891,x78892)+E(x78891,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x78891),f782(x78892,x78891,x78893))),f781(x78892,x78891,x78893)),x78892)+P1(f775(f775(f233(a1),x78891),f780(x78892,x78891,x78893))) % 186.05/186.63 [7890]P141(x78903,x78901,x78902)+E(x78901,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x78901),f787(x78902,x78901,x78903))),f786(x78902,x78901,x78903)),x78902)+P1(f775(f775(f233(a1),x78901),f785(x78902,x78901,x78903))) % 186.05/186.63 [7901]P140(x79013,x79011,x79012)+E(x79011,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79011),f784(x79012,x79011,x79013))),f780(x79012,x79011,x79013)),x79012)+P1(f775(f775(f232(a1),f2(a1)),f781(x79012,x79011,x79013))) % 186.05/186.63 [7902]P141(x79023,x79021,x79022)+E(x79021,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79021),f788(x79022,x79021,x79023))),f785(x79022,x79021,x79023)),x79022)+P1(f775(f775(f232(a1),f2(a1)),f786(x79022,x79021,x79023))) % 186.05/186.63 [7949]P140(x79493,x79491,x79492)+~P1(f775(x79493,x79492))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79491),f782(x79492,x79491,x79493))),f781(x79492,x79491,x79493)),x79492)+P1(f775(f775(f233(a1),x79491),f780(x79492,x79491,x79493))) % 186.05/186.63 [7960]P141(x79603,x79601,x79602)+E(f775(f775(f82(a1),f775(f775(f83(a1),x79601),f787(x79602,x79601,x79603))),f786(x79602,x79601,x79603)),x79602)+P1(f775(f775(f233(a1),x79601),f785(x79602,x79601,x79603)))+~P1(f775(x79603,f2(a1))) % 186.05/186.63 [7966]P140(x79663,x79661,x79662)+~P1(f775(x79663,x79662))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79661),f784(x79662,x79661,x79663))),f780(x79662,x79661,x79663)),x79662)+P1(f775(f775(f232(a1),f2(a1)),f781(x79662,x79661,x79663))) % 186.05/186.63 [7973]P141(x79733,x79731,x79732)+E(f775(f775(f82(a1),f775(f775(f83(a1),x79731),f788(x79732,x79731,x79733))),f785(x79732,x79731,x79733)),x79732)+P1(f775(f775(f232(a1),f2(a1)),f786(x79732,x79731,x79733)))+~P1(f775(x79733,f2(a1))) % 186.05/186.63 [7983]P140(x79833,x79831,x79832)+E(x79831,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79831),f782(x79832,x79831,x79833))),f781(x79832,x79831,x79833)),x79832)+~P1(f775(x79833,f780(x79832,x79831,x79833))) % 186.05/186.63 [7984]P141(x79843,x79841,x79842)+E(x79841,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79841),f787(x79842,x79841,x79843))),f786(x79842,x79841,x79843)),x79842)+~P1(f775(x79843,f788(x79842,x79841,x79843))) % 186.05/186.63 [7985]P140(x79853,x79851,x79852)+E(x79851,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79851),f784(x79852,x79851,x79853))),f780(x79852,x79851,x79853)),x79852)+~P1(f775(x79853,f781(x79852,x79851,x79853))) % 186.05/186.63 [7986]P141(x79863,x79861,x79862)+E(x79861,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x79861),f788(x79862,x79861,x79863))),f785(x79862,x79861,x79863)),x79862)+~P1(f775(x79863,f787(x79862,x79861,x79863))) % 186.05/186.63 [8039]P140(x80393,x80391,x80392)+~P1(f775(x80393,x80392))+E(f775(f775(f82(a1),f775(f775(f83(a1),x80391),f782(x80392,x80391,x80393))),f781(x80392,x80391,x80393)),x80392)+~P1(f775(x80393,f780(x80392,x80391,x80393))) % 186.05/186.63 [8040]P140(x80403,x80401,x80402)+~P1(f775(x80403,x80402))+E(f775(f775(f82(a1),f775(f775(f83(a1),x80401),f784(x80402,x80401,x80403))),f780(x80402,x80401,x80403)),x80402)+~P1(f775(x80403,f781(x80402,x80401,x80403))) % 186.05/186.63 [8052]P141(x80523,x80521,x80522)+E(f775(f775(f82(a1),f775(f775(f83(a1),x80521),f787(x80522,x80521,x80523))),f786(x80522,x80521,x80523)),x80522)+~P1(f775(x80523,f788(x80522,x80521,x80523)))+~P1(f775(x80523,f2(a1))) % 186.05/186.63 [8053]P141(x80533,x80531,x80532)+E(f775(f775(f82(a1),f775(f775(f83(a1),x80531),f788(x80532,x80531,x80533))),f785(x80532,x80531,x80533)),x80532)+~P1(f775(x80533,f787(x80532,x80531,x80533)))+~P1(f775(x80533,f2(a1))) % 186.05/186.63 [8151]P140(x81513,x81511,x81512)+E(x81511,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81511),f782(x81512,x81511,x81513))),f781(x81512,x81511,x81513)),x81512)+P1(f775(f775(f232(a1),f780(x81512,x81511,x81513)),f2(a1))) % 186.05/186.63 [8152]P141(x81523,x81521,x81522)+E(x81521,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81521),f787(x81522,x81521,x81523))),f786(x81522,x81521,x81523)),x81522)+P1(f775(f775(f232(a1),f785(x81522,x81521,x81523)),f2(a1))) % 186.05/186.63 [8190]P140(x81903,x81901,x81902)+~P1(f775(x81903,x81902))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81901),f782(x81902,x81901,x81903))),f781(x81902,x81901,x81903)),x81902)+P1(f775(f775(f232(a1),f780(x81902,x81901,x81903)),f2(a1))) % 186.05/186.63 [8195]P141(x81953,x81951,x81952)+E(f775(f775(f82(a1),f775(f775(f83(a1),x81951),f787(x81952,x81951,x81953))),f786(x81952,x81951,x81953)),x81952)+~P1(f775(x81953,f2(a1)))+P1(f775(f775(f232(a1),f785(x81952,x81951,x81953)),f2(a1))) % 186.05/186.63 [8326]P140(x83263,x83261,x83262)+E(x83261,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x83261),f784(x83262,x83261,x83263))),f780(x83262,x83261,x83263)),x83262)+E(f775(f775(f82(a1),f775(f775(f83(a1),x83261),f782(x83262,x83261,x83263))),f781(x83262,x83261,x83263)),x83262) % 186.05/186.63 [8327]P141(x83273,x83271,x83272)+E(x83271,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x83271),f788(x83272,x83271,x83273))),f785(x83272,x83271,x83273)),x83272)+E(f775(f775(f82(a1),f775(f775(f83(a1),x83271),f787(x83272,x83271,x83273))),f786(x83272,x83271,x83273)),x83272) % 186.05/186.63 [8350]P140(x83503,x83501,x83502)+~P1(f775(x83503,x83502))+E(f775(f775(f82(a1),f775(f775(f83(a1),x83501),f784(x83502,x83501,x83503))),f780(x83502,x83501,x83503)),x83502)+E(f775(f775(f82(a1),f775(f775(f83(a1),x83501),f782(x83502,x83501,x83503))),f781(x83502,x83501,x83503)),x83502) % 186.05/186.63 [8362]P141(x83623,x83621,x83622)+E(f775(f775(f82(a1),f775(f775(f83(a1),x83621),f788(x83622,x83621,x83623))),f785(x83622,x83621,x83623)),x83622)+E(f775(f775(f82(a1),f775(f775(f83(a1),x83621),f787(x83622,x83621,x83623))),f786(x83622,x83621,x83623)),x83622)+~P1(f775(x83623,f2(a1))) % 186.05/186.63 [8956]~P119(x89561)+~E(x89563,f2(x89561))+~E(x89562,f2(x89561))+P1(f775(f775(f232(x89561),f775(f775(f82(x89561),f775(f775(f83(x89561),x89562),x89562)),f775(f775(f83(x89561),x89563),x89563))),f2(x89561))) % 186.05/186.63 [9955]~P110(x99551)+~E(x99553,f2(x99551))+~E(x99552,f2(x99551))+P1(f775(f775(f232(x99551),f775(f775(f82(x99551),f775(f775(f242(x99551),x99552),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99551),x99553),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))),f2(x99551))) % 186.05/186.63 [4707]~E(x47073,x47071)+~P113(x47072)+E(x47071,f2(x47072))+E(f775(f775(f283(x47072),x47073),x47071),f80(x47072)) % 186.05/186.63 [4758]~P95(x47581)+~E(x47583,f180(x47581))+~E(x47582,f180(x47581))+E(f775(f775(f103(x47581),x47582),x47583),f180(x47581)) % 186.05/186.63 [4759]~P94(x47591)+~E(x47593,f239(x47591))+~E(x47592,f239(x47591))+E(f775(f775(f104(x47591),x47592),x47593),f239(x47591)) % 186.05/186.63 [4845]~P113(x48453)+E(x48451,x48452)+E(x48452,f2(x48453))+~E(f775(f775(f283(x48453),x48451),x48452),f80(x48453)) % 186.05/186.63 [4861]~P134(x48612)+E(x48611,f2(x48612))+E(x48613,f2(x48612))+~E(f775(f775(f83(x48612),x48613),x48611),f2(x48612)) % 186.05/186.63 [4863]~P127(x48632)+E(x48631,f2(x48632))+E(x48633,f2(x48632))+~E(f775(f775(f83(x48632),x48633),x48631),f2(x48632)) % 186.05/186.63 [5232]~P111(x52323)+E(x52321,x52322)+E(x52321,f775(f81(x52323),x52322))+~E(f775(f775(f83(x52323),x52321),x52321),f775(f775(f83(x52323),x52322),x52322)) % 186.05/186.63 [5268]~P90(x52681)+E(f775(f81(x52681),x52682),x52683)+~E(f775(f775(f103(x52681),x52682),x52683),f239(x52681))+~E(f775(f775(f104(x52681),x52682),x52683),f180(x52681)) % 186.05/186.63 [5343]~P110(x53433)+E(x53431,x53432)+P1(f775(f775(f233(x53433),x53432),x53431))+P1(f775(f775(f233(x53433),x53431),x53432)) % 186.05/186.63 [5349]~P100(x53493)+E(x53491,x53492)+P1(f775(f775(f233(x53493),x53492),x53491))+P1(f775(f775(f233(x53493),x53491),x53492)) % 186.05/186.63 [5350]~E(x53502,x53503)+~P100(x53501)+P1(f775(f775(f232(x53501),x53502),x53503))+P1(f775(f775(f233(x53501),x53502),x53503)) % 186.05/186.63 [5596]~P99(x55963)+E(x55961,x55962)+~P1(f775(f775(f232(x55963),x55962),x55961))+P1(f775(f775(f233(x55963),x55962),x55961)) % 186.05/186.63 [5602]~P99(x56023)+E(x56021,x56022)+~P1(f775(f775(f232(x56023),x56021),x56022))+P1(f775(f775(f233(x56023),x56021),x56022)) % 186.05/186.63 [5604]~P100(x56043)+E(x56041,x56042)+~P1(f775(f775(f232(x56043),x56041),x56042))+P1(f775(f775(f233(x56043),x56041),x56042)) % 186.05/186.63 [5716]P140(x57161,x57162,x57163)+~P1(f775(x57161,x57163))+P1(f775(f775(f233(a1),x57162),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x57162)) % 186.05/186.63 [5767]P141(x57671,x57672,x57673)+~P1(f775(x57671,f2(a1)))+P1(f775(f775(f233(a1),x57672),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x57672)) % 186.05/186.63 [5771]~P93(x57711)+E(f775(f775(f103(x57711),x57712),f12(x57711,x57713)),x57712)+~P1(f775(f63(x57711),x57713))+~P1(f775(f775(f334(x57711),x57712),x57713)) % 186.05/186.63 [5772]~P93(x57721)+E(f775(f775(f104(x57721),x57722),f15(x57721,x57723)),x57722)+~P1(f775(f63(x57721),x57723))+~P1(f775(f775(f334(x57721),x57722),x57723)) % 186.05/186.63 [5805]~P100(x58051)+E(f775(f775(f236(x58051),x58052),f17(x58051,x58053)),f17(x58051,x58053))+~P1(f775(f63(x58051),x58053))+~P1(f775(f775(f334(x58051),x58052),x58053)) % 186.05/186.63 [5806]~P100(x58061)+E(f775(f775(f179(x58061),x58062),f16(x58061,x58063)),f16(x58061,x58063))+~P1(f775(f63(x58061),x58063))+~P1(f775(f775(f334(x58061),x58062),x58063)) % 186.05/186.63 [5807]~P93(x58071)+E(f775(f775(f103(x58071),x58072),f15(x58071,x58073)),f15(x58071,x58073))+~P1(f775(f63(x58071),x58073))+~P1(f775(f775(f334(x58071),x58072),x58073)) % 186.05/186.63 [5808]~P93(x58081)+E(f775(f775(f104(x58081),x58082),f12(x58081,x58083)),f12(x58081,x58083))+~P1(f775(f63(x58081),x58083))+~P1(f775(f775(f334(x58081),x58082),x58083)) % 186.05/186.63 [5848]E(x58481,x58482)+~P99(x58483)+~P1(f775(f775(f232(x58483),x58482),x58481))+~P1(f775(f775(f232(x58483),x58481),x58482)) % 186.05/186.63 [5990]~P103(x59901)+P1(f775(f775(f232(x59901),x59903),x59902))+~P1(f775(f775(f232(x59901),x59902),x59903))+P1(f775(f775(f233(x59901),x59902),x59903)) % 186.05/186.63 [6014]~P100(x60141)+~P1(f775(f63(x60141),x60143))+P1(f775(f775(f232(x60141),x60142),f16(x60141,x60143)))+~P1(f775(f775(f334(x60141),x60142),x60143)) % 186.05/186.63 [6068]~P100(x60681)+E(f775(f775(f236(x60681),x60682),f13(x60681,f179(x60681),x60683)),x60682)+~P1(f775(f63(x60681),x60683))+~P1(f775(f775(f334(x60681),x60682),x60683)) % 186.05/186.63 [6069]~P100(x60691)+E(f775(f775(f179(x60691),x60692),f14(x60691,f236(x60691),x60693)),x60692)+~P1(f775(f63(x60691),x60693))+~P1(f775(f775(f334(x60691),x60692),x60693)) % 186.05/186.63 [6210]E(x62101,x62102)+~E(f775(f775(f3(a850),x62101),x62103),f775(f775(f3(a850),x62102),x62103))+~P1(f775(f775(f232(a850),x62103),x62101))+~P1(f775(f775(f232(a850),x62103),x62102)) % 186.05/186.63 [6238]~P100(x62381)+~P1(f775(f63(x62381),x62382))+~P1(f775(f775(f334(x62381),x62383),x62382))+P1(f775(f775(f232(x62381),f17(x62381,x62382)),x62383)) % 186.05/186.63 [6305]P140(x63052,x63051,x63053)+E(x63051,f2(a1))+P1(f775(f775(f233(a1),x63051),f780(x63053,x63051,x63052)))+P1(f775(f775(f233(a1),f2(a1)),x63051)) % 186.05/186.63 [6306]P141(x63062,x63061,x63063)+E(x63061,f2(a1))+P1(f775(f775(f233(a1),x63061),f785(x63063,x63061,x63062)))+P1(f775(f775(f233(a1),f2(a1)),x63061)) % 186.05/186.63 [6307]~P100(x63071)+E(f775(f775(f236(x63071),x63072),f14(x63071,f236(x63071),x63073)),f14(x63071,f236(x63071),x63073))+~P1(f775(f63(x63071),x63073))+~P1(f775(f775(f334(x63071),x63072),x63073)) % 186.05/186.63 [6308]~P100(x63081)+E(f775(f775(f179(x63081),x63082),f13(x63081,f179(x63081),x63083)),f13(x63081,f179(x63081),x63083))+~P1(f775(f63(x63081),x63083))+~P1(f775(f775(f334(x63081),x63082),x63083)) % 186.05/186.63 [6315]~P1(f775(x63151,x63152))+P1(f775(x63151,f810(x63152,x63151,x63153)))+P1(f775(x63151,f2(a850)))+~P1(f775(f775(f233(a850),x63152),x63153)) % 186.05/186.63 [6374]~P1(f775(x63741,x63742))+~P1(f775(f63(x63743),x63742))+P1(f775(x63741,f482(x63741,x63742,x63743)))+P1(f775(x63741,f180(f857(x63743,a844)))) % 186.05/186.63 [6389]~P110(x63891)+~P88(x63891)+P1(f775(f775(f233(x63891),f775(f106(x63891),x63892)),f775(f106(x63891),x63893)))+~P1(f775(f775(f233(a1),x63892),x63893)) % 186.05/186.63 [6390]~P110(x63901)+~P88(x63901)+P1(f775(f775(f232(x63901),f775(f106(x63901),x63902)),f775(f106(x63901),x63903)))+~P1(f775(f775(f232(a1),x63902),x63903)) % 186.05/186.63 [6393]~P1(f775(x63931,x63933))+~P1(f775(f63(x63932),x63933))+P1(f775(f63(x63932),f482(x63931,x63933,x63932)))+P1(f775(x63931,f180(f857(x63932,a844)))) % 186.05/186.63 [6427]P140(x64271,x64272,x64273)+~P1(f775(x64271,x64273))+P1(f775(f775(f233(a1),x64272),f780(x64273,x64272,x64271)))+P1(f775(f775(f233(a1),f2(a1)),x64272)) % 186.05/186.63 [6467]P141(x64671,x64672,x64673)+P1(f775(f775(f233(a1),x64672),f785(x64673,x64672,x64671)))+~P1(f775(x64671,f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x64672)) % 186.05/186.63 [6495]~P102(x64951)+~P89(x64951)+E(f775(f775(f236(x64951),f775(f106(x64951),x64952)),f775(f106(x64951),x64953)),f775(f106(x64951),x64953))+P1(f775(f775(f232(x64951),f775(f106(x64951),x64952)),f775(f106(x64951),x64953))) % 186.05/186.63 [6496]~P102(x64961)+~P89(x64961)+E(f775(f775(f179(x64961),f775(f106(x64961),x64962)),f775(f106(x64961),x64963)),f775(f106(x64961),x64962))+P1(f775(f775(f232(x64961),f775(f106(x64961),x64962)),f775(f106(x64961),x64963))) % 186.05/186.63 [6558]P140(x65582,x65581,x65583)+E(x65581,f2(a1))+~P1(f775(x65582,f780(x65583,x65581,x65582)))+P1(f775(f775(f233(a1),f2(a1)),x65581)) % 186.05/186.63 [6559]P141(x65592,x65591,x65593)+E(x65591,f2(a1))+~P1(f775(x65592,f788(x65593,x65591,x65592)))+P1(f775(f775(f233(a1),f2(a1)),x65591)) % 186.05/186.63 [6654]P140(x66541,x66542,x66543)+~P1(f775(x66541,x66543))+~P1(f775(x66541,f780(x66543,x66542,x66541)))+P1(f775(f775(f233(a1),f2(a1)),x66542)) % 186.05/186.63 [6684]P141(x66841,x66842,x66843)+~P1(f775(x66841,f788(x66843,x66842,x66841)))+~P1(f775(x66841,f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x66842)) % 186.05/186.63 [6801]~P88(x68013)+~P110(x68013)+~P1(f775(f775(f233(x68013),f775(f106(x68013),x68011)),f775(f106(x68013),x68012)))+P1(f775(f775(f233(a1),x68011),x68012)) % 186.05/186.63 [6802]~P88(x68023)+~P110(x68023)+~P1(f775(f775(f232(x68023),f775(f106(x68023),x68021)),f775(f106(x68023),x68022)))+P1(f775(f775(f232(a1),x68021),x68022)) % 186.05/186.63 [6831]~P100(x68311)+~P18(x68311,x68313)+P18(x68311,f775(f775(f140(x68311),x68312),x68313))+~P1(f775(f775(f232(x68311),x68312),f763(x68313,x68312,x68311))) % 186.05/186.63 [6832]~P100(x68321)+~P18(x68321,x68323)+P18(x68321,f775(f775(f140(x68321),x68322),x68323))+~P1(f775(f775(f232(x68321),x68322),f764(x68323,x68322,x68321))) % 186.05/186.63 [6919]P140(x69192,x69191,x69193)+E(x69191,f2(a1))+P1(f775(f775(f233(a1),x69191),f2(a1)))+P1(f775(f775(f233(a1),f781(x69193,x69191,x69192)),x69191)) % 186.05/186.63 [6920]P141(x69202,x69201,x69203)+E(x69201,f2(a1))+P1(f775(f775(f233(a1),x69201),f2(a1)))+P1(f775(f775(f233(a1),f786(x69203,x69201,x69202)),x69201)) % 186.05/186.63 [6959]P140(x69592,x69591,x69593)+E(x69591,f2(a1))+P1(f775(f775(f232(a1),f780(x69593,x69591,x69592)),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x69591)) % 186.05/186.63 [6960]P141(x69602,x69601,x69603)+E(x69601,f2(a1))+P1(f775(f775(f232(a1),f785(x69603,x69601,x69602)),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x69601)) % 186.05/186.63 [6978]~P100(x69781)+~P18(x69781,x69783)+E(f775(f775(f138(x69781,x69781,f7(x69781)),x69782),f151(x69781,x69782,x69783)),x69783)+~P1(f775(f775(f334(x69781),x69782),f775(f158(x69781),x69783))) % 186.05/186.63 [7028]P140(x70281,x70282,x70283)+~P1(f775(x70281,x70283))+P1(f775(f775(f233(a1),x70282),f2(a1)))+P1(f775(f775(f233(a1),f781(x70283,x70282,x70281)),x70282)) % 186.05/186.63 [7034]~P102(x70341)+~P89(x70341)+E(f775(f775(f236(x70341),f775(f106(x70341),x70342)),f775(f106(x70341),x70343)),f775(f106(x70341),x70342))+~P1(f775(f775(f232(x70341),f775(f106(x70341),x70342)),f775(f106(x70341),x70343))) % 186.05/186.63 [7035]~P102(x70351)+~P89(x70351)+E(f775(f775(f179(x70351),f775(f106(x70351),x70352)),f775(f106(x70351),x70353)),f775(f106(x70351),x70353))+~P1(f775(f775(f232(x70351),f775(f106(x70351),x70352)),f775(f106(x70351),x70353))) % 186.05/186.63 [7048]P141(x70481,x70482,x70483)+~P1(f775(x70481,f2(a1)))+P1(f775(f775(f233(a1),x70482),f2(a1)))+P1(f775(f775(f233(a1),f786(x70483,x70482,x70481)),x70482)) % 186.05/186.63 [7058]P140(x70581,x70582,x70583)+~P1(f775(x70581,x70583))+P1(f775(f775(f232(a1),f780(x70583,x70582,x70581)),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x70582)) % 186.05/186.63 [7082]P141(x70821,x70822,x70823)+~P1(f775(x70821,f2(a1)))+P1(f775(f775(f232(a1),f785(x70823,x70822,x70821)),f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x70822)) % 186.05/186.63 [7109]~P1(f775(x71091,x71092))+P1(f775(x71091,f2(a850)))+~P1(f775(f775(f233(a850),x71092),x71093))+P1(f775(f775(f233(a850),f810(x71092,x71091,x71093)),x71093)) % 186.05/186.63 [7126]~P100(x71261)+~P18(x71261,x71263)+P18(x71261,f775(f775(f140(x71261),x71262),x71263))+P1(f775(f775(f334(x71261),f763(x71263,x71262,x71261)),f775(f158(x71261),x71263))) % 186.05/186.63 [7127]~P100(x71271)+~P18(x71271,x71273)+P18(x71271,f775(f775(f140(x71271),x71272),x71273))+P1(f775(f775(f334(x71271),f764(x71273,x71272,x71271)),f775(f158(x71271),x71273))) % 186.05/186.63 [7249]~P100(x72491)+~P9(x72491)+~P1(f775(f775(f233(x72491),x72493),f44(x72491,x72492)))+P1(f775(f775(f334(x72491),f671(x72492,x72493,x72491)),x72492)) % 186.05/186.63 [7418]~P100(x74181)+~P9(x74181)+~P1(f775(f775(f233(x74181),f45(x74181,x74183)),x74182))+P1(f775(f775(f334(x74181),f675(x74182,x74183,x74181)),x74183)) % 186.05/186.63 [7419]~P100(x74191)+~P9(x74191)+~P1(f775(f775(f233(x74191),f45(x74191,x74193)),x74192))+P1(f775(f775(f233(x74191),f675(x74192,x74193,x74191)),x74192)) % 186.05/186.63 [7433]P140(x74332,x74331,x74333)+E(x74331,f2(a1))+P1(f775(f775(f233(a1),x74331),f780(x74333,x74331,x74332)))+P1(f775(f775(f233(a1),f781(x74333,x74331,x74332)),x74331)) % 186.05/186.63 [7434]P141(x74342,x74341,x74343)+E(x74341,f2(a1))+P1(f775(f775(f233(a1),x74341),f785(x74343,x74341,x74342)))+P1(f775(f775(f233(a1),f786(x74343,x74341,x74342)),x74341)) % 186.05/186.63 [7530]P140(x75303,x75301,x75302)+E(x75301,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x75301),f784(x75302,x75301,x75303))),f780(x75302,x75301,x75303)),x75302)+P1(f775(f775(f233(a1),f2(a1)),x75301)) % 186.05/186.63 [7531]P141(x75313,x75311,x75312)+E(x75311,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x75311),f788(x75312,x75311,x75313))),f785(x75312,x75311,x75313)),x75312)+P1(f775(f775(f233(a1),f2(a1)),x75311)) % 186.05/186.63 [7533]~P123(x75331)+~P1(f775(f775(f233(x75331),x75333),f2(x75331)))+P1(f775(f775(f233(x75331),f775(f775(f83(x75331),x75332),x75333)),f2(x75331)))+~P1(f775(f775(f233(x75331),f2(x75331)),x75332)) % 186.05/186.63 [7534]~P123(x75341)+~P1(f775(f775(f233(x75341),x75342),f2(x75341)))+P1(f775(f775(f233(x75341),f775(f775(f83(x75341),x75342),x75343)),f2(x75341)))+~P1(f775(f775(f233(x75341),f2(x75341)),x75343)) % 186.05/186.63 [7535]~P62(x75351)+~P1(f775(f775(f233(x75351),x75353),f2(x75351)))+P1(f775(f775(f233(x75351),f775(f775(f283(x75351),x75352),x75353)),f2(x75351)))+~P1(f775(f775(f233(x75351),f2(x75351)),x75352)) % 186.05/186.63 [7536]~P62(x75361)+~P1(f775(f775(f233(x75361),x75362),f2(x75361)))+P1(f775(f775(f233(x75361),f775(f775(f283(x75361),x75362),x75363)),f2(x75361)))+~P1(f775(f775(f233(x75361),f2(x75361)),x75363)) % 186.05/186.63 [7537]~P63(x75371)+~P1(f775(f775(f233(x75371),x75373),f2(x75371)))+P1(f775(f775(f233(x75371),f775(f775(f283(x75371),x75372),x75373)),f2(x75371)))+~P1(f775(f775(f233(x75371),f2(x75371)),x75372)) % 186.05/186.63 [7538]~P63(x75381)+~P1(f775(f775(f233(x75381),x75382),f2(x75381)))+P1(f775(f775(f233(x75381),f775(f775(f283(x75381),x75382),x75383)),f2(x75381)))+~P1(f775(f775(f233(x75381),f2(x75381)),x75383)) % 186.05/186.63 [7540]~P119(x75401)+~P1(f775(f775(f232(x75401),x75403),f2(x75401)))+P1(f775(f775(f232(x75401),f775(f775(f83(x75401),x75402),x75403)),f2(x75401)))+~P1(f775(f775(f232(x75401),f2(x75401)),x75402)) % 186.05/186.63 [7541]~P119(x75411)+~P1(f775(f775(f232(x75411),x75412),f2(x75411)))+P1(f775(f775(f232(x75411),f775(f775(f83(x75411),x75412),x75413)),f2(x75411)))+~P1(f775(f775(f232(x75411),f2(x75411)),x75413)) % 186.05/186.63 [7543]~P128(x75431)+~P1(f775(f775(f232(x75431),x75433),f2(x75431)))+P1(f775(f775(f232(x75431),f775(f775(f83(x75431),x75432),x75433)),f2(x75431)))+~P1(f775(f775(f232(x75431),f2(x75431)),x75432)) % 186.05/186.63 [7545]~P128(x75451)+~P1(f775(f775(f232(x75451),x75452),f2(x75451)))+P1(f775(f775(f232(x75451),f775(f775(f83(x75451),x75452),x75453)),f2(x75451)))+~P1(f775(f775(f232(x75451),f2(x75451)),x75453)) % 186.05/186.63 [7546]~P62(x75461)+~P1(f775(f775(f232(x75461),x75463),f2(x75461)))+P1(f775(f775(f232(x75461),f775(f775(f283(x75461),x75462),x75463)),f2(x75461)))+~P1(f775(f775(f232(x75461),f2(x75461)),x75462)) % 186.05/186.63 [7547]~P62(x75471)+~P1(f775(f775(f232(x75471),x75472),f2(x75471)))+P1(f775(f775(f232(x75471),f775(f775(f283(x75471),x75472),x75473)),f2(x75471)))+~P1(f775(f775(f232(x75471),f2(x75471)),x75473)) % 186.05/186.63 [7548]~P63(x75481)+~P1(f775(f775(f233(x75481),x75483),f2(x75481)))+P1(f775(f775(f232(x75481),f775(f775(f283(x75481),x75482),x75483)),f2(x75481)))+~P1(f775(f775(f232(x75481),f2(x75481)),x75482)) % 186.05/186.63 [7549]~P63(x75491)+~P1(f775(f775(f232(x75491),x75492),f2(x75491)))+P1(f775(f775(f232(x75491),f775(f775(f283(x75491),x75492),x75493)),f2(x75491)))+~P1(f775(f775(f233(x75491),f2(x75491)),x75493)) % 186.05/186.63 [7565]P140(x75651,x75652,x75653)+~P1(f775(x75651,x75653))+P1(f775(f775(f233(a1),x75652),f780(x75653,x75652,x75651)))+P1(f775(f775(f233(a1),f781(x75653,x75652,x75651)),x75652)) % 186.05/186.63 [7578]P141(x75781,x75782,x75783)+P1(f775(f775(f233(a1),x75782),f785(x75783,x75782,x75781)))+~P1(f775(x75781,f2(a1)))+P1(f775(f775(f233(a1),f786(x75783,x75782,x75781)),x75782)) % 186.05/186.63 [7630]P140(x76302,x76301,x76303)+E(x76301,f2(a1))+~P1(f775(x76302,f780(x76303,x76301,x76302)))+P1(f775(f775(f233(a1),f781(x76303,x76301,x76302)),x76301)) % 186.05/186.63 [7631]P141(x76312,x76311,x76313)+E(x76311,f2(a1))+~P1(f775(x76312,f788(x76313,x76311,x76312)))+P1(f775(f775(f233(a1),f786(x76313,x76311,x76312)),x76311)) % 186.05/186.63 [7640]P140(x76403,x76401,x76402)+~P1(f775(x76403,x76402))+E(f775(f775(f82(a1),f775(f775(f83(a1),x76401),f784(x76402,x76401,x76403))),f780(x76402,x76401,x76403)),x76402)+P1(f775(f775(f233(a1),f2(a1)),x76401)) % 186.05/186.63 [7658]P141(x76583,x76581,x76582)+E(f775(f775(f82(a1),f775(f775(f83(a1),x76581),f788(x76582,x76581,x76583))),f785(x76582,x76581,x76583)),x76582)+~P1(f775(x76583,f2(a1)))+P1(f775(f775(f233(a1),f2(a1)),x76581)) % 186.05/186.63 [7682]~P1(f775(x76821,x76823))+~P1(f775(f63(x76822),x76823))+P1(f775(f775(f334(x76822),f483(x76821,x76823,x76822)),f482(x76821,x76823,x76822)))+P1(f775(x76821,f180(f857(x76822,a844)))) % 186.05/186.63 [7692]P140(x76921,x76922,x76923)+~P1(f775(x76921,x76923))+~P1(f775(x76921,f780(x76923,x76922,x76921)))+P1(f775(f775(f233(a1),f781(x76923,x76922,x76921)),x76922)) % 186.05/186.63 [7698]P141(x76981,x76982,x76983)+~P1(f775(x76981,f788(x76983,x76982,x76981)))+~P1(f775(x76981,f2(a1)))+P1(f775(f775(f233(a1),f786(x76983,x76982,x76981)),x76982)) % 186.05/186.63 [7806]~P62(x78061)+~P1(f775(f775(f233(x78061),f775(f775(f283(x78061),x78063),x78062)),f2(x78061)))+P1(f775(f775(f233(x78061),x78062),f2(x78061)))+P1(f775(f775(f233(x78061),f2(x78061)),x78062)) % 186.05/186.63 [7807]~P62(x78071)+~P1(f775(f775(f233(x78071),f775(f775(f283(x78071),x78072),x78073)),f2(x78071)))+P1(f775(f775(f233(x78071),x78072),f2(x78071)))+P1(f775(f775(f233(x78071),f2(x78071)),x78072)) % 186.05/186.63 [7808]~P119(x78081)+~P1(f775(f775(f232(x78081),f775(f775(f83(x78081),x78083),x78082)),f2(x78081)))+P1(f775(f775(f232(x78081),x78082),f2(x78081)))+P1(f775(f775(f232(x78081),f2(x78081)),x78082)) % 186.05/186.63 [7809]~P119(x78091)+~P1(f775(f775(f232(x78091),f775(f775(f83(x78091),x78092),x78093)),f2(x78091)))+P1(f775(f775(f232(x78091),x78092),f2(x78091)))+P1(f775(f775(f232(x78091),f2(x78091)),x78092)) % 186.05/186.63 [7810]~P62(x78101)+~P1(f775(f775(f232(x78101),f775(f775(f283(x78101),x78103),x78102)),f2(x78101)))+P1(f775(f775(f232(x78101),x78102),f2(x78101)))+P1(f775(f775(f232(x78101),f2(x78101)),x78102)) % 186.05/186.63 [7811]~P62(x78111)+~P1(f775(f775(f232(x78111),f775(f775(f283(x78111),x78112),x78113)),f2(x78111)))+P1(f775(f775(f232(x78111),x78112),f2(x78111)))+P1(f775(f775(f232(x78111),f2(x78111)),x78112)) % 186.05/186.63 [7837]~P62(x78371)+~P1(f775(f775(f233(x78371),f775(f775(f283(x78371),x78372),x78373)),f2(x78371)))+P1(f775(f775(f233(x78371),f2(x78371)),x78372))+P1(f775(f775(f233(x78371),f2(x78371)),x78373)) % 186.05/186.63 [7838]~P119(x78381)+~P1(f775(f775(f232(x78381),f775(f775(f83(x78381),x78382),x78383)),f2(x78381)))+P1(f775(f775(f232(x78381),f2(x78381)),x78382))+P1(f775(f775(f232(x78381),f2(x78381)),x78383)) % 186.05/186.63 [7839]~P62(x78391)+~P1(f775(f775(f232(x78391),f775(f775(f283(x78391),x78392),x78393)),f2(x78391)))+P1(f775(f775(f232(x78391),f2(x78391)),x78392))+P1(f775(f775(f232(x78391),f2(x78391)),x78393)) % 186.05/186.63 [7858]P140(x78582,x78581,x78583)+E(x78581,f2(a1))+P1(f775(f775(f232(a1),f780(x78583,x78581,x78582)),f2(a1)))+P1(f775(f775(f233(a1),f781(x78583,x78581,x78582)),x78581)) % 186.05/186.63 [7859]P141(x78592,x78591,x78593)+E(x78591,f2(a1))+P1(f775(f775(f232(a1),f785(x78593,x78591,x78592)),f2(a1)))+P1(f775(f775(f233(a1),f786(x78593,x78591,x78592)),x78591)) % 186.05/186.63 [7865]~P117(x78651)+~P1(f775(f775(f233(x78651),x78652),f80(x78651)))+P1(f775(f775(f233(x78651),f775(f775(f242(x78651),x78652),f775(a114,x78653))),f80(x78651)))+~P1(f775(f775(f233(x78651),f2(x78651)),x78652)) % 186.05/186.63 [7919]~P100(x79191)+~E(x79193,f115(x79191))+~P18(x79191,f775(f142(x79191),x79193))+E(f775(f132(x79191,x79191,f775(f9(x79191,x79191,x79191),f179(x79191)),x79192),f775(f142(x79191),x79193)),x79192) % 186.05/186.63 [7921]P140(x79211,x79212,x79213)+~P1(f775(x79211,x79213))+P1(f775(f775(f232(a1),f780(x79213,x79212,x79211)),f2(a1)))+P1(f775(f775(f233(a1),f781(x79213,x79212,x79211)),x79212)) % 186.05/186.63 [7933]P141(x79331,x79332,x79333)+~P1(f775(x79331,f2(a1)))+P1(f775(f775(f232(a1),f785(x79333,x79332,x79331)),f2(a1)))+P1(f775(f775(f233(a1),f786(x79333,x79332,x79331)),x79332)) % 186.05/186.63 [8146]P140(x81463,x81461,x81462)+E(x81461,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81461),f784(x81462,x81461,x81463))),f780(x81462,x81461,x81463)),x81462)+P1(f775(f775(f233(a1),f781(x81462,x81461,x81463)),x81461)) % 186.05/186.63 [8147]P141(x81473,x81471,x81472)+E(x81471,f2(a1))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81471),f788(x81472,x81471,x81473))),f785(x81472,x81471,x81473)),x81472)+P1(f775(f775(f233(a1),f786(x81472,x81471,x81473)),x81471)) % 186.05/186.63 [8182]P140(x81823,x81821,x81822)+~P1(f775(x81823,x81822))+E(f775(f775(f82(a1),f775(f775(f83(a1),x81821),f784(x81822,x81821,x81823))),f780(x81822,x81821,x81823)),x81822)+P1(f775(f775(f233(a1),f781(x81822,x81821,x81823)),x81821)) % 186.05/186.63 [8183]~P66(x81831)+~P70(x81831)+~P38(x81833)+E(f775(f775(f8(a850,x81831),f775(f775(f10(a1,x81831,a850),x81832),f102(a1))),f775(f303(a1,a850,a107),x81833)),f775(f775(f8(a1,x81831),x81832),x81833)) % 186.05/186.63 [8184]~P66(x81841)+~P70(x81841)+~P38(x81843)+E(f775(f775(f11(a850,x81841),f775(f775(f10(a1,x81841,a850),x81842),f102(a1))),f775(f303(a1,a850,a107),x81843)),f775(f775(f11(a1,x81841),x81842),x81843)) % 186.05/186.63 [8192]P141(x81923,x81921,x81922)+E(f775(f775(f82(a1),f775(f775(f83(a1),x81921),f788(x81922,x81921,x81923))),f785(x81922,x81921,x81923)),x81922)+~P1(f775(x81923,f2(a1)))+P1(f775(f775(f233(a1),f786(x81922,x81921,x81923)),x81921)) % 186.05/186.63 [8210]~E(x82102,f2(a850))+~E(f775(f240(a850,a850),x82103),f2(a850))+~E(x82101,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x82103)),x82102)),f775(f250(a850,a850),x82103)))+P1(f775(f55(x82101,x82102),x82103)) % 186.05/186.63 [9058]P1(f775(f775(f232(a1),x90581),f2(a1)))+~P1(f775(f775(f233(a1),f775(f775(f82(a1),f775(f775(f83(a1),x90582),x90581)),x90583)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x90582))+~P1(f775(f775(f232(a1),f2(a1)),x90583)) % 186.05/186.63 [5665]~P93(x56652)+E(x56651,f180(f857(x56652,a844)))+~P1(f775(f63(x56652),x56651))+E(f15(x56652,f775(f775(f302(x56652),x56653),x56651)),f775(f775(f103(x56652),x56653),f15(x56652,x56651))) % 186.05/186.63 [5666]~P100(x56662)+E(x56661,f180(f857(x56662,a844)))+~P1(f775(f63(x56662),x56661))+E(f16(x56662,f775(f775(f302(x56662),x56663),x56661)),f775(f775(f179(x56662),x56663),f16(x56662,x56661))) % 186.05/186.63 [5667]~P100(x56672)+E(x56671,f180(f857(x56672,a844)))+~P1(f775(f63(x56672),x56671))+E(f17(x56672,f775(f775(f302(x56672),x56673),x56671)),f775(f775(f236(x56672),x56673),f17(x56672,x56671))) % 186.05/186.63 [5668]~P93(x56682)+E(x56681,f180(f857(x56682,a844)))+~P1(f775(f63(x56682),x56681))+E(f12(x56682,f775(f775(f302(x56682),x56683),x56681)),f775(f775(f104(x56682),x56683),f12(x56682,x56681))) % 186.05/186.63 [5987]~P119(x59871)+~E(x59873,f2(x59871))+~E(x59872,f2(x59871))+E(f775(f775(f82(x59871),f775(f775(f83(x59871),x59872),x59872)),f775(f775(f83(x59871),x59873),x59873)),f2(x59871)) % 186.05/186.63 [6062]~P91(x60622)+E(x60621,f180(f857(x60622,a844)))+~P1(f775(f63(x60622),x60621))+E(f775(f65(x60622,f83(x60622)),f775(f775(f302(x60622),x60623),x60621)),f775(f775(f83(x60622),x60623),f775(f65(x60622,f83(x60622)),x60621))) % 186.05/186.63 [6188]~P100(x61882)+E(x61881,f180(f857(x61882,a844)))+~P1(f775(f63(x61882),x61881))+E(f13(x61882,f179(x61882),f775(f775(f302(x61882),x61883),x61881)),f775(f775(f179(x61882),x61883),f13(x61882,f179(x61882),x61881))) % 186.05/186.63 [6189]~P100(x61892)+E(x61891,f180(f857(x61892,a844)))+~P1(f775(f63(x61892),x61891))+E(f14(x61892,f236(x61892),f775(f775(f302(x61892),x61893),x61891)),f775(f775(f236(x61892),x61893),f14(x61892,f236(x61892),x61891))) % 186.05/186.63 [6719]~P64(x67191)+~P1(f775(f63(x67191),x67193))+E(f775(f65(x67191,f83(x67191)),f775(f775(f302(x67191),x67192),x67193)),f775(f775(f66(x67191,x67191,f83(x67191)),x67192),x67193))+P1(f775(f775(f334(x67191),x67192),x67193)) % 186.05/186.63 [6806]~E(f775(f775(f82(a1),x68062),f775(f775(f83(a1),x68063),x68061)),x68063)+~P1(f775(f775(f233(a1),f2(a1)),x68063))+P1(f775(f775(f232(a1),f80(a1)),x68061))+~P1(f775(f775(f233(a1),x68062),x68063)) % 186.05/186.63 [6837]~E(f775(f775(f82(a1),x68372),f775(f775(f83(a1),x68373),x68371)),x68373)+P1(f775(f775(f232(a1),x68371),f80(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x68373))+~P1(f775(f775(f232(a1),f2(a1)),x68372)) % 186.05/186.63 [6855]E(x68551,f2(a850))+~P1(f775(f55(x68553,x68551),x68552))+~P1(f775(f775(f233(a850),f2(a850)),x68551))+P1(f775(f775(f233(a850),f775(f250(a850,a850),x68552)),x68551)) % 186.05/186.63 [6884]~P132(x68841)+~P1(f775(f775(f232(x68841),x68842),f2(x68841)))+~P1(f775(f775(f232(x68841),x68843),f2(x68841)))+E(f775(f775(f83(x68841),f775(f77(x68841),x68842)),f775(f77(x68841),x68843)),f775(f77(x68841),f775(f775(f83(x68841),x68842),x68843))) % 186.05/186.63 [6936]~P132(x69361)+~P1(f775(f775(f232(x69361),x69362),f2(x69361)))+E(f775(f775(f83(x69361),f775(f77(x69361),x69362)),f775(f77(x69361),x69363)),f775(f77(x69361),f775(f775(f83(x69361),x69362),x69363)))+~P1(f775(f775(f232(x69361),f2(x69361)),x69363)) % 186.05/186.63 [6937]~P132(x69371)+~P1(f775(f775(f232(x69371),x69373),f2(x69371)))+E(f775(f775(f83(x69371),f775(f77(x69371),x69372)),f775(f77(x69371),x69373)),f775(f77(x69371),f775(f775(f83(x69371),x69372),x69373)))+~P1(f775(f775(f232(x69371),f2(x69371)),x69372)) % 186.05/186.63 [6987]~P132(x69871)+E(f775(f775(f83(x69871),f775(f77(x69871),x69872)),f775(f77(x69871),x69873)),f775(f77(x69871),f775(f775(f83(x69871),x69872),x69873)))+~P1(f775(f775(f232(x69871),f2(x69871)),x69872))+~P1(f775(f775(f232(x69871),f2(x69871)),x69873)) % 186.05/186.63 [7005]~P119(x70051)+~P1(f775(f775(f233(x70051),x70053),f2(x70051)))+~P1(f775(f775(f233(x70051),x70052),f2(x70051)))+P1(f775(f775(f233(x70051),f2(x70051)),f775(f775(f83(x70051),x70052),x70053))) % 186.05/186.63 [7006]~P62(x70061)+~P1(f775(f775(f233(x70061),x70063),f2(x70061)))+~P1(f775(f775(f233(x70061),x70062),f2(x70061)))+P1(f775(f775(f233(x70061),f2(x70061)),f775(f775(f283(x70061),x70062),x70063))) % 186.05/186.63 [7007]~P63(x70071)+~P1(f775(f775(f233(x70071),x70073),f2(x70071)))+~P1(f775(f775(f233(x70071),x70072),f2(x70071)))+P1(f775(f775(f233(x70071),f2(x70071)),f775(f775(f283(x70071),x70072),x70073))) % 186.05/186.63 [7008]~P119(x70081)+~P1(f775(f775(f232(x70081),x70083),f2(x70081)))+~P1(f775(f775(f232(x70081),x70082),f2(x70081)))+P1(f775(f775(f232(x70081),f2(x70081)),f775(f775(f83(x70081),x70082),x70083))) % 186.05/186.63 [7010]~P129(x70101)+~P1(f775(f775(f232(x70101),x70103),f2(x70101)))+~P1(f775(f775(f232(x70101),x70102),f2(x70101)))+P1(f775(f775(f232(x70101),f2(x70101)),f775(f775(f83(x70101),x70102),x70103))) % 186.05/186.63 [7011]~P62(x70111)+~P1(f775(f775(f232(x70111),x70113),f2(x70111)))+~P1(f775(f775(f232(x70111),x70112),f2(x70111)))+P1(f775(f775(f232(x70111),f2(x70111)),f775(f775(f283(x70111),x70112),x70113))) % 186.05/186.63 [7012]~P63(x70121)+~P1(f775(f775(f233(x70121),x70123),f2(x70121)))+~P1(f775(f775(f232(x70121),x70122),f2(x70121)))+P1(f775(f775(f232(x70121),f2(x70121)),f775(f775(f283(x70121),x70122),x70123))) % 186.05/186.63 [7013]~P117(x70131)+~P1(f775(f775(f233(a850),f2(a850)),x70133))+~P1(f775(f775(f233(x70131),f80(x70131)),x70132))+P1(f775(f775(f233(x70131),f80(x70131)),f775(f775(f242(x70131),x70132),x70133))) % 186.05/186.63 [7110]~P81(x71101)+~P1(f775(f775(f233(x71101),f2(x71101)),x71103))+~P1(f775(f775(f233(x71101),f2(x71101)),x71102))+P1(f775(f775(f233(x71101),f2(x71101)),f775(f775(f82(x71101),x71102),x71103))) % 186.05/186.63 [7113]~P123(x71131)+~P1(f775(f775(f233(x71131),f2(x71131)),x71133))+~P1(f775(f775(f233(x71131),f2(x71131)),x71132))+P1(f775(f775(f233(x71131),f2(x71131)),f775(f775(f83(x71131),x71132),x71133))) % 186.05/186.63 [7114]~P62(x71141)+~P1(f775(f775(f233(x71141),f2(x71141)),x71143))+~P1(f775(f775(f233(x71141),f2(x71141)),x71142))+P1(f775(f775(f233(x71141),f2(x71141)),f775(f775(f283(x71141),x71142),x71143))) % 186.05/186.63 [7115]~P63(x71151)+~P1(f775(f775(f233(x71151),f2(x71151)),x71153))+~P1(f775(f775(f233(x71151),f2(x71151)),x71152))+P1(f775(f775(f233(x71151),f2(x71151)),f775(f775(f283(x71151),x71152),x71153))) % 186.05/186.63 [7116]~P117(x71161)+~P1(f775(f775(f233(x71161),f80(x71161)),x71163))+~P1(f775(f775(f233(x71161),f80(x71161)),x71162))+P1(f775(f775(f233(x71161),f80(x71161)),f775(f775(f83(x71161),x71162),x71163))) % 186.05/186.63 [7118]~P119(x71181)+~P1(f775(f775(f232(x71181),f2(x71181)),x71183))+~P1(f775(f775(f232(x71181),f2(x71181)),x71182))+P1(f775(f775(f232(x71181),f2(x71181)),f775(f775(f83(x71181),x71182),x71183))) % 186.05/186.63 [7119]~P128(x71191)+~P1(f775(f775(f232(x71191),f2(x71191)),x71193))+~P1(f775(f775(f232(x71191),f2(x71191)),x71192))+P1(f775(f775(f232(x71191),f2(x71191)),f775(f775(f83(x71191),x71192),x71193))) % 186.05/186.63 [7120]~P129(x71201)+~P1(f775(f775(f232(x71201),f2(x71201)),x71203))+~P1(f775(f775(f232(x71201),f2(x71201)),x71202))+P1(f775(f775(f232(x71201),f2(x71201)),f775(f775(f83(x71201),x71202),x71203))) % 186.05/186.63 [7121]~P62(x71211)+~P1(f775(f775(f232(x71211),f2(x71211)),x71213))+~P1(f775(f775(f232(x71211),f2(x71211)),x71212))+P1(f775(f775(f232(x71211),f2(x71211)),f775(f775(f283(x71211),x71212),x71213))) % 186.05/186.63 [7122]~P63(x71221)+~P1(f775(f775(f233(x71221),f2(x71221)),x71223))+~P1(f775(f775(f232(x71221),f2(x71221)),x71222))+P1(f775(f775(f232(x71221),f2(x71221)),f775(f775(f283(x71221),x71222),x71223))) % 186.05/186.63 [7200]~P93(x72001)+~P1(f775(f63(x72001),x72003))+E(f15(x72001,f775(f775(f302(x72001),x72002),x72003)),x72002)+~E(f775(f775(f3(f857(x72001,a844)),x72003),f775(f775(f302(x72001),x72002),f180(f857(x72001,a844)))),f180(f857(x72001,a844))) % 186.05/186.63 [7201]~P100(x72011)+~P1(f775(f63(x72011),x72013))+E(f16(x72011,f775(f775(f302(x72011),x72012),x72013)),x72012)+~E(f775(f775(f3(f857(x72011,a844)),x72013),f775(f775(f302(x72011),x72012),f180(f857(x72011,a844)))),f180(f857(x72011,a844))) % 186.05/186.63 [7202]~P100(x72021)+~P1(f775(f63(x72021),x72023))+E(f17(x72021,f775(f775(f302(x72021),x72022),x72023)),x72022)+~E(f775(f775(f3(f857(x72021,a844)),x72023),f775(f775(f302(x72021),x72022),f180(f857(x72021,a844)))),f180(f857(x72021,a844))) % 186.05/186.63 [7203]~P93(x72031)+~P1(f775(f63(x72031),x72033))+E(f12(x72031,f775(f775(f302(x72031),x72032),x72033)),x72032)+~E(f775(f775(f3(f857(x72031,a844)),x72033),f775(f775(f302(x72031),x72032),f180(f857(x72031,a844)))),f180(f857(x72031,a844))) % 186.05/186.63 [7204]~P62(x72041)+P1(f775(f775(f233(x72041),x72042),f2(x72041)))+P1(f775(f775(f233(x72041),f2(x72041)),x72043))+~P1(f775(f775(f233(x72041),f2(x72041)),f775(f775(f283(x72041),x72043),x72042))) % 186.05/186.63 [7205]~P62(x72051)+P1(f775(f775(f233(x72051),x72052),f2(x72051)))+P1(f775(f775(f233(x72051),f2(x72051)),x72053))+~P1(f775(f775(f233(x72051),f2(x72051)),f775(f775(f283(x72051),x72052),x72053))) % 186.05/186.63 [7206]~P62(x72061)+P1(f775(f775(f233(x72061),x72062),f2(x72061)))+P1(f775(f775(f233(x72061),f2(x72061)),x72062))+~P1(f775(f775(f233(x72061),f2(x72061)),f775(f775(f283(x72061),x72063),x72062))) % 186.05/186.63 [7207]~P62(x72071)+P1(f775(f775(f233(x72071),x72072),f2(x72071)))+P1(f775(f775(f233(x72071),f2(x72071)),x72072))+~P1(f775(f775(f233(x72071),f2(x72071)),f775(f775(f283(x72071),x72072),x72073))) % 186.05/186.63 [7208]~P119(x72081)+P1(f775(f775(f232(x72081),x72082),f2(x72081)))+P1(f775(f775(f232(x72081),f2(x72081)),x72083))+~P1(f775(f775(f232(x72081),f2(x72081)),f775(f775(f83(x72081),x72083),x72082))) % 186.05/186.63 [7209]~P119(x72091)+P1(f775(f775(f232(x72091),x72092),f2(x72091)))+P1(f775(f775(f232(x72091),f2(x72091)),x72093))+~P1(f775(f775(f232(x72091),f2(x72091)),f775(f775(f83(x72091),x72092),x72093))) % 186.05/186.63 [7210]~P62(x72101)+P1(f775(f775(f232(x72101),x72102),f2(x72101)))+P1(f775(f775(f232(x72101),f2(x72101)),x72103))+~P1(f775(f775(f232(x72101),f2(x72101)),f775(f775(f283(x72101),x72103),x72102))) % 186.05/186.63 [7211]~P62(x72111)+P1(f775(f775(f232(x72111),x72112),f2(x72111)))+P1(f775(f775(f232(x72111),f2(x72111)),x72113))+~P1(f775(f775(f232(x72111),f2(x72111)),f775(f775(f283(x72111),x72112),x72113))) % 186.05/186.63 [7212]~P119(x72121)+P1(f775(f775(f232(x72121),x72122),f2(x72121)))+P1(f775(f775(f232(x72121),f2(x72121)),x72122))+~P1(f775(f775(f232(x72121),f2(x72121)),f775(f775(f83(x72121),x72123),x72122))) % 186.05/186.63 [7213]~P119(x72131)+P1(f775(f775(f232(x72131),x72132),f2(x72131)))+P1(f775(f775(f232(x72131),f2(x72131)),x72132))+~P1(f775(f775(f232(x72131),f2(x72131)),f775(f775(f83(x72131),x72132),x72133))) % 186.05/186.63 [7214]~P62(x72141)+P1(f775(f775(f232(x72141),x72142),f2(x72141)))+P1(f775(f775(f232(x72141),f2(x72141)),x72142))+~P1(f775(f775(f232(x72141),f2(x72141)),f775(f775(f283(x72141),x72143),x72142))) % 186.05/186.63 [7215]~P62(x72151)+P1(f775(f775(f232(x72151),x72152),f2(x72151)))+P1(f775(f775(f232(x72151),f2(x72151)),x72152))+~P1(f775(f775(f232(x72151),f2(x72151)),f775(f775(f283(x72151),x72152),x72153))) % 186.05/186.63 [7300]~P1(f775(f775(f279(a850),x73001),x73003))+P1(f775(f775(f279(a850),x73001),x73002))+~P1(f775(f775(f232(a850),x73002),x73003))+~P1(f775(f775(f279(a850),x73001),f775(f775(f3(a850),x73003),x73002))) % 186.05/186.63 [7301]~P1(f775(f775(f279(a850),x73011),x73013))+P1(f775(f775(f279(a850),x73011),x73012))+~P1(f775(f775(f232(a850),x73013),x73012))+~P1(f775(f775(f279(a850),x73011),f775(f775(f3(a850),x73012),x73013))) % 186.05/186.63 [7316]~E(f775(f775(f104(f857(x73161,a844)),f775(f158(x73161),x73162)),f775(f158(x73161),x73163)),f180(f857(x73161,a844)))+~P1(f775(f127(x73161),x73163))+~P1(f775(f127(x73161),x73162))+P1(f775(f127(x73161),f775(f775(f125(x73161),x73162),x73163))) % 186.05/186.63 [7317]~P100(x73171)+~P1(f775(f63(x73171),x73173))+E(f13(x73171,f179(x73171),f775(f775(f302(x73171),x73172),x73173)),x73172)+~E(f775(f775(f3(f857(x73171,a844)),x73173),f775(f775(f302(x73171),x73172),f180(f857(x73171,a844)))),f180(f857(x73171,a844))) % 186.05/186.63 [7318]~P100(x73181)+~P1(f775(f63(x73181),x73183))+E(f14(x73181,f236(x73181),f775(f775(f302(x73181),x73182),x73183)),x73182)+~E(f775(f775(f3(f857(x73181,a844)),x73183),f775(f775(f302(x73181),x73182),f180(f857(x73181,a844)))),f180(f857(x73181,a844))) % 186.05/186.63 [7336]~P110(x73361)+~P1(f775(f775(f233(x73361),x73362),x73363))+~P1(f775(f775(f233(x73361),f775(f81(x73361),x73362)),x73363))+P1(f775(f775(f233(x73361),f775(f77(x73361),x73362)),x73363)) % 186.05/186.63 [7338]~P79(x73381)+~P1(f775(f775(f232(x73381),x73382),x73383))+~P1(f775(f775(f232(x73381),f775(f81(x73381),x73382)),x73383))+P1(f775(f775(f232(x73381),f775(f77(x73381),x73382)),x73383)) % 186.05/186.63 [7407]~P123(x74071)+P1(f775(f775(f233(x74071),f2(x74071)),x74072))+~P1(f775(f775(f233(x74071),f2(x74071)),x74073))+~P1(f775(f775(f233(x74071),f2(x74071)),f775(f775(f83(x74071),x74073),x74072))) % 186.05/186.63 [7408]~P123(x74081)+P1(f775(f775(f233(x74081),f2(x74081)),x74082))+~P1(f775(f775(f233(x74081),f2(x74081)),x74083))+~P1(f775(f775(f233(x74081),f2(x74081)),f775(f775(f83(x74081),x74082),x74083))) % 186.05/186.63 [7715]E(x77151,x77152)+~P1(f775(f63(x77153),x77151))+~P1(f775(f775(f232(a850),f775(f42(x77153),x77151)),f775(f42(x77153),x77152)))+~P1(f775(f775(f232(f857(x77153,a844)),x77152),x77151)) % 186.05/186.63 [7862]~P1(f775(f775(f233(a1),x78621),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x78622))+~P1(f775(f775(f232(a1),x78622),x78623))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x78621),x78622)),f775(f775(f43(a1),x78621),x78623))) % 186.05/186.63 [7873]~P1(f775(f775(f233(a1),f2(a1)),x78733))+~P1(f775(f775(f232(a1),f2(a1)),x78731))+~P1(f775(f775(f232(a1),x78733),x78732))+P1(f775(f775(f232(a1),f775(f775(f43(a1),x78731),x78732)),f775(f775(f43(a1),x78731),x78733))) % 186.05/186.63 [8008]E(f775(x80081,f814(x80082,x80081,x80083)),x80082)+~P1(f775(f775(f232(a1),x80082),f775(x80081,x80083)))+P1(f775(f775(f233(a850),f815(x80082,x80081,x80083)),x80083))+~P1(f775(f775(f232(a1),f775(x80081,f2(a850))),x80082)) % 186.05/186.63 [8009]E(f775(x80091,f816(x80092,x80091,x80093)),x80092)+~P1(f775(f775(f232(a1),x80092),f775(x80091,x80093)))+P1(f775(f775(f233(a850),f817(x80092,x80091,x80093)),x80093))+~P1(f775(f775(f232(a1),f775(x80091,f2(a850))),x80092)) % 186.05/186.63 [8106]~P1(f775(f63(x81061),x81063))+~P1(f775(f775(f233(a850),f775(f42(x81061),x81062)),f775(f42(x81061),x81063)))+~P1(f775(f775(f232(f857(x81061,a844)),x81062),x81063))+P1(f775(f775(f233(f857(x81061,a844)),x81062),x81063)) % 186.05/186.63 [8135]E(f775(f775(f3(a1),f418(x81353,x81351,x81352)),f419(x81353,x81351,x81352)),x81351)+E(f775(f775(f82(a1),x81351),x81352),x81351)+~P1(f775(f775(f233(a1),f2(a1)),x81352))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x81351),f80(a1))),x81353)) % 186.05/186.63 [8136]E(f775(f775(f82(a1),f420(x81363,x81361,x81362)),f421(x81363,x81361,x81362)),x81361)+E(f775(f775(f3(a1),x81361),x81362),x81361)+~P1(f775(f775(f233(a1),f2(a1)),x81362))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x81361),f80(a1))),x81363)) % 186.05/186.63 [8188]~P1(f775(f775(f232(a850),x81883),x81881))+P1(f775(f775(f233(a850),x81881),x81882))+~P1(f775(f775(f232(a850),x81883),x81882))+~P1(f775(f775(f233(a850),f775(f775(f3(a850),x81881),x81883)),f775(f775(f3(a850),x81882),x81883))) % 186.05/186.63 [8189]~P1(f775(f775(f232(a850),x81893),x81891))+P1(f775(f775(f232(a850),x81891),x81892))+~P1(f775(f775(f232(a850),x81893),x81892))+~P1(f775(f775(f232(a850),f775(f775(f3(a850),x81891),x81893)),f775(f775(f3(a850),x81892),x81893))) % 186.05/186.63 [8203]~P100(x82032)+E(x82031,f115(x82032))+~P18(x82032,f775(f142(x82032),x82031))+E(f775(f132(x82032,x82032,f775(f9(x82032,x82032,x82032),f179(x82032)),x82033),f775(f142(x82032),x82031)),f775(f775(f179(x82032),f775(f775(f153(x82032),x82031),f2(a850))),x82033)) % 186.05/186.63 [8268]E(f775(f775(f82(a1),x82681),x82682),x82681)+~P1(f775(f775(f233(a1),f2(a1)),x82682))+P1(f775(f775(f334(a1),f418(x82683,x82681,x82682)),x82683))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x82681),f80(a1))),x82683)) % 186.05/186.63 [8269]E(f775(f775(f3(a1),x82691),x82692),x82691)+~P1(f775(f775(f233(a1),f2(a1)),x82692))+P1(f775(f775(f334(a1),f420(x82693,x82691,x82692)),x82693))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x82691),f80(a1))),x82693)) % 186.05/186.63 [8348]~P1(f775(f775(f232(a1),x83481),f775(x83482,x83483)))+P1(f775(f775(f232(a850),f814(x83481,x83482,x83483)),x83483))+P1(f775(f775(f233(a850),f815(x83481,x83482,x83483)),x83483))+~P1(f775(f775(f232(a1),f775(x83482,f2(a850))),x83481)) % 186.05/186.63 [8349]~P1(f775(f775(f232(a1),x83491),f775(x83492,x83493)))+P1(f775(f775(f232(a850),f816(x83491,x83492,x83493)),x83493))+P1(f775(f775(f233(a850),f817(x83491,x83492,x83493)),x83493))+~P1(f775(f775(f232(a1),f775(x83492,f2(a850))),x83491)) % 186.05/186.63 [8424]E(f775(f775(f82(a1),x84241),x84242),x84241)+~P1(f775(f775(f233(a1),f2(a1)),x84242))+P1(f775(f775(f334(a1),f419(x84243,x84241,x84242)),f295(a1,f80(a1),x84242)))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x84241),f80(a1))),x84243)) % 186.05/186.63 [8425]E(f775(f775(f3(a1),x84251),x84252),x84251)+~P1(f775(f775(f233(a1),f2(a1)),x84252))+P1(f775(f775(f334(a1),f421(x84253,x84251,x84252)),f295(a1,f80(a1),x84252)))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x84251),f80(a1))),x84253)) % 186.05/186.63 [8550]~P117(x85501)+~P1(f775(f775(f233(x85501),x85502),f80(x85501)))+~P1(f775(f775(f233(x85501),f2(x85501)),x85502))+P1(f775(f775(f233(x85501),f775(f775(f83(x85501),x85502),f775(f775(f242(x85501),x85502),x85503))),f775(f775(f242(x85501),x85502),x85503))) % 186.05/186.63 [8625]~P1(f775(x86251,x86252))+P1(f775(x86251,f2(a850)))+~P1(f775(f775(f233(a850),x86252),x86253))+~P1(f775(x86251,f52(a850,f775(a114,f810(x86252,x86251,x86253)),x86253))) % 186.05/186.63 [8755]E(f835(x87551,x87552,x87553),f2(a850))+P1(f775(f775(x87551,x87553),x87552))+P1(f775(f775(x87551,f835(x87551,x87552,x87553)),f52(a850,f834(x87551,x87552,x87553),f835(x87551,x87552,x87553))))+~P1(f775(f321(f856(a850,a850),a214),f775(f775(f241(a850,a850),x87553),x87552))) % 186.05/186.63 [8787]~P29(x87871,x87871,x87872,x87873)+E(f775(f303(x87871,x87871,x87872),x87873),x87873)+~P1(f775(f63(x87871),x87873))+~P1(f775(f775(f232(f857(x87871,a844)),f775(f303(x87871,x87871,x87872),x87873)),x87873)) % 186.05/186.63 [9007]P1(f775(f775(x90071,x90072),x90073))+~P1(f775(f775(f233(a1),f833(x90071,x90073,x90072)),f2(a1)))+P1(f775(f775(x90071,f775(f81(a1),f830(x90071,x90073,x90072))),f775(f81(a1),f833(x90071,x90073,x90072))))+~P1(f775(f321(f856(a1,a1),a216),f775(f775(f241(a1,a1),x90072),x90073))) % 186.05/186.63 [9165]P1(f775(f775(x91651,x91652),x91653))+P1(f775(f775(x91651,f775(f775(f82(a1),f394(x91651,x91653,x91652)),f80(a1))),f395(x91651,x91653,x91652)))+~P1(f775(f775(f232(a1),f394(x91651,x91653,x91652)),f395(x91651,x91653,x91652)))+~P1(f775(f321(f856(a1,a1),a168),f775(f775(f241(a1,a1),x91652),x91653))) % 186.05/186.63 [9838]E(f775(x98381,f814(x98382,x98381,x98383)),x98382)+~P1(f775(f775(f232(a1),x98382),f775(x98381,x98383)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x98381,f775(f775(f82(a850),f815(x98382,x98381,x98383)),f80(a850)))),f775(x98381,f815(x98382,x98381,x98383))))),f80(a1)))+~P1(f775(f775(f232(a1),f775(x98381,f2(a850))),x98382)) % 186.05/186.63 [9839]E(f775(x98391,f816(x98392,x98391,x98393)),x98392)+~P1(f775(f775(f232(a1),x98392),f775(x98391,x98393)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x98391,f775(f775(f82(a850),f817(x98392,x98391,x98393)),f80(a850)))),f775(x98391,f817(x98392,x98391,x98393))))),f80(a1)))+~P1(f775(f775(f232(a1),f775(x98391,f2(a850))),x98392)) % 186.05/186.63 [9843]~P1(f775(f775(f232(a1),x98431),f775(x98432,x98433)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x98432,f775(f775(f82(a850),f815(x98431,x98432,x98433)),f80(a850)))),f775(x98432,f815(x98431,x98432,x98433))))),f80(a1)))+P1(f775(f775(f232(a850),f814(x98431,x98432,x98433)),x98433))+~P1(f775(f775(f232(a1),f775(x98432,f2(a850))),x98431)) % 186.05/186.63 [9844]~P1(f775(f775(f232(a1),x98441),f775(x98442,x98443)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x98442,f775(f775(f82(a850),f817(x98441,x98442,x98443)),f80(a850)))),f775(x98442,f817(x98441,x98442,x98443))))),f80(a1)))+P1(f775(f775(f232(a850),f816(x98441,x98442,x98443)),x98443))+~P1(f775(f775(f232(a1),f775(x98442,f2(a850))),x98441)) % 186.05/186.63 [9898]E(x98981,x98982)+~E(f775(f132(f851(x98983),f851(x98983),f125(x98983),f115(x98983)),x98981),f775(f132(f851(x98983),f851(x98983),f125(x98983),f115(x98983)),x98982))+~E(f775(f181(f851(f851(x98983))),x98981),f775(f181(f851(f851(x98983))),x98982))+~P1(f775(f775(f251(f851(x98983),f851(x98983),a844),f775(f775(f9(f851(x98983),f857(f851(x98983),a850),f857(f851(x98983),a844)),f775(f775(f10(f857(a850,a844),f857(f857(f851(x98983),a850),f857(f851(x98983),a844)),f851(x98983)),f10(a850,a844,f851(x98983))),f775(f775(f10(a850,f857(a850,a844),f851(x98983)),a330),f181(f851(x98983))))),f181(f851(x98983)))),f771(x98981,x98982,x98983))) % 186.05/186.63 [9899]E(x98991,x98992)+~E(f775(f132(f851(x98993),f851(x98993),f125(x98993),f115(x98993)),x98991),f775(f132(f851(x98993),f851(x98993),f125(x98993),f115(x98993)),x98992))+~E(f775(f181(f851(f851(x98993))),x98991),f775(f181(f851(f851(x98993))),x98992))+~P1(f775(f775(f251(f851(x98993),f851(x98993),a844),f775(f775(f9(f851(x98993),f857(f851(x98993),a850),f857(f851(x98993),a844)),f775(f775(f10(f857(a850,a844),f857(f857(f851(x98993),a850),f857(f851(x98993),a844)),f851(x98993)),f10(a850,a844,f851(x98993))),f775(f775(f10(a850,f857(a850,a844),f851(x98993)),a330),f181(f851(x98993))))),f181(f851(x98993)))),f772(x98992,x98991,x98993))) % 186.05/186.63 [6708]~E(f80(a850),f2(a850))+~P1(f775(f63(x67081),x67083))+~P1(f775(f63(x67081),x67082))+E(f775(f775(f82(a850),f775(f42(x67081),x67082)),f775(f42(x67081),x67083)),f775(f42(x67081),f775(f775(f103(f857(x67081,a844)),x67082),x67083))) % 186.05/186.63 [7128]~P100(x71281)+~P1(f775(f63(x71281),x71282))+~P1(f775(f775(f334(x71281),x71283),x71282))+P1(f775(f775(f232(x71281),f775(f65(x71281,f236(x71281)),x71282)),x71283)) % 186.05/186.63 [7129]~P98(x71291)+~P1(f775(f63(x71291),x71292))+~P1(f775(f775(f334(x71291),x71293),x71292))+P1(f775(f775(f232(x71291),f775(f65(x71291,f104(x71291)),x71292)),x71293)) % 186.05/186.63 [7404]~P1(f775(f63(x74041),x74043))+~P1(f775(f63(x74041),x74042))+~E(f775(f775(f104(f857(x74041,a844)),x74042),x74043),f180(f857(x74041,a844)))+E(f775(f775(f82(a850),f775(f42(x74041),x74042)),f775(f42(x74041),x74043)),f775(f42(x74041),f775(f775(f103(f857(x74041,a844)),x74042),x74043))) % 186.05/186.63 [8193]~P36(x81931,x81933)+~P36(x81931,x81932)+~E(f775(f775(f104(f857(x81931,a844)),f775(f261(x81931,x81931),x81932)),f775(f259(x81931,x81931),x81933)),f180(f857(x81931,a844)))+P36(x81931,f775(f775(f103(f857(f856(x81931,x81931),a844)),x81932),x81933)) % 186.05/186.63 [8281]E(x82811,f775(f775(f43(a850),x82812),x82813))+~P1(f775(f775(f233(a850),f2(a850)),x82813))+~P1(f775(f775(f233(a850),x82812),f775(f775(f83(a850),x82813),f775(a114,x82811))))+~P1(f775(f775(f232(a850),f775(f775(f83(a850),x82813),x82811)),x82812)) % 186.05/186.63 [8422]~P1(f775(f63(x84221),x84222))+~P1(f775(f63(x84221),x84223))+E(f775(f775(f82(a850),f775(f42(x84221),x84222)),f775(f42(x84221),x84223)),f775(f42(x84221),f775(f775(f103(f857(x84221,a844)),x84222),x84223)))+P1(f775(f775(f334(x84221),f508(x84223,x84222,x84221)),f775(f775(f104(f857(x84221,a844)),x84222),x84223))) % 186.05/186.63 [8766]~P119(x87662)+~E(x87661,f2(x87662))+~E(x87663,f2(x87662))+~P1(f775(f775(f233(x87662),f2(x87662)),f775(f775(f82(x87662),f775(f775(f83(x87662),x87663),x87663)),f775(f775(f83(x87662),x87661),x87661)))) % 186.05/186.63 [9237]~P36(x92371,x92373)+~P36(x92371,x92372)+P36(x92371,f775(f775(f103(f857(f856(x92371,x92371),a844)),x92372),x92373))+~P1(f775(f775(f232(f857(f856(x92371,x92371),a844)),f775(f775(f281(x92371,x92371,x92371),x92372),x92373)),x92372)) % 186.05/186.63 [9363]~P1(f775(x93631,x93633))+~P1(f775(f63(x93632),x93633))+P1(f775(x93631,f180(f857(x93632,a844))))+~P1(f775(x93631,f775(f775(f3(f857(x93632,a844)),f482(x93631,x93633,x93632)),f775(f775(f302(x93632),f483(x93631,x93633,x93632)),f180(f857(x93632,a844)))))) % 186.05/186.63 [8579]~P1(f775(f775(f233(a1),f2(a1)),x85793))+P1(f775(f775(f232(a1),f2(a1)),x85791))+~P1(f775(f775(f233(a1),x85792),x85793))+~P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),f775(f775(f83(a1),x85793),x85791)),x85792))) % 186.05/186.63 [8599]~P93(x85991)+~P1(f775(f63(x85991),x85992))+E(f775(f775(f3(f857(x85991,a844)),x85992),f775(f775(f302(x85991),x85993),f180(f857(x85991,a844)))),f180(f857(x85991,a844)))+E(f775(f775(f103(x85991),x85993),f15(x85991,f775(f775(f3(f857(x85991,a844)),x85992),f775(f775(f302(x85991),x85993),f180(f857(x85991,a844)))))),f15(x85991,f775(f775(f302(x85991),x85993),x85992))) % 186.05/186.63 [8600]~P100(x86001)+~P1(f775(f63(x86001),x86002))+E(f775(f775(f3(f857(x86001,a844)),x86002),f775(f775(f302(x86001),x86003),f180(f857(x86001,a844)))),f180(f857(x86001,a844)))+E(f775(f775(f179(x86001),x86003),f16(x86001,f775(f775(f3(f857(x86001,a844)),x86002),f775(f775(f302(x86001),x86003),f180(f857(x86001,a844)))))),f16(x86001,f775(f775(f302(x86001),x86003),x86002))) % 186.05/186.63 [8601]~P100(x86011)+~P1(f775(f63(x86011),x86012))+E(f775(f775(f3(f857(x86011,a844)),x86012),f775(f775(f302(x86011),x86013),f180(f857(x86011,a844)))),f180(f857(x86011,a844)))+E(f775(f775(f236(x86011),x86013),f17(x86011,f775(f775(f3(f857(x86011,a844)),x86012),f775(f775(f302(x86011),x86013),f180(f857(x86011,a844)))))),f17(x86011,f775(f775(f302(x86011),x86013),x86012))) % 186.05/186.63 [8602]~P93(x86021)+~P1(f775(f63(x86021),x86022))+E(f775(f775(f3(f857(x86021,a844)),x86022),f775(f775(f302(x86021),x86023),f180(f857(x86021,a844)))),f180(f857(x86021,a844)))+E(f775(f775(f104(x86021),x86023),f12(x86021,f775(f775(f3(f857(x86021,a844)),x86022),f775(f775(f302(x86021),x86023),f180(f857(x86021,a844)))))),f12(x86021,f775(f775(f302(x86021),x86023),x86022))) % 186.05/186.63 [8664]~P100(x86641)+~P1(f775(f63(x86641),x86642))+E(f775(f775(f3(f857(x86641,a844)),x86642),f775(f775(f302(x86641),x86643),f180(f857(x86641,a844)))),f180(f857(x86641,a844)))+E(f775(f775(f179(x86641),x86643),f13(x86641,f179(x86641),f775(f775(f3(f857(x86641,a844)),x86642),f775(f775(f302(x86641),x86643),f180(f857(x86641,a844)))))),f13(x86641,f179(x86641),f775(f775(f302(x86641),x86643),x86642))) % 186.05/186.63 [8665]~P100(x86651)+~P1(f775(f63(x86651),x86652))+E(f775(f775(f3(f857(x86651,a844)),x86652),f775(f775(f302(x86651),x86653),f180(f857(x86651,a844)))),f180(f857(x86651,a844)))+E(f775(f775(f236(x86651),x86653),f14(x86651,f236(x86651),f775(f775(f3(f857(x86651,a844)),x86652),f775(f775(f302(x86651),x86653),f180(f857(x86651,a844)))))),f14(x86651,f236(x86651),f775(f775(f302(x86651),x86653),x86652))) % 186.05/186.63 [9179]E(x91791,x91792)+~E(f775(f132(f851(x91793),f851(x91793),f125(x91793),f115(x91793)),x91791),f775(f132(f851(x91793),f851(x91793),f125(x91793),f115(x91793)),x91792))+~E(f775(f181(f851(f851(x91793))),x91791),f775(f181(f851(f851(x91793))),x91792))+P1(f775(f775(f334(f856(f851(x91793),f851(x91793))),f771(x91791,x91792,x91793)),f775(f158(f856(f851(x91793),f851(x91793))),f775(f775(f167(f851(x91793),f851(x91793)),x91792),x91791)))) % 186.05/186.63 [9180]E(x91801,x91802)+~E(f775(f132(f851(x91803),f851(x91803),f125(x91803),f115(x91803)),x91801),f775(f132(f851(x91803),f851(x91803),f125(x91803),f115(x91803)),x91802))+~E(f775(f181(f851(f851(x91803))),x91801),f775(f181(f851(f851(x91803))),x91802))+P1(f775(f775(f334(f856(f851(x91803),f851(x91803))),f772(x91802,x91801,x91803)),f775(f158(f856(f851(x91803),f851(x91803))),f775(f775(f167(f851(x91803),f851(x91803)),x91801),x91802)))) % 186.05/186.63 [9989]~P72(x99892)+E(x99891,f180(f857(x99892,a844)))+~P1(f775(f63(x99892),x99891))+E(f16(x99892,f775(f256(x99892),f775(f775(f10(f857(x99892,a844),a844,x99892),f89(x99892)),f775(f775(f9(x99892,f857(x99892,a844),f857(x99892,a844)),f775(f775(f10(f857(x99892,f857(a844,a844)),f857(f857(x99892,a844),f857(x99892,a844)),x99892),f20(x99892,a844,a844)),f775(f775(f10(f857(x99892,a844),f857(x99892,f857(a844,a844)),x99892),f775(f10(a844,f857(a844,a844),x99892),a331)),f775(f775(f9(x99892,f857(x99892,x99892),f857(x99892,a844)),f775(f775(f10(f857(x99892,a844),f857(f857(x99892,x99892),f857(x99892,a844)),x99892),f10(x99892,a844,x99892)),a330)),f775(f82(x99892),x99893))))),f775(f775(f9(x99892,f857(x99892,a844),a844),f334(x99892)),x99891))))),f775(f775(f82(x99892),x99893),f16(x99892,x99891))) % 186.05/186.63 [9990]~P72(x99902)+E(x99901,f180(f857(x99902,a844)))+~P1(f775(f63(x99902),x99901))+E(f17(x99902,f775(f256(x99902),f775(f775(f10(f857(x99902,a844),a844,x99902),f89(x99902)),f775(f775(f9(x99902,f857(x99902,a844),f857(x99902,a844)),f775(f775(f10(f857(x99902,f857(a844,a844)),f857(f857(x99902,a844),f857(x99902,a844)),x99902),f20(x99902,a844,a844)),f775(f775(f10(f857(x99902,a844),f857(x99902,f857(a844,a844)),x99902),f775(f10(a844,f857(a844,a844),x99902),a331)),f775(f775(f9(x99902,f857(x99902,x99902),f857(x99902,a844)),f775(f775(f10(f857(x99902,a844),f857(f857(x99902,x99902),f857(x99902,a844)),x99902),f10(x99902,a844,x99902)),a330)),f775(f82(x99902),x99903))))),f775(f775(f9(x99902,f857(x99902,a844),a844),f334(x99902)),x99901))))),f775(f775(f82(x99902),x99903),f17(x99902,x99901))) % 186.05/186.63 [9991]~P97(x99912)+E(x99911,f180(f857(x99912,a844)))+~P1(f775(f63(x99912),x99911))+E(f12(x99912,f775(f256(x99912),f775(f775(f10(f857(x99912,a844),a844,x99912),f89(x99912)),f775(f775(f9(x99912,f857(x99912,a844),f857(x99912,a844)),f775(f775(f10(f857(x99912,f857(a844,a844)),f857(f857(x99912,a844),f857(x99912,a844)),x99912),f20(x99912,a844,a844)),f775(f775(f10(f857(x99912,a844),f857(x99912,f857(a844,a844)),x99912),f775(f10(a844,f857(a844,a844),x99912),a331)),f775(f775(f9(x99912,f857(x99912,x99912),f857(x99912,a844)),f775(f775(f10(f857(x99912,a844),f857(f857(x99912,x99912),f857(x99912,a844)),x99912),f10(x99912,a844,x99912)),a330)),f775(f103(x99912),x99913))))),f775(f775(f9(x99912,f857(x99912,a844),a844),f334(x99912)),x99911))))),f775(f775(f103(x99912),x99913),f12(x99912,x99911))) % 186.05/186.63 [9992]~P97(x99922)+E(x99921,f180(f857(x99922,a844)))+~P1(f775(f63(x99922),x99921))+E(f15(x99922,f775(f256(x99922),f775(f775(f10(f857(x99922,a844),a844,x99922),f89(x99922)),f775(f775(f9(x99922,f857(x99922,a844),f857(x99922,a844)),f775(f775(f10(f857(x99922,f857(a844,a844)),f857(f857(x99922,a844),f857(x99922,a844)),x99922),f20(x99922,a844,a844)),f775(f775(f10(f857(x99922,a844),f857(x99922,f857(a844,a844)),x99922),f775(f10(a844,f857(a844,a844),x99922),a331)),f775(f775(f9(x99922,f857(x99922,x99922),f857(x99922,a844)),f775(f775(f10(f857(x99922,a844),f857(f857(x99922,x99922),f857(x99922,a844)),x99922),f10(x99922,a844,x99922)),a330)),f775(f104(x99922),x99923))))),f775(f775(f9(x99922,f857(x99922,a844),a844),f334(x99922)),x99921))))),f775(f775(f104(x99922),x99923),f15(x99922,x99921))) % 186.05/186.63 [9993]~P100(x99932)+E(x99931,f180(f857(x99932,a844)))+~P1(f775(f63(x99932),x99931))+E(f13(x99932,f179(x99932),f775(f256(x99932),f775(f775(f10(f857(x99932,a844),a844,x99932),f89(x99932)),f775(f775(f9(x99932,f857(x99932,a844),f857(x99932,a844)),f775(f775(f10(f857(x99932,f857(a844,a844)),f857(f857(x99932,a844),f857(x99932,a844)),x99932),f20(x99932,a844,a844)),f775(f775(f10(f857(x99932,a844),f857(x99932,f857(a844,a844)),x99932),f775(f10(a844,f857(a844,a844),x99932),a331)),f775(f775(f9(x99932,f857(x99932,x99932),f857(x99932,a844)),f775(f775(f10(f857(x99932,a844),f857(f857(x99932,x99932),f857(x99932,a844)),x99932),f10(x99932,a844,x99932)),a330)),f775(f236(x99932),x99933))))),f775(f775(f9(x99932,f857(x99932,a844),a844),f334(x99932)),x99931))))),f775(f775(f236(x99932),x99933),f13(x99932,f179(x99932),x99931))) % 186.05/186.63 [9994]~P100(x99942)+E(x99941,f180(f857(x99942,a844)))+~P1(f775(f63(x99942),x99941))+E(f14(x99942,f236(x99942),f775(f256(x99942),f775(f775(f10(f857(x99942,a844),a844,x99942),f89(x99942)),f775(f775(f9(x99942,f857(x99942,a844),f857(x99942,a844)),f775(f775(f10(f857(x99942,f857(a844,a844)),f857(f857(x99942,a844),f857(x99942,a844)),x99942),f20(x99942,a844,a844)),f775(f775(f10(f857(x99942,a844),f857(x99942,f857(a844,a844)),x99942),f775(f10(a844,f857(a844,a844),x99942),a331)),f775(f775(f9(x99942,f857(x99942,x99942),f857(x99942,a844)),f775(f775(f10(f857(x99942,a844),f857(f857(x99942,x99942),f857(x99942,a844)),x99942),f10(x99942,a844,x99942)),a330)),f775(f179(x99942),x99943))))),f775(f775(f9(x99942,f857(x99942,a844),a844),f334(x99942)),x99941))))),f775(f775(f179(x99942),x99943),f14(x99942,f236(x99942),x99941))) % 186.05/186.63 [9723]~P110(x97231)+~E(x97233,f2(x97231))+~E(x97232,f2(x97231))+E(f775(f775(f82(x97231),f775(f775(f242(x97231),x97232),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x97231),x97233),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f2(x97231)) % 186.05/186.63 [9883]~P117(x98831)+~P1(f775(f775(f232(x98831),f2(x98831)),x98833))+P1(f775(f775(f232(x98831),x98832),x98833))+~P1(f775(f775(f232(x98831),f775(f775(f242(x98831),x98832),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x98831),x98833),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))))) % 186.05/186.63 [9929]~P110(x99292)+~E(x99291,f2(x99292))+~E(x99293,f2(x99292))+~P1(f775(f775(f233(x99292),f2(x99292)),f775(f775(f82(x99292),f775(f775(f242(x99292),x99293),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))),f775(f775(f242(x99292),x99291),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))))) % 186.05/186.63 [9153]E(x91531,x91532)+~E(f752(x91531,x91532,x91534,x91533),f754(x91531,x91532,x91534,x91533))+P1(f775(f775(f334(f856(f851(x91533),f851(x91533))),f775(f775(f241(f851(x91533),f851(x91533)),x91532),x91531)),f137(x91533,x91534)))+P1(f775(f775(f334(f856(f851(x91533),f851(x91533))),f775(f775(f241(f851(x91533),f851(x91533)),x91531),x91532)),f137(x91533,x91534))) % 186.05/186.63 [4744]~P60(x47442)+~E(x47444,f2(x47442))+~E(x47441,f2(x47442))+E(x47441,f775(f775(f283(x47442),x47443),x47444)) % 186.05/186.63 [4745]~P60(x47451)+~E(x47453,f2(x47451))+~E(x47454,f2(x47451))+E(f775(f775(f283(x47451),x47452),x47453),x47454) % 186.05/186.63 [4852]~P60(x48522)+E(x48521,f2(x48522))+~E(x48523,f2(x48522))+~E(x48521,f775(f775(f283(x48522),x48524),x48523)) % 186.05/186.63 [4853]~P60(x48532)+E(x48531,f2(x48532))+~E(x48533,f2(x48532))+~E(f775(f775(f283(x48532),x48534),x48533),x48531) % 186.05/186.63 [5032]~P113(x50322)+E(x50321,f2(x50322))+~E(f775(f775(f283(x50322),x50323),x50321),x50324)+E(x50323,f775(f775(f83(x50322),x50324),x50321)) % 186.05/186.63 [5034]~P113(x50342)+E(x50341,f2(x50342))+~E(f775(f775(f83(x50342),x50343),x50341),x50344)+E(x50343,f775(f775(f283(x50342),x50344),x50341)) % 186.05/186.63 [5035]~P60(x50352)+E(x50351,f2(x50352))+~E(f775(f775(f283(x50352),x50353),x50351),x50354)+E(x50353,f775(f775(f83(x50352),x50354),x50351)) % 186.05/186.63 [5036]~P60(x50362)+E(x50361,f2(x50362))+~E(f775(f775(f83(x50362),x50363),x50361),x50364)+E(x50363,f775(f775(f283(x50362),x50364),x50361)) % 186.05/186.63 [5037]~P113(x50372)+E(x50371,f2(x50372))+~E(x50373,f775(f775(f283(x50372),x50374),x50371))+E(f775(f775(f83(x50372),x50373),x50371),x50374) % 186.05/186.63 [5039]~P113(x50392)+E(x50391,f2(x50392))+~E(x50393,f775(f775(f83(x50392),x50394),x50391))+E(f775(f775(f283(x50392),x50393),x50391),x50394) % 186.05/186.63 [5040]~P60(x50402)+E(x50401,f2(x50402))+~E(x50403,f775(f775(f283(x50402),x50404),x50401))+E(f775(f775(f83(x50402),x50403),x50401),x50404) % 186.05/186.63 [5041]~P60(x50412)+E(x50411,f2(x50412))+~E(x50413,f775(f775(f83(x50412),x50414),x50411))+E(f775(f775(f283(x50412),x50413),x50411),x50414) % 186.05/186.63 [5074]~P60(x50742)+~E(x50741,f2(x50742))+~E(f775(f775(f83(x50742),x50741),x50744),x50743)+E(x50741,f775(f775(f283(x50742),x50743),x50744)) % 186.05/186.63 [5075]~P60(x50751)+~E(x50754,f2(x50751))+~E(x50752,f775(f775(f83(x50751),x50754),x50753))+E(f775(f775(f283(x50751),x50752),x50753),x50754) % 186.05/186.63 [5142]~E(x51423,x51424)+~E(x51422,x51423)+~P99(x51421)+E(f295(x51421,x51422,x51423),f775(f775(f302(x51421),x51424),f180(f857(x51421,a844)))) % 186.05/186.63 [5337]~E(f134(x53372,x53371),x53374)+~E(f116(x53372,x53371),x53373)+E(x53371,f115(x53372))+E(f775(f775(f125(x53372),x53373),f775(f775(f140(x53372),x53374),f115(x53372))),x53371) % 186.05/186.63 [5955]~P117(x59553)+E(x59551,x59552)+~E(f775(f775(f242(x59553),x59554),x59551),f775(f775(f242(x59553),x59554),x59552))+~P1(f775(f775(f233(x59553),f80(x59553)),x59554)) % 186.05/186.63 [5956]E(x59561,x59562)+~E(f775(f775(f302(x59563),x59564),x59561),f775(f775(f302(x59563),x59564),x59562))+P1(f775(f775(f334(x59563),x59564),x59562))+P1(f775(f775(f334(x59563),x59564),x59561)) % 186.05/186.63 [5994]E(f775(x59941,x59942),f2(a850))+~E(f775(f775(f8(x59943,a850),x59941),x59944),f2(a850))+~P1(f775(f63(x59943),x59944))+~P1(f775(f775(f334(x59943),x59942),x59944)) % 186.05/186.63 [5995]E(f775(x59951,x59952),f80(a850))+~E(f775(f775(f11(x59953,a850),x59951),x59954),f80(a850))+~P1(f775(f63(x59953),x59954))+~P1(f775(f775(f334(x59953),x59952),x59954)) % 186.05/186.63 [6220]~P99(x62201)+~P1(f775(f775(f233(x62201),x62204),x62203))+P1(f775(f775(f233(x62201),x62202),x62203))+~P1(f775(f775(f233(x62201),x62202),x62204)) % 186.05/186.63 [6221]~P99(x62211)+~P1(f775(f775(f232(x62211),x62214),x62213))+P1(f775(f775(f233(x62211),x62212),x62213))+~P1(f775(f775(f233(x62211),x62212),x62214)) % 186.05/186.63 [6222]~P99(x62221)+~P1(f775(f775(f232(x62221),x62222),x62224))+P1(f775(f775(f233(x62221),x62222),x62223))+~P1(f775(f775(f233(x62221),x62224),x62223)) % 186.05/186.63 [6223]~P103(x62231)+~P1(f775(f775(f233(x62231),x62232),x62234))+P1(f775(f775(f233(x62231),x62232),x62233))+~P1(f775(f775(f233(x62231),x62234),x62233)) % 186.05/186.63 [6224]~P103(x62241)+~P1(f775(f775(f232(x62241),x62242),x62244))+P1(f775(f775(f233(x62241),x62242),x62243))+~P1(f775(f775(f233(x62241),x62244),x62243)) % 186.05/186.63 [6225]~P103(x62251)+~P1(f775(f775(f232(x62251),x62254),x62253))+P1(f775(f775(f233(x62251),x62252),x62253))+~P1(f775(f775(f233(x62251),x62252),x62254)) % 186.05/186.63 [6226]~P99(x62261)+~P1(f775(f775(f232(x62261),x62264),x62263))+P1(f775(f775(f232(x62261),x62262),x62263))+~P1(f775(f775(f232(x62261),x62262),x62264)) % 186.05/186.63 [6227]~P103(x62271)+~P1(f775(f775(f232(x62271),x62272),x62274))+P1(f775(f775(f232(x62271),x62272),x62273))+~P1(f775(f775(f232(x62271),x62274),x62273)) % 186.05/186.63 [6228]~P85(x62281)+~P1(f775(f775(f279(x62281),x62282),x62284))+P1(f775(f775(f279(x62281),x62282),x62283))+~P1(f775(f775(f279(x62281),x62284),x62283)) % 186.05/186.63 [6473]~P9(x64731)+~P1(f775(f775(f232(x64731),x64732),f45(x64731,x64734)))+P1(f775(f775(f232(x64731),x64732),x64733))+~P1(f775(f775(f334(x64731),x64733),x64734)) % 186.05/186.63 [6624]~P100(x66241)+~P18(x66241,f775(f775(f140(x66241),x66242),x66244))+~P1(f775(f775(f334(x66241),x66243),f775(f158(x66241),x66244)))+P1(f775(f775(f232(x66241),x66242),x66243)) % 186.05/186.63 [6717]~P9(x67171)+~P1(f775(f775(f232(x67171),f44(x67171,x67174)),x67173))+P1(f775(f775(f232(x67171),x67172),x67173))+~P1(f775(f775(f334(x67171),x67172),x67174)) % 186.05/186.63 [6870]~P7(x68701)+P1(f775(f775(f279(x68701),x68702),f52(x68701,x68703,x68704)))+~P1(f775(f775(f279(x68701),x68702),x68704))+~P1(f775(f775(f279(x68701),x68702),x68703)) % 186.05/186.63 [7131]~P100(x71311)+E(f775(f775(f103(f857(x71311,a844)),f775(f294(x71311,x71312),x71313)),f775(f294(x71311,x71313),x71314)),f775(f294(x71311,x71312),x71314))+~P1(f775(f775(f232(x71311),x71313),x71314))+~P1(f775(f775(f232(x71311),x71312),x71313)) % 186.05/186.63 [7218]~P7(x72181)+~P1(f775(f775(f279(x72181),x72182),f52(x72181,x72183,x72184)))+P1(f775(f775(f279(x72181),x72182),x72183))+~P1(f775(f775(f279(x72181),x72182),x72184)) % 186.05/186.63 [7259]~P100(x72591)+E(f775(f775(f103(f857(x72591,a844)),f775(f294(x72591,x72592),x72593)),f295(x72591,x72593,x72594)),f295(x72591,x72592,x72594))+~P1(f775(f775(f232(x72591),x72593),x72594))+~P1(f775(f775(f232(x72591),x72592),x72593)) % 186.05/186.63 [7273]~P99(x72731)+~P50(a850,x72731,f279(a850),x72732)+P1(f775(f775(f232(x72731),f775(x72732,x72733)),f775(x72732,x72734)))+~P1(f775(f775(f279(a850),x72733),x72734)) % 186.05/186.63 [7327]~P100(x73271)+E(f775(f775(f103(f857(x73271,a844)),f298(x73271,x73272,x73273)),f775(f294(x73271,x73273),x73274)),f298(x73271,x73272,x73274))+~P1(f775(f775(f233(x73271),x73272),x73273))+~P1(f775(f775(f232(x73271),x73273),x73274)) % 186.05/186.63 [7350]~P100(x73501)+E(f775(f775(f103(f857(x73501,a844)),f295(x73501,x73502,x73503)),f298(x73501,x73503,x73504)),f775(f294(x73501,x73502),x73504))+~P1(f775(f775(f233(x73501),x73503),x73504))+~P1(f775(f775(f232(x73501),x73502),x73503)) % 186.05/186.63 [7385]~P100(x73851)+E(f775(f775(f103(f857(x73851,a844)),f295(x73851,x73852,x73853)),f297(x73851,x73853,x73854)),f295(x73851,x73852,x73854))+~P1(f775(f775(f232(x73851),x73853),x73854))+~P1(f775(f775(f232(x73851),x73852),x73853)) % 186.05/186.63 [7386]~P100(x73861)+E(f775(f775(f103(f857(x73861,a844)),f297(x73861,x73862,x73863)),f297(x73861,x73863,x73864)),f297(x73861,x73862,x73864))+~P1(f775(f775(f232(x73861),x73863),x73864))+~P1(f775(f775(f232(x73861),x73862),x73863)) % 186.05/186.63 [7387]~P100(x73871)+E(f775(f775(f103(f857(x73871,a844)),f297(x73871,x73872,x73873)),f298(x73871,x73873,x73874)),f298(x73871,x73872,x73874))+~P1(f775(f775(f233(x73871),x73873),x73874))+~P1(f775(f775(f232(x73871),x73872),x73873)) % 186.05/186.63 [7388]~P100(x73881)+E(f775(f775(f103(f857(x73881,a844)),f298(x73881,x73882,x73883)),f295(x73881,x73883,x73884)),f297(x73881,x73882,x73884))+~P1(f775(f775(f233(x73881),x73882),x73883))+~P1(f775(f775(f232(x73881),x73883),x73884)) % 186.05/186.63 [8178]P29(x81781,x81782,f527(x81783,x81782,x81784,x81781),x81784)+~P1(f775(f63(x81782),x81783))+~P1(f775(f63(x81781),x81784))+~P1(f775(f775(f232(a850),f775(f42(x81781),x81784)),f775(f42(x81782),x81783))) % 186.05/186.63 [8248]~P70(x82481)+~E(f775(x82483,f623(x82483,x82484,x82482,x82481)),f80(x82481))+E(f775(f775(f775(f67(x82481,x82482,f83(x82481)),x82483),f80(x82481)),x82484),f80(x82481))+~P1(f775(f63(x82482),x82484)) % 186.05/186.63 [8522]~P117(x85221)+~P1(f775(f775(f232(x85221),f2(x85221)),x85223))+P1(f775(f775(f232(x85221),x85222),x85223))+~P1(f775(f775(f232(x85221),f775(f775(f242(x85221),x85222),f775(a114,x85224))),f775(f775(f242(x85221),x85223),f775(a114,x85224)))) % 186.05/186.63 [8852]~P70(x88521)+E(f775(f775(f775(f67(x88521,x88522,f83(x88521)),x88523),f80(x88521)),x88524),f80(x88521))+~P1(f775(f63(x88522),x88524))+P1(f775(f775(f334(x88522),f623(x88523,x88524,x88522,x88521)),x88524)) % 186.05/186.63 [9104]~P12(x91042,x91043,x91044)+~P1(f775(f63(x91042),x91043))+~P1(f775(f775(f279(a850),x91041),f775(f42(x91042),f517(x91041,x91044,x91043,x91042))))+P1(f775(f775(f279(a850),x91041),f775(f42(x91042),x91043))) % 186.05/186.63 [9302]~P1(f775(f775(f279(a850),x93021),x93023))+~P1(f775(f775(f279(a850),x93021),x93022))+~P1(f775(f775(f279(a850),x93024),x93023))+~P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x93021,x93023)),f282(a850,f279(a850),x93022,x93024))) % 186.05/186.63 [9308]~P1(f775(f775(f232(a1),x93084),f2(a1)))+P1(f775(f775(f232(a1),f775(f775(f82(a1),f775(f775(f83(a1),x93081),f52(a1,x93082,x93083))),x93084)),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x93083))+~P1(f775(f775(f233(a1),x93081),x93084)) % 186.05/186.63 [9714]~P1(f775(f63(x97141),x97142))+~P1(f775(f775(f334(x97141),x97144),x97142))+~P1(f775(f775(f334(x97141),x97143),x97142))+P1(f775(f775(f233(a850),f775(f42(x97141),f775(f775(f3(f857(x97141,a844)),f775(f775(f3(f857(x97141,a844)),x97142),f775(f775(f302(x97141),x97143),f180(f857(x97141,a844))))),f775(f775(f302(x97141),x97144),f180(f857(x97141,a844)))))),f775(f42(x97141),x97142))) % 186.05/186.63 [6780]~P136(x67803)+~P112(x67803)+P1(f775(x67801,f838(x67802,x67801,x67803)))+~P1(f775(x67801,f775(f775(f83(x67803),x67802),x67804))) % 186.05/186.63 [6840]~P100(x68401)+~P1(f775(f775(f233(x68401),x68402),x68404))+~P1(f775(f775(f233(x68401),x68402),x68403))+P1(f775(f775(f233(x68401),x68402),f775(f775(f236(x68401),x68403),x68404))) % 186.05/186.63 [6843]~P100(x68431)+~P1(f775(f775(f232(x68431),x68432),x68434))+~P1(f775(f775(f232(x68431),x68432),x68433))+P1(f775(f775(f232(x68431),x68432),f775(f775(f236(x68431),x68433),x68434))) % 186.05/186.63 [6846]~P98(x68461)+~P1(f775(f775(f232(x68461),x68462),x68464))+~P1(f775(f775(f232(x68461),x68462),x68463))+P1(f775(f775(f232(x68461),x68462),f775(f775(f104(x68461),x68463),x68464))) % 186.05/186.63 [6847]~P85(x68471)+~P1(f775(f775(f279(x68471),x68472),x68474))+~P1(f775(f775(f279(x68471),x68472),x68473))+P1(f775(f775(f279(x68471),x68472),f775(f775(f82(x68471),x68473),x68474))) % 186.05/186.63 [6848]~P104(x68481)+~P1(f775(f775(f279(x68481),x68482),x68484))+~P1(f775(f775(f279(x68481),x68482),x68483))+P1(f775(f775(f279(x68481),x68482),f775(f775(f3(x68481),x68483),x68484))) % 186.05/186.63 [6868]~P61(x68682)+E(x68681,f2(x68682))+E(f775(f775(f283(x68682),f775(f775(f242(x68682),x68681),x68683)),f775(f775(f242(x68682),x68681),x68684)),f775(f775(f242(x68682),x68681),f775(f775(f3(a850),x68683),x68684)))+~P1(f775(f775(f232(a850),x68684),x68683)) % 186.05/186.63 [6913]~P100(x69131)+~P18(x69131,f775(f775(f140(x69131),x69133),x69134))+P18(x69131,f775(f775(f140(x69131),x69132),f775(f775(f140(x69131),x69133),x69134)))+~P1(f775(f775(f232(x69131),x69132),x69133)) % 186.05/186.63 [6953]~P81(x69531)+~P1(f775(f775(f232(x69531),f2(x69531)),x69533))+~P1(f775(f775(f233(x69531),x69532),x69534))+P1(f775(f775(f233(x69531),x69532),f775(f775(f82(x69531),x69533),x69534))) % 186.05/186.63 [6954]~P81(x69541)+~P1(f775(f775(f232(x69541),x69542),x69544))+~P1(f775(f775(f233(x69541),f2(x69541)),x69543))+P1(f775(f775(f233(x69541),x69542),f775(f775(f82(x69541),x69543),x69544))) % 186.05/186.63 [6955]~P117(x69551)+~P1(f775(f775(f233(x69551),f2(x69551)),x69553))+~P1(f775(f775(f233(x69551),x69552),x69554))+P1(f775(f775(f233(x69551),x69552),f775(f775(f82(x69551),x69553),x69554))) % 186.05/186.63 [6956]~P81(x69561)+~P1(f775(f775(f232(x69561),f2(x69561)),x69564))+~P1(f775(f775(f232(x69561),x69562),x69563))+P1(f775(f775(f232(x69561),x69562),f775(f775(f82(x69561),x69563),x69564))) % 186.05/186.63 [6957]~P81(x69571)+~P1(f775(f775(f232(x69571),f2(x69571)),x69573))+~P1(f775(f775(f232(x69571),x69572),x69574))+P1(f775(f775(f232(x69571),x69572),f775(f775(f82(x69571),x69573),x69574))) % 186.05/186.63 [6991]~P100(x69911)+P1(f775(f775(f233(x69911),x69912),x69913))+P1(f775(f775(f233(x69911),x69912),x69914))+~P1(f775(f775(f233(x69911),x69912),f775(f775(f179(x69911),x69914),x69913))) % 186.05/186.63 [6992]~P100(x69921)+P1(f775(f775(f232(x69921),x69922),x69923))+P1(f775(f775(f232(x69921),x69922),x69924))+~P1(f775(f775(f232(x69921),x69922),f775(f775(f179(x69921),x69924),x69923))) % 186.05/186.63 [7676]~P63(x76761)+~P1(f775(f775(f233(x76761),x76764),f2(x76761)))+~P1(f775(f775(f233(x76761),x76763),f775(f775(f283(x76761),x76762),x76764)))+P1(f775(f775(f233(x76761),x76762),f775(f775(f83(x76761),x76763),x76764))) % 186.05/186.63 [7677]~P63(x76771)+~P1(f775(f775(f233(x76771),x76774),f2(x76771)))+~P1(f775(f775(f233(x76771),x76773),f775(f775(f83(x76771),x76772),x76774)))+P1(f775(f775(f233(x76771),x76772),f775(f775(f283(x76771),x76773),x76774))) % 186.05/186.63 [7678]~P63(x76781)+~P1(f775(f775(f233(x76781),x76784),f2(x76781)))+~P1(f775(f775(f232(x76781),x76783),f775(f775(f283(x76781),x76782),x76784)))+P1(f775(f775(f232(x76781),x76782),f775(f775(f83(x76781),x76783),x76784))) % 186.05/186.63 [7679]~P63(x76791)+~P1(f775(f775(f233(x76791),x76794),f2(x76791)))+~P1(f775(f775(f232(x76791),x76793),f775(f775(f83(x76791),x76792),x76794)))+P1(f775(f775(f232(x76791),x76792),f775(f775(f283(x76791),x76793),x76794))) % 186.05/186.63 [7792]~P119(x77921)+~P1(f775(f775(f233(x77921),x77923),f2(x77921)))+~P1(f775(f775(f233(x77921),x77924),x77922))+P1(f775(f775(f233(x77921),f775(f775(f83(x77921),x77922),x77923)),f775(f775(f83(x77921),x77924),x77923))) % 186.05/186.63 [7793]~P119(x77931)+~P1(f775(f775(f233(x77931),x77932),f2(x77931)))+~P1(f775(f775(f233(x77931),x77934),x77933))+P1(f775(f775(f233(x77931),f775(f775(f83(x77931),x77932),x77933)),f775(f775(f83(x77931),x77932),x77934))) % 186.05/186.63 [7794]~P63(x77941)+~P1(f775(f775(f233(x77941),x77943),f2(x77941)))+~P1(f775(f775(f233(x77941),x77944),x77942))+P1(f775(f775(f233(x77941),f775(f775(f283(x77941),x77942),x77943)),f775(f775(f283(x77941),x77944),x77943))) % 186.05/186.63 [7795]~P119(x77951)+~P1(f775(f775(f233(x77951),x77952),f2(x77951)))+~P1(f775(f775(f232(x77951),x77954),x77953))+P1(f775(f775(f232(x77951),f775(f775(f83(x77951),x77952),x77953)),f775(f775(f83(x77951),x77952),x77954))) % 186.05/186.63 [7796]~P129(x77961)+~P1(f775(f775(f232(x77961),x77962),f2(x77961)))+~P1(f775(f775(f232(x77961),x77964),x77963))+P1(f775(f775(f232(x77961),f775(f775(f83(x77961),x77962),x77963)),f775(f775(f83(x77961),x77962),x77964))) % 186.05/186.63 [7797]~P129(x77971)+~P1(f775(f775(f232(x77971),x77973),f2(x77971)))+~P1(f775(f775(f232(x77971),x77974),x77972))+P1(f775(f775(f232(x77971),f775(f775(f83(x77971),x77972),x77973)),f775(f775(f83(x77971),x77974),x77973))) % 186.05/186.63 [7798]~P62(x77981)+~P1(f775(f775(f232(x77981),x77983),f2(x77981)))+~P1(f775(f775(f232(x77981),x77984),x77982))+P1(f775(f775(f232(x77981),f775(f775(f283(x77981),x77982),x77983)),f775(f775(f283(x77981),x77984),x77983))) % 186.05/186.63 [7800]~P117(x78001)+~P1(f775(f775(f233(x78001),f80(x78001)),x78002))+~P1(f775(f775(f233(a850),x78003),x78004))+P1(f775(f775(f233(x78001),f775(f775(f242(x78001),x78002),x78003)),f775(f775(f242(x78001),x78002),x78004))) % 186.05/186.63 [7801]~P117(x78011)+~P1(f775(f775(f233(x78011),f80(x78011)),x78012))+~P1(f775(f775(f232(a850),x78013),x78014))+P1(f775(f775(f232(x78011),f775(f775(f242(x78011),x78012),x78013)),f775(f775(f242(x78011),x78012),x78014))) % 186.05/186.63 [7802]~P117(x78021)+~P1(f775(f775(f232(x78021),f80(x78021)),x78022))+~P1(f775(f775(f232(a850),x78023),x78024))+P1(f775(f775(f232(x78021),f775(f775(f242(x78021),x78022),x78023)),f775(f775(f242(x78021),x78022),x78024))) % 186.05/186.63 [7829]P1(f775(f775(f233(a850),f2(a850)),f775(x78291,x78292)))+~P1(f775(f63(x78293),x78294))+~P1(f775(f775(f334(x78293),x78292),x78294))+~P1(f775(f775(f233(a850),f2(a850)),f775(f775(f11(x78293,a850),x78291),x78294))) % 186.05/186.63 [7841]~P123(x78411)+~P1(f775(f775(f233(x78411),x78413),x78414))+~P1(f775(f775(f233(x78411),f2(x78411)),x78412))+P1(f775(f775(f233(x78411),f775(f775(f83(x78411),x78412),x78413)),f775(f775(f83(x78411),x78412),x78414))) % 186.05/186.63 [7842]~P115(x78421)+~P1(f775(f775(f233(x78421),x78423),x78424))+~P1(f775(f775(f233(x78421),f2(x78421)),x78422))+P1(f775(f775(f233(x78421),f775(f775(f83(x78421),x78422),x78423)),f775(f775(f83(x78421),x78422),x78424))) % 186.05/186.63 [7843]~P119(x78431)+~P1(f775(f775(f233(x78431),x78432),x78434))+~P1(f775(f775(f233(x78431),f2(x78431)),x78433))+P1(f775(f775(f233(x78431),f775(f775(f83(x78431),x78432),x78433)),f775(f775(f83(x78431),x78434),x78433))) % 186.05/186.63 [7844]~P123(x78441)+~P1(f775(f775(f233(x78441),x78442),x78444))+~P1(f775(f775(f233(x78441),f2(x78441)),x78443))+P1(f775(f775(f233(x78441),f775(f775(f83(x78441),x78442),x78443)),f775(f775(f83(x78441),x78444),x78443))) % 186.05/186.63 [7845]~P119(x78451)+~P1(f775(f775(f233(x78451),x78453),x78454))+~P1(f775(f775(f233(x78451),f2(x78451)),x78452))+P1(f775(f775(f233(x78451),f775(f775(f83(x78451),x78452),x78453)),f775(f775(f83(x78451),x78452),x78454))) % 186.05/186.63 [7846]~P63(x78461)+~P1(f775(f775(f233(x78461),x78462),x78464))+~P1(f775(f775(f233(x78461),f2(x78461)),x78463))+P1(f775(f775(f233(x78461),f775(f775(f283(x78461),x78462),x78463)),f775(f775(f283(x78461),x78464),x78463))) % 186.05/186.63 [7847]~P119(x78471)+~P1(f775(f775(f233(x78471),f2(x78471)),x78472))+~P1(f775(f775(f232(x78471),x78473),x78474))+P1(f775(f775(f232(x78471),f775(f775(f83(x78471),x78472),x78473)),f775(f775(f83(x78471),x78472),x78474))) % 186.05/186.63 [7848]~P131(x78481)+~P1(f775(f775(f232(x78481),x78483),x78484))+~P1(f775(f775(f232(x78481),f2(x78481)),x78482))+P1(f775(f775(f232(x78481),f775(f775(f83(x78481),x78482),x78483)),f775(f775(f83(x78481),x78482),x78484))) % 186.05/186.63 [7849]~P130(x78491)+~P1(f775(f775(f232(x78491),x78493),x78494))+~P1(f775(f775(f232(x78491),f2(x78491)),x78492))+P1(f775(f775(f232(x78491),f775(f775(f83(x78491),x78492),x78493)),f775(f775(f83(x78491),x78492),x78494))) % 186.05/186.63 [7850]~P131(x78501)+~P1(f775(f775(f232(x78501),x78502),x78504))+~P1(f775(f775(f232(x78501),f2(x78501)),x78503))+P1(f775(f775(f232(x78501),f775(f775(f83(x78501),x78502),x78503)),f775(f775(f83(x78501),x78504),x78503))) % 186.05/186.63 [7851]~P117(x78511)+~P1(f775(f775(f232(x78511),x78512),x78514))+~P1(f775(f775(f232(x78511),f2(x78511)),x78512))+P1(f775(f775(f232(x78511),f775(f775(f242(x78511),x78512),x78513)),f775(f775(f242(x78511),x78514),x78513))) % 186.05/186.63 [7852]~P62(x78521)+~P1(f775(f775(f232(x78521),x78522),x78524))+~P1(f775(f775(f232(x78521),f2(x78521)),x78523))+P1(f775(f775(f232(x78521),f775(f775(f283(x78521),x78522),x78523)),f775(f775(f283(x78521),x78524),x78523))) % 186.05/186.63 [7891]~P102(x78912)+P1(f775(f775(f232(f857(x78911,x78912)),x78914),x78913))+~P1(f775(f775(f232(f857(x78911,x78912)),x78913),x78914))+P1(f775(f775(f233(f857(x78911,x78912)),x78913),x78914)) % 186.05/186.63 [7935]P1(f775(f775(f334(x79351),x79352),x79353))+P1(f775(f775(f334(x79351),x79352),x79354))+~P1(f775(f775(f232(f857(x79351,a844)),x79354),x79353))+P1(f775(f775(f233(f857(x79351,a844)),x79354),f775(f775(f302(x79351),x79352),x79353))) % 186.05/186.63 [8042]~P111(x80422)+E(x80421,f2(x80422))+P1(f775(f775(f279(x80422),x80423),x80424))+~P1(f775(f775(f279(x80422),f775(f775(f83(x80422),x80423),x80421)),f775(f775(f83(x80422),x80424),x80421))) % 186.05/186.63 [8043]~P111(x80432)+E(x80431,f2(x80432))+P1(f775(f775(f279(x80432),x80433),x80434))+~P1(f775(f775(f279(x80432),f775(f775(f83(x80432),x80431),x80433)),f775(f775(f83(x80432),x80431),x80434))) % 186.05/186.63 [8087]P1(f775(f775(f334(x80871),x80872),x80873))+P1(f775(f775(f334(x80871),x80872),x80874))+~P1(f775(f775(f233(f857(x80871,a844)),x80874),f775(f775(f302(x80871),x80872),x80873)))+P1(f775(f775(f232(f857(x80871,a844)),x80874),x80873)) % 186.05/186.63 [8156]~P119(x81561)+P1(f775(f775(f233(x81561),x81563),x81562))+P1(f775(f775(f233(x81561),x81562),x81563))+~P1(f775(f775(f233(x81561),f775(f775(f83(x81561),x81564),x81562)),f775(f775(f83(x81561),x81564),x81563))) % 186.05/186.63 [8157]~P119(x81571)+P1(f775(f775(f233(x81571),x81573),x81572))+P1(f775(f775(f233(x81571),x81572),x81573))+~P1(f775(f775(f233(x81571),f775(f775(f83(x81571),x81572),x81574)),f775(f775(f83(x81571),x81573),x81574))) % 186.05/186.63 [8168]~P119(x81681)+P1(f775(f775(f233(x81681),x81684),f2(x81681)))+P1(f775(f775(f233(x81681),x81682),x81683))+~P1(f775(f775(f233(x81681),f775(f775(f83(x81681),x81682),x81684)),f775(f775(f83(x81681),x81683),x81684))) % 186.05/186.63 [8169]~P119(x81691)+P1(f775(f775(f233(x81691),x81694),f2(x81691)))+P1(f775(f775(f233(x81691),x81692),x81693))+~P1(f775(f775(f233(x81691),f775(f775(f83(x81691),x81694),x81692)),f775(f775(f83(x81691),x81694),x81693))) % 186.05/186.63 [8172]~P119(x81721)+P1(f775(f775(f233(x81721),x81722),x81723))+P1(f775(f775(f233(x81721),f2(x81721)),x81724))+~P1(f775(f775(f233(x81721),f775(f775(f83(x81721),x81724),x81723)),f775(f775(f83(x81721),x81724),x81722))) % 186.05/186.63 [8173]~P119(x81731)+P1(f775(f775(f233(x81731),x81732),x81733))+P1(f775(f775(f233(x81731),f2(x81731)),x81734))+~P1(f775(f775(f233(x81731),f775(f775(f83(x81731),x81733),x81734)),f775(f775(f83(x81731),x81732),x81734))) % 186.05/186.63 [8186]~P119(x81861)+P1(f775(f775(f233(x81861),x81862),f2(x81861)))+P1(f775(f775(f233(x81861),f2(x81861)),x81862))+~P1(f775(f775(f233(x81861),f775(f775(f83(x81861),x81863),x81862)),f775(f775(f83(x81861),x81864),x81862))) % 186.05/186.63 [8187]~P119(x81871)+P1(f775(f775(f233(x81871),x81872),f2(x81871)))+P1(f775(f775(f233(x81871),f2(x81871)),x81872))+~P1(f775(f775(f233(x81871),f775(f775(f83(x81871),x81872),x81873)),f775(f775(f83(x81871),x81872),x81874))) % 186.05/186.63 [8211]~P119(x82111)+~P1(f775(f775(f233(x82111),x82114),f2(x82111)))+P1(f775(f775(f233(x82111),x82112),x82113))+~P1(f775(f775(f233(x82111),f775(f775(f83(x82111),x82114),x82113)),f775(f775(f83(x82111),x82114),x82112))) % 186.05/186.63 [8212]~P119(x82121)+~P1(f775(f775(f233(x82121),x82124),f2(x82121)))+P1(f775(f775(f232(x82121),x82122),x82123))+~P1(f775(f775(f232(x82121),f775(f775(f83(x82121),x82124),x82123)),f775(f775(f83(x82121),x82124),x82122))) % 186.05/186.63 [8224]~P117(x82243)+~P1(f775(f775(f233(x82243),f80(x82243)),x82244))+P1(f775(f775(f233(a850),x82241),x82242))+~P1(f775(f775(f233(x82243),f775(f775(f242(x82243),x82244),x82241)),f775(f775(f242(x82243),x82244),x82242))) % 186.05/186.63 [8226]~P117(x82263)+~P1(f775(f775(f233(x82263),f80(x82263)),x82264))+P1(f775(f775(f232(a850),x82261),x82262))+~P1(f775(f775(f232(x82263),f775(f775(f242(x82263),x82264),x82261)),f775(f775(f242(x82263),x82264),x82262))) % 186.05/186.63 [8236]~P119(x82361)+P1(f775(f775(f233(x82361),x82362),x82363))+~P1(f775(f775(f233(x82361),f2(x82361)),x82364))+~P1(f775(f775(f233(x82361),f775(f775(f83(x82361),x82364),x82362)),f775(f775(f83(x82361),x82364),x82363))) % 186.05/186.63 [8237]~P123(x82371)+P1(f775(f775(f233(x82371),x82372),x82373))+~P1(f775(f775(f232(x82371),f2(x82371)),x82374))+~P1(f775(f775(f233(x82371),f775(f775(f83(x82371),x82374),x82372)),f775(f775(f83(x82371),x82374),x82373))) % 186.05/186.63 [8238]~P125(x82381)+P1(f775(f775(f233(x82381),x82382),x82383))+~P1(f775(f775(f232(x82381),f2(x82381)),x82384))+~P1(f775(f775(f233(x82381),f775(f775(f83(x82381),x82384),x82382)),f775(f775(f83(x82381),x82384),x82383))) % 186.05/186.63 [8239]~P117(x82391)+~P1(f775(f775(f232(x82391),f2(x82391)),x82393))+P1(f775(f775(f233(x82391),x82392),x82393))+~P1(f775(f775(f233(x82391),f775(f775(f242(x82391),x82392),x82394)),f775(f775(f242(x82391),x82393),x82394))) % 186.05/186.63 [8240]~P123(x82401)+P1(f775(f775(f233(x82401),x82402),x82403))+~P1(f775(f775(f232(x82401),f2(x82401)),x82404))+~P1(f775(f775(f233(x82401),f775(f775(f83(x82401),x82402),x82404)),f775(f775(f83(x82401),x82403),x82404))) % 186.05/186.63 [8241]~P125(x82411)+P1(f775(f775(f233(x82411),x82412),x82413))+~P1(f775(f775(f232(x82411),f2(x82411)),x82414))+~P1(f775(f775(f233(x82411),f775(f775(f83(x82411),x82412),x82414)),f775(f775(f83(x82411),x82413),x82414))) % 186.05/186.63 [8242]~P119(x82421)+P1(f775(f775(f232(x82421),x82422),x82423))+~P1(f775(f775(f233(x82421),f2(x82421)),x82424))+~P1(f775(f775(f232(x82421),f775(f775(f83(x82421),x82424),x82422)),f775(f775(f83(x82421),x82424),x82423))) % 186.05/186.63 [8243]~P123(x82431)+P1(f775(f775(f232(x82431),x82432),x82433))+~P1(f775(f775(f233(x82431),f2(x82431)),x82434))+~P1(f775(f775(f232(x82431),f775(f775(f83(x82431),x82434),x82432)),f775(f775(f83(x82431),x82434),x82433))) % 186.05/186.63 [8244]~P123(x82441)+P1(f775(f775(f232(x82441),x82442),x82443))+~P1(f775(f775(f233(x82441),f2(x82441)),x82444))+~P1(f775(f775(f232(x82441),f775(f775(f83(x82441),x82442),x82444)),f775(f775(f83(x82441),x82443),x82444))) % 186.05/186.63 [8284]P1(f775(f775(f334(x82841),x82842),x82843))+~P1(f775(f775(f232(f857(x82841,a844)),x82843),x82844))+~P1(f775(f775(f233(f857(x82841,a844)),x82843),x82844))+P1(f775(f775(f233(f857(x82841,a844)),x82843),f775(f775(f302(x82841),x82842),x82844))) % 186.05/186.63 [8319]~P136(x83191)+~P112(x83191)+P1(f775(f775(f279(x83191),x83192),f775(f775(f82(x83191),f838(x83192,x83193,x83191)),f2(x83191))))+~P1(f775(x83193,f775(f775(f83(x83191),x83192),x83194))) % 186.05/186.63 [8645]E(f775(f775(f3(a1),f346(x86451,x86452,x86453,x86454)),f347(x86451,x86452,x86453,x86454)),x86454)+~P1(f775(f775(f233(a1),f2(a1)),x86453))+~P1(f775(f775(f232(a1),x86451),x86454))+P1(f775(f775(f232(a1),x86451),f775(f775(f82(a1),x86454),x86453))) % 186.05/186.63 [8646]E(f775(f775(f3(a1),f355(x86461,x86462,x86463,x86464)),f356(x86461,x86462,x86463,x86464)),x86464)+~P1(f775(f775(f233(a1),f2(a1)),x86463))+~P1(f775(f775(f233(a1),x86461),x86464))+P1(f775(f775(f233(a1),x86461),f775(f775(f82(a1),x86464),x86463))) % 186.05/186.63 [8772]~E(f775(f775(f153(x87721),x87723),f757(x87724,x87723,x87721,x87722)),f775(f775(f153(x87721),x87724),f757(x87724,x87723,x87721,x87722)))+E(f775(f775(f159(x87721),x87722),x87723),f775(f775(f159(x87721),x87722),x87724))+~P1(f775(f775(f232(a850),x87722),f775(f181(f851(x87721)),x87723)))+~P1(f775(f775(f232(a850),x87722),f775(f181(f851(x87721)),x87724))) % 186.05/186.63 [8823]~P1(f775(f775(f233(a1),f2(a1)),x88233))+~P1(f775(f775(f232(a1),x88231),x88234))+P1(f775(f775(f334(a1),f346(x88231,x88232,x88233,x88234)),x88232))+P1(f775(f775(f232(a1),x88231),f775(f775(f82(a1),x88234),x88233))) % 186.05/186.63 [8824]~P1(f775(f775(f233(a1),f2(a1)),x88243))+~P1(f775(f775(f233(a1),x88241),x88244))+P1(f775(f775(f334(a1),f355(x88241,x88242,x88243,x88244)),x88242))+P1(f775(f775(f233(a1),x88241),f775(f775(f82(a1),x88244),x88243))) % 186.05/186.63 [8861]~P100(x88611)+~P1(f775(f63(x88611),x88613))+~P1(f775(f775(f334(x88611),x88614),x88613))+P1(f775(f775(f232(x88611),f775(f775(f66(x88611,x88611,f236(x88611)),x88612),x88613)),f775(f775(f236(x88611),x88614),x88612))) % 186.05/186.63 [8862]~P98(x88621)+~P1(f775(f63(x88621),x88623))+~P1(f775(f775(f334(x88621),x88624),x88623))+P1(f775(f775(f232(x88621),f775(f775(f66(x88621,x88621,f104(x88621)),x88622),x88623)),f775(f775(f104(x88621),x88624),x88622))) % 186.05/186.63 [8871]~P12(x88712,x88713,x88714)+~P1(f775(f63(x88712),x88713))+P1(f775(f775(f279(a850),x88711),f775(f42(x88712),x88713)))+P1(f775(f775(f334(f857(x88712,a844)),f517(x88711,x88714,x88713,x88712)),f775(f775(f61(x88712),x88713),x88714))) % 186.05/186.63 [8910]E(f775(f775(f159(x89101),x89102),x89103),f775(f775(f159(x89101),x89102),x89104))+P1(f775(f775(f233(a850),f757(x89103,x89104,x89101,x89102)),x89102))+~P1(f775(f775(f232(a850),x89102),f775(f181(f851(x89101)),x89103)))+~P1(f775(f775(f232(a850),x89102),f775(f181(f851(x89101)),x89104))) % 186.05/186.63 [8915]~P1(f775(f775(f233(a1),f2(a1)),x89153))+~P1(f775(f775(f233(a1),x89151),x89152))+P1(f775(f775(f334(a1),f356(x89151,x89154,x89153,x89152)),f295(a1,f80(a1),x89153)))+P1(f775(f775(f233(a1),x89151),f775(f775(f82(a1),x89152),x89153))) % 186.05/186.63 [8916]~P1(f775(f775(f233(a1),f2(a1)),x89163))+~P1(f775(f775(f232(a1),x89161),x89162))+P1(f775(f775(f334(a1),f347(x89161,x89164,x89163,x89162)),f295(a1,f80(a1),x89163)))+P1(f775(f775(f232(a1),x89161),f775(f775(f82(a1),x89162),x89163))) % 186.05/186.63 [9079]~E(f166(x90791,x90792,x90793),f166(x90791,x90792,x90794))+E(f775(f158(f856(x90791,x90792)),x90793),f775(f158(f856(x90791,x90792)),x90794))+~P1(f775(f127(x90791),f775(f775(f143(f856(x90791,x90792),x90791),f240(x90791,x90792)),x90794)))+~P1(f775(f127(x90791),f775(f775(f143(f856(x90791,x90792),x90791),f240(x90791,x90792)),x90793))) % 186.05/186.63 [9082]E(f166(x90821,x90822,x90823),f166(x90821,x90822,x90824))+~E(f775(f158(f856(x90821,x90822)),x90823),f775(f158(f856(x90821,x90822)),x90824))+~P1(f775(f127(x90821),f775(f775(f143(f856(x90821,x90822),x90821),f240(x90821,x90822)),x90824)))+~P1(f775(f127(x90821),f775(f775(f143(f856(x90821,x90822),x90821),f240(x90821,x90822)),x90823))) % 186.05/186.63 [9199]~P100(x91991)+~P1(f775(f63(x91991),x91994))+P1(f775(f775(f334(x91991),f690(x91992,x91993,x91994,x91991)),x91994))+P1(f775(f775(f232(x91991),f775(f775(f66(x91991,x91991,f179(x91991)),x91992),x91994)),f775(f775(f179(x91991),x91993),x91992))) % 186.05/186.63 [9200]~P92(x92001)+~P1(f775(f63(x92001),x92004))+P1(f775(f775(f334(x92001),f694(x92002,x92003,x92004,x92001)),x92004))+P1(f775(f775(f232(x92001),f775(f775(f66(x92001,x92001,f103(x92001)),x92002),x92004)),f775(f775(f103(x92001),x92003),x92002))) % 186.05/186.63 [9326]~P100(x93261)+~P1(f775(f63(x93261),x93263))+~P1(f775(f775(f232(x93261),f690(x93262,x93264,x93263,x93261)),x93264))+P1(f775(f775(f232(x93261),f775(f775(f66(x93261,x93261,f179(x93261)),x93262),x93263)),f775(f775(f179(x93261),x93264),x93262))) % 186.05/186.63 [9327]~P92(x93271)+~P1(f775(f63(x93271),x93273))+~P1(f775(f775(f232(x93271),f694(x93272,x93274,x93273,x93271)),x93274))+P1(f775(f775(f232(x93271),f775(f775(f66(x93271,x93271,f103(x93271)),x93272),x93273)),f775(f775(f103(x93271),x93274),x93272))) % 186.05/186.63 [9329]~P1(f775(f775(f233(a1),f2(a1)),x93293))+~P1(f775(f775(f232(a1),f2(a1)),x93294))+~P1(f775(f775(f233(a1),x93294),x93291))+P1(f775(f775(f233(a1),f775(f775(f82(a1),f775(f775(f83(a1),x93291),f52(a1,x93292,x93293))),x93294)),f775(f775(f83(a1),x93291),x93293))) % 186.05/186.63 [9589]~P99(x95891)+P1(f775(f775(f233(x95891),f775(x95892,x95893)),f775(x95892,x95894)))+~P1(f775(f775(f233(a850),x95893),x95894))+~P1(f775(f775(f233(x95891),f775(x95892,f650(x95894,x95893,x95892,x95891))),f775(x95892,f775(a114,f650(x95894,x95893,x95892,x95891))))) % 186.05/186.63 [9590]~P99(x95901)+P1(f775(f775(f233(x95901),f775(x95902,x95903)),f775(x95902,x95904)))+~P1(f775(f775(f233(a850),x95903),x95904))+~P1(f775(f775(f233(x95901),f775(x95902,f663(x95904,x95903,x95902,x95901))),f775(x95902,f775(a114,f663(x95904,x95903,x95902,x95901))))) % 186.05/186.63 [9591]~P99(x95913)+~P1(f775(f775(f233(x95913),f775(x95914,x95911)),f775(x95914,x95912)))+P1(f775(f775(f233(a850),x95911),x95912))+~P1(f775(f775(f233(x95913),f775(x95914,f650(x95912,x95911,x95914,x95913))),f775(x95914,f775(a114,f650(x95912,x95911,x95914,x95913))))) % 186.05/186.63 [9684]E(x96841,x96842)+P1(f775(f775(f334(f856(f851(x96843),f851(x96843))),f775(f775(f241(f851(x96843),f851(x96843)),x96842),x96841)),f137(x96843,x96844)))+P1(f775(f775(f334(f856(f851(x96843),f851(x96843))),f775(f775(f241(f851(x96843),f851(x96843)),x96841),x96842)),f137(x96843,x96844)))+~P1(f775(f775(f334(f856(x96843,x96843)),f775(f775(f241(x96843,x96843),f752(x96841,x96842,x96844,x96843)),f754(x96841,x96842,x96844,x96843))),x96844)) % 186.05/186.63 [9685]E(x96851,x96852)+P1(f775(f775(f334(f856(f851(x96853),f851(x96853))),f775(f775(f241(f851(x96853),f851(x96853)),x96852),x96851)),f137(x96853,x96854)))+P1(f775(f775(f334(f856(f851(x96853),f851(x96853))),f775(f775(f241(f851(x96853),f851(x96853)),x96851),x96852)),f137(x96853,x96854)))+~P1(f775(f775(f334(f856(x96853,x96853)),f775(f775(f241(x96853,x96853),f754(x96851,x96852,x96854,x96853)),f752(x96851,x96852,x96854,x96853))),x96854)) % 186.05/186.63 [7374]~P100(x73741)+~P1(f775(f775(f233(x73741),x73743),x73744))+~P1(f775(f775(f233(x73741),x73742),x73744))+P1(f775(f775(f233(x73741),f775(f775(f179(x73741),x73742),x73743)),x73744)) % 186.05/186.63 [7377]~P100(x73771)+~P1(f775(f775(f232(x73771),x73773),x73774))+~P1(f775(f775(f232(x73771),x73772),x73774))+P1(f775(f775(f232(x73771),f775(f775(f179(x73771),x73772),x73773)),x73774)) % 186.05/186.63 [7380]~P92(x73801)+~P1(f775(f775(f232(x73801),x73803),x73804))+~P1(f775(f775(f232(x73801),x73802),x73804))+P1(f775(f775(f232(x73801),f775(f775(f103(x73801),x73802),x73803)),x73804)) % 186.05/186.63 [7621]~P7(x76211)+E(f775(f775(f82(x76211),f775(f775(f43(x76211),x76212),x76213)),f775(f775(f43(x76211),x76214),x76213)),f775(f775(f43(x76211),f775(f775(f82(x76211),x76212),x76214)),x76213))+~P1(f775(f775(f279(x76211),x76213),x76214))+~P1(f775(f775(f279(x76211),x76213),x76212)) % 186.05/186.63 [7699]~E(x76991,x76993)+E(f130(a850,f775(f294(a850,x76991),x76992)),f775(f775(f140(a850),x76993),x76994))+~E(f130(a850,f775(f294(a850,f775(f775(f82(a850),x76991),f80(a850))),x76992)),x76994)+~P1(f775(f775(f233(a850),x76991),x76992)) % 186.05/186.63 [7710]~P100(x77101)+P1(f775(f775(f233(x77101),x77102),x77103))+P1(f775(f775(f233(x77101),x77104),x77103))+~P1(f775(f775(f233(x77101),f775(f775(f236(x77101),x77104),x77102)),x77103)) % 186.05/186.63 [7711]~P100(x77111)+P1(f775(f775(f232(x77111),x77112),x77113))+P1(f775(f775(f232(x77111),x77114),x77113))+~P1(f775(f775(f232(x77111),f775(f775(f236(x77111),x77114),x77112)),x77113)) % 186.05/186.63 [7992]~P62(x79921)+~P1(f775(f775(f233(x79921),f2(x79921)),x79923))+~P1(f775(f775(f233(x79921),x79922),f775(f775(f283(x79921),x79924),x79923)))+P1(f775(f775(f233(x79921),f775(f775(f83(x79921),x79922),x79923)),x79924)) % 186.05/186.63 [7993]~P63(x79931)+~P1(f775(f775(f233(x79931),f2(x79931)),x79933))+~P1(f775(f775(f233(x79931),x79932),f775(f775(f283(x79931),x79934),x79933)))+P1(f775(f775(f233(x79931),f775(f775(f83(x79931),x79932),x79933)),x79934)) % 186.05/186.63 [7994]~P62(x79941)+~P1(f775(f775(f233(x79941),f2(x79941)),x79943))+~P1(f775(f775(f233(x79941),x79942),f775(f775(f83(x79941),x79944),x79943)))+P1(f775(f775(f233(x79941),f775(f775(f283(x79941),x79942),x79943)),x79944)) % 186.05/186.63 [7996]~P63(x79961)+~P1(f775(f775(f233(x79961),f2(x79961)),x79963))+~P1(f775(f775(f233(x79961),x79962),f775(f775(f83(x79961),x79964),x79963)))+P1(f775(f775(f233(x79961),f775(f775(f283(x79961),x79962),x79963)),x79964)) % 186.05/186.63 [7997]~P62(x79971)+~P1(f775(f775(f233(x79971),f2(x79971)),x79973))+~P1(f775(f775(f232(x79971),x79972),f775(f775(f283(x79971),x79974),x79973)))+P1(f775(f775(f232(x79971),f775(f775(f83(x79971),x79972),x79973)),x79974)) % 186.05/186.63 [7998]~P63(x79981)+~P1(f775(f775(f233(x79981),f2(x79981)),x79983))+~P1(f775(f775(f232(x79981),x79982),f775(f775(f283(x79981),x79984),x79983)))+P1(f775(f775(f232(x79981),f775(f775(f83(x79981),x79982),x79983)),x79984)) % 186.05/186.63 [7999]~P62(x79991)+~P1(f775(f775(f233(x79991),f2(x79991)),x79993))+~P1(f775(f775(f232(x79991),x79992),f775(f775(f83(x79991),x79994),x79993)))+P1(f775(f775(f232(x79991),f775(f775(f283(x79991),x79992),x79993)),x79994)) % 186.05/186.63 [8001]~P63(x80011)+~P1(f775(f775(f233(x80011),f2(x80011)),x80013))+~P1(f775(f775(f232(x80011),x80012),f775(f775(f83(x80011),x80014),x80013)))+P1(f775(f775(f232(x80011),f775(f775(f283(x80011),x80012),x80013)),x80014)) % 186.05/186.63 [8125]~P62(x81251)+~P1(f775(f775(f233(x81251),f2(x81251)),x81254))+P1(f775(f775(f233(x81251),x81252),f775(f775(f83(x81251),x81253),x81254)))+~P1(f775(f775(f233(x81251),f775(f775(f283(x81251),x81252),x81254)),x81253)) % 186.05/186.63 [8126]~P62(x81261)+~P1(f775(f775(f233(x81261),f2(x81261)),x81264))+P1(f775(f775(f233(x81261),x81262),f775(f775(f283(x81261),x81263),x81264)))+~P1(f775(f775(f233(x81261),f775(f775(f83(x81261),x81262),x81264)),x81263)) % 186.05/186.63 [8128]~P63(x81281)+~P1(f775(f775(f233(x81281),f2(x81281)),x81284))+P1(f775(f775(f233(x81281),x81282),f775(f775(f83(x81281),x81283),x81284)))+~P1(f775(f775(f233(x81281),f775(f775(f283(x81281),x81282),x81284)),x81283)) % 186.05/186.63 [8129]~P63(x81291)+~P1(f775(f775(f233(x81291),f2(x81291)),x81294))+P1(f775(f775(f233(x81291),x81292),f775(f775(f283(x81291),x81293),x81294)))+~P1(f775(f775(f233(x81291),f775(f775(f83(x81291),x81292),x81294)),x81293)) % 186.05/186.63 [8130]~P62(x81301)+~P1(f775(f775(f233(x81301),f2(x81301)),x81304))+P1(f775(f775(f232(x81301),x81302),f775(f775(f83(x81301),x81303),x81304)))+~P1(f775(f775(f232(x81301),f775(f775(f283(x81301),x81302),x81304)),x81303)) % 186.05/186.63 [8131]~P62(x81311)+~P1(f775(f775(f233(x81311),f2(x81311)),x81314))+P1(f775(f775(f232(x81311),x81312),f775(f775(f283(x81311),x81313),x81314)))+~P1(f775(f775(f232(x81311),f775(f775(f83(x81311),x81312),x81314)),x81313)) % 186.05/186.63 [8133]~P63(x81331)+~P1(f775(f775(f233(x81331),f2(x81331)),x81334))+P1(f775(f775(f232(x81331),x81332),f775(f775(f83(x81331),x81333),x81334)))+~P1(f775(f775(f232(x81331),f775(f775(f283(x81331),x81332),x81334)),x81333)) % 186.05/186.63 [8134]~P63(x81341)+~P1(f775(f775(f233(x81341),f2(x81341)),x81344))+P1(f775(f775(f232(x81341),x81342),f775(f775(f283(x81341),x81343),x81344)))+~P1(f775(f775(f232(x81341),f775(f775(f83(x81341),x81342),x81344)),x81343)) % 186.05/186.63 [8289]~P63(x82891)+~P1(f775(f775(f233(x82891),x82893),f2(x82891)))+~P1(f775(f775(f233(x82891),f775(f775(f283(x82891),x82894),x82893)),x82892))+P1(f775(f775(f233(x82891),f775(f775(f83(x82891),x82892),x82893)),x82894)) % 186.05/186.63 [8290]~P63(x82901)+~P1(f775(f775(f233(x82901),x82903),f2(x82901)))+~P1(f775(f775(f233(x82901),f775(f775(f83(x82901),x82904),x82903)),x82902))+P1(f775(f775(f233(x82901),f775(f775(f283(x82901),x82902),x82903)),x82904)) % 186.05/186.63 [8291]~P63(x82911)+~P1(f775(f775(f233(x82911),x82913),f2(x82911)))+~P1(f775(f775(f232(x82911),f775(f775(f283(x82911),x82914),x82913)),x82912))+P1(f775(f775(f232(x82911),f775(f775(f83(x82911),x82912),x82913)),x82914)) % 186.05/186.63 [8292]~P63(x82921)+~P1(f775(f775(f233(x82921),x82923),f2(x82921)))+~P1(f775(f775(f232(x82921),f775(f775(f83(x82921),x82924),x82923)),x82922))+P1(f775(f775(f232(x82921),f775(f775(f283(x82921),x82922),x82923)),x82924)) % 186.05/186.63 [8305]~P1(f775(x83051,x83054))+~P1(f775(f775(f233(a850),x83052),f775(f775(f83(a850),x83053),f775(a114,x83054))))+P1(f775(x83051,f775(f775(f43(a850),x83052),x83053)))+~P1(f775(f775(f232(a850),f775(f775(f83(a850),x83053),x83054)),x83052)) % 186.05/186.63 [8520]~P100(x85201)+~P1(f775(f63(x85201),x85204))+~P1(f775(f775(f334(x85201),x85202),x85204))+P1(f775(f775(f232(x85201),f775(f775(f179(x85201),x85202),x85203)),f775(f775(f66(x85201,x85201,f179(x85201)),x85203),x85204))) % 186.05/186.63 [8521]~P92(x85211)+~P1(f775(f63(x85211),x85214))+~P1(f775(f775(f334(x85211),x85212),x85214))+P1(f775(f775(f232(x85211),f775(f775(f103(x85211),x85212),x85213)),f775(f775(f66(x85211,x85211,f103(x85211)),x85213),x85214))) % 186.05/186.63 [8647]~P1(f775(f63(x86471),x86472))+E(f775(f42(x86471),f775(f775(f3(f857(x86471,a844)),x86472),f775(f775(f302(x86471),x86473),x86474))),f775(f775(f3(a850),f775(f42(x86471),f775(f775(f3(f857(x86471,a844)),x86472),x86474))),f80(a850)))+P1(f775(f775(f334(x86471),x86473),x86474))+~P1(f775(f775(f334(x86471),x86473),x86472)) % 186.05/186.63 [8711]E(f775(f775(f82(a1),f348(x87111,x87112,x87113,x87114)),f349(x87111,x87112,x87113,x87114)),x87114)+~P1(f775(f775(f233(a1),f2(a1)),x87113))+~P1(f775(f775(f232(a1),x87114),x87111))+P1(f775(f775(f232(a1),f775(f775(f3(a1),x87114),x87113)),x87111)) % 186.05/186.63 [8712]E(f775(f775(f82(a1),f357(x87121,x87122,x87123,x87124)),f358(x87121,x87122,x87123,x87124)),x87124)+~P1(f775(f775(f233(a1),f2(a1)),x87123))+~P1(f775(f775(f233(a1),x87124),x87121))+P1(f775(f775(f233(a1),f775(f775(f3(a1),x87124),x87123)),x87121)) % 186.05/186.63 [8895]~P1(f775(f775(f233(a1),f2(a1)),x88953))+~P1(f775(f775(f232(a1),x88954),x88951))+P1(f775(f775(f334(a1),f348(x88951,x88952,x88953,x88954)),x88952))+P1(f775(f775(f232(a1),f775(f775(f3(a1),x88954),x88953)),x88951)) % 186.05/186.63 [8896]~P1(f775(f775(f233(a1),f2(a1)),x88963))+~P1(f775(f775(f233(a1),x88964),x88961))+P1(f775(f775(f334(a1),f357(x88961,x88962,x88963,x88964)),x88962))+P1(f775(f775(f233(a1),f775(f775(f3(a1),x88964),x88963)),x88961)) % 186.05/186.63 [8975]~P1(f775(f775(f233(a1),f2(a1)),x89752))+~P1(f775(f775(f233(a1),x89751),x89753))+P1(f775(f775(f334(a1),f358(x89753,x89754,x89752,x89751)),f295(a1,f80(a1),x89752)))+P1(f775(f775(f233(a1),f775(f775(f3(a1),x89751),x89752)),x89753)) % 186.05/186.63 [8976]~P1(f775(f775(f233(a1),f2(a1)),x89762))+~P1(f775(f775(f232(a1),x89761),x89763))+P1(f775(f775(f334(a1),f349(x89763,x89764,x89762,x89761)),f295(a1,f80(a1),x89762)))+P1(f775(f775(f232(a1),f775(f775(f3(a1),x89761),x89762)),x89763)) % 186.05/186.63 [8997]~P1(f775(f775(f233(a1),f2(a1)),x89973))+~P1(f775(f775(f232(a1),f2(a1)),x89974))+~P1(f775(f775(f233(a1),x89974),x89971))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),f775(f775(f83(a1),x89971),f52(a1,x89972,x89973))),x89974))) % 186.05/186.63 [9055]~P100(x90551)+~P1(f775(f63(x90551),x90554))+~P1(f775(f775(f232(x90551),x90552),f689(x90553,x90552,x90554,x90551)))+P1(f775(f775(f232(x90551),f775(f775(f236(x90551),x90552),x90553)),f775(f775(f66(x90551,x90551,f236(x90551)),x90553),x90554))) % 186.05/186.63 [9056]~P98(x90561)+~P1(f775(f63(x90561),x90564))+~P1(f775(f775(f232(x90561),x90562),f693(x90563,x90562,x90564,x90561)))+P1(f775(f775(f232(x90561),f775(f775(f104(x90561),x90562),x90563)),f775(f775(f66(x90561,x90561,f104(x90561)),x90563),x90564))) % 186.05/186.63 [9069]~P1(f775(f775(f232(a1),x90694),f2(a1)))+~P1(f775(f775(f233(a1),f2(a1)),x90692))+~P1(f775(f775(f233(a1),x90691),x90694))+P1(f775(f775(f233(a1),f775(f775(f83(a1),x90691),x90692)),f775(f775(f82(a1),f775(f775(f83(a1),x90691),f52(a1,x90693,x90692))),x90694))) % 186.05/186.63 [9091]P1(f775(f63(x90911),x90912))+~P1(f775(f63(x90911),x90913))+~P1(f775(f775(f334(f857(x90911,a844)),x90912),f775(f775(f61(x90911),x90913),x90914)))+~P1(f775(f775(f232(f857(f856(x90911,x90911),a844)),x90914),f775(f775(f248(x90911,x90911),x90913),f775(f18(f857(x90911,a844),x90911),x90913)))) % 186.05/186.63 [9114]~P100(x91141)+~P1(f775(f63(x91141),x91144))+P1(f775(f775(f334(x91141),f689(x91142,x91143,x91144,x91141)),x91144))+P1(f775(f775(f232(x91141),f775(f775(f236(x91141),x91143),x91142)),f775(f775(f66(x91141,x91141,f236(x91141)),x91142),x91144))) % 186.05/186.63 [9115]~P98(x91151)+~P1(f775(f63(x91151),x91154))+P1(f775(f775(f334(x91151),f693(x91152,x91153,x91154,x91151)),x91154))+P1(f775(f775(f232(x91151),f775(f775(f104(x91151),x91153),x91152)),f775(f775(f66(x91151,x91151,f104(x91151)),x91152),x91154))) % 186.05/186.63 [9487]~P1(f775(f63(x94872),x94874))+~P1(f775(f63(x94871),x94873))+~P1(f775(f775(f232(a850),f775(f42(x94872),x94874)),f775(f42(x94871),x94873)))+P1(f775(f775(f232(f857(x94871,a844)),f775(f303(x94872,x94871,f527(x94873,x94871,x94874,x94872)),x94874)),x94873)) % 186.05/186.63 [9152]~P1(f775(f775(f334(x91521),x91522),x91524))+P1(f775(f775(f334(x91521),x91522),x91523))+~P1(f775(f775(f233(f857(x91521,a844)),x91524),f775(f775(f302(x91521),x91522),x91523)))+P1(f775(f775(f233(f857(x91521,a844)),f775(f775(f3(f857(x91521,a844)),x91524),f775(f775(f302(x91521),x91522),f180(f857(x91521,a844))))),x91523)) % 186.05/186.63 [9304]~P1(f775(f775(f334(x93041),x93042),x93044))+P1(f775(f775(f334(x93041),x93042),x93043))+P1(f775(f775(f233(f857(x93041,a844)),x93044),f775(f775(f302(x93041),x93042),x93043)))+~P1(f775(f775(f233(f857(x93041,a844)),f775(f775(f3(f857(x93041,a844)),x93044),f775(f775(f302(x93041),x93042),f180(f857(x93041,a844))))),x93043)) % 186.05/186.63 [9332]P1(f775(f775(f334(x93321),x93322),x93323))+~P1(f775(f775(f232(f857(x93321,a844)),x93324),x93323))+P1(f775(f775(f233(f857(x93321,a844)),x93324),f775(f775(f302(x93321),x93322),x93323)))+~P1(f775(f775(f233(f857(x93321,a844)),f775(f775(f3(f857(x93321,a844)),x93324),f775(f775(f302(x93321),x93322),f180(f857(x93321,a844))))),x93323)) % 186.05/186.63 [9337]~P1(f775(f775(f334(x93371),x93373),x93372))+~P1(f775(f775(f233(f857(x93371,a844)),x93372),x93374))+P1(f775(f775(f233(f857(x93371,a844)),x93372),f775(f775(f302(x93371),x93373),x93374)))+~P1(f775(f775(f233(f857(x93371,a844)),f775(f775(f3(f857(x93371,a844)),x93372),f775(f775(f302(x93371),x93373),f180(f857(x93371,a844))))),x93374)) % 186.05/186.63 [9349]~P1(f775(f775(f232(f857(x93491,a844)),x93492),x93494))+~P1(f775(f775(f233(f857(x93491,a844)),x93492),x93494))+P1(f775(f775(f233(f857(x93491,a844)),x93492),f775(f775(f302(x93491),x93493),x93494)))+~P1(f775(f775(f233(f857(x93491,a844)),f775(f775(f3(f857(x93491,a844)),x93492),f775(f775(f302(x93491),x93493),f180(f857(x93491,a844))))),x93494)) % 186.05/186.63 [9676]E(f775(f775(f153(x96761),f775(f775(f153(f851(x96761)),f164(x96761,x96762)),x96763)),x96764),f775(f775(f153(x96761),f775(f775(f153(f851(x96761)),x96762),x96764)),x96763))+~P1(f775(f775(f233(a850),x96763),f775(f181(f851(f851(x96761))),f164(x96761,x96762))))+~P18(a850,f775(f142(a850),f775(f775(f143(f851(x96761),a850),f181(f851(x96761))),x96762)))+~P1(f775(f775(f233(a850),x96764),f775(f181(f851(f851(x96761))),f775(f126(f851(x96761),f775(f775(f10(a850,a844,f851(x96761)),f775(f233(a850),x96763)),f181(f851(x96761)))),x96762)))) % 186.05/186.63 [9697]~P1(f775(f775(f334(f856(a850,a850)),x96974),x96971))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x96974),x96972)),a40))+~P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x96971),x96973)),a70))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x96971),f775(f775(f302(f856(a850,a850)),x96972),x96973))),a70)) % 186.05/186.63 [9698]~P1(f775(f775(f334(f856(a850,a850)),x96984),x96981))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x96984),x96982)),a72))+~P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x96981),x96983)),a73))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x96981),f775(f775(f302(f856(a850,a850)),x96982),x96983))),a73)) % 186.05/186.63 [9710]~P1(f775(f775(f334(f856(a850,a850)),x97104),x97103))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x97101),x97104)),a40))+~P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x97102),x97103)),a41))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f775(f775(f302(f856(a850,a850)),x97101),x97102)),x97103)),a41)) % 186.05/186.63 [9711]~P1(f775(f775(f334(f856(a850,a850)),x97114),x97113))+~P1(f775(f775(f334(f856(f856(a850,a850),f856(a850,a850))),f775(f775(f241(f856(a850,a850),f856(a850,a850)),x97111),x97114)),a72))+~P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),x97112),x97113)),a71))+P1(f775(f775(f334(f856(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844))),f775(f775(f241(f857(f856(a850,a850),a844),f857(f856(a850,a850),a844)),f775(f775(f302(f856(a850,a850)),x97111),x97112)),x97113)),a71)) % 186.05/186.63 [5903]~P11(x59034,x59031)+~P1(f775(f775(x59031,x59032),x59035))+P1(f775(f775(x59031,x59032),x59033))+~P1(f775(f775(x59031,x59035),x59033)) % 186.05/186.63 [5170]~P6(x51705)+E(x51701,x51702)+~E(x51703,x51704)+~E(f775(f775(f3(x51705),x51703),x51704),f775(f775(f3(x51705),x51701),x51702)) % 186.05/186.63 [6015]~P21(x60155,x60151,x60153)+E(f775(f775(x60151,x60152),f775(x60153,x60154)),f775(x60153,x60154))+~P1(f775(f63(x60155),x60154))+~P1(f775(f775(f334(x60155),x60152),x60154)) % 186.05/186.63 [6212]~P77(x62121)+~E(f775(f775(f3(x62121),x62124),x62125),f775(f775(f3(x62121),x62122),x62123))+~P1(f775(f775(f233(x62121),x62124),x62125))+P1(f775(f775(f233(x62121),x62122),x62123)) % 186.05/186.63 [6214]~P77(x62141)+~E(f775(f775(f3(x62141),x62144),x62145),f775(f775(f3(x62141),x62142),x62143))+~P1(f775(f775(f232(x62141),x62144),x62145))+P1(f775(f775(f232(x62141),x62142),x62143)) % 186.05/186.63 [7219]~E(x72192,f775(f775(f140(x72191),x72194),x72195))+P1(f775(f775(f334(f851(x72191)),x72192),f149(x72191,x72193)))+~P1(f775(f775(f334(f851(x72191)),x72195),f149(x72191,x72193)))+~P1(f775(f775(f334(x72191),x72194),x72193)) % 186.05/186.63 [7653]~E(f775(f181(f851(x76531)),x76533),f775(f181(f851(x76532)),x76534))+~E(f775(f775(f143(f856(x76531,x76532),x76532),f250(x76531,x76532)),x76535),x76534)+~E(f775(f775(f143(f856(x76531,x76532),x76531),f240(x76531,x76532)),x76535),x76533)+E(f775(f775(f167(x76531,x76532),x76533),x76534),x76535) % 186.05/186.63 [7989]~P99(x79891)+P1(f775(f775(f233(f857(x79891,a844)),f295(x79891,x79892,x79893)),f295(x79891,x79894,x79895)))+~P1(f775(f775(f232(x79891),x79894),x79895))+P1(f775(f775(f232(x79891),x79892),x79893)) % 186.05/186.63 [8081]~P99(x80811)+P1(f775(f775(f232(f857(x80811,a844)),f295(x80811,x80812,x80813)),f295(x80811,x80814,x80815)))+~P1(f775(f775(f232(x80811),x80813),x80815))+~P1(f775(f775(f232(x80811),x80814),x80812)) % 186.05/186.63 [8199]~P100(x81991)+P1(f775(f775(f232(x81991),x81992),x81993))+P1(f775(f775(f232(x81991),x81994),x81993))+~P1(f775(f775(f232(f857(x81991,a844)),f775(f294(x81991,x81993),x81992)),f775(f294(x81991,x81994),x81995))) % 186.05/186.63 [8200]~P100(x82001)+P1(f775(f775(f232(x82001),x82002),x82003))+P1(f775(f775(f232(x82001),x82002),x82004))+~P1(f775(f775(f232(f857(x82001,a844)),f775(f294(x82001,x82003),x82002)),f775(f294(x82001,x82005),x82004))) % 186.05/186.63 [8440]~P99(x84401)+~P1(f775(f775(f233(f857(x84401,a844)),f295(x84401,x84404,x84402)),f295(x84401,x84405,x84403)))+P1(f775(f775(f232(x84401),x84402),x84403))+~P1(f775(f775(f232(x84401),x84404),x84402)) % 186.05/186.63 [8441]~P99(x84411)+~P1(f775(f775(f232(f857(x84411,a844)),f295(x84411,x84414,x84412)),f295(x84411,x84415,x84413)))+P1(f775(f775(f232(x84411),x84412),x84413))+~P1(f775(f775(f232(x84411),x84414),x84412)) % 186.05/186.63 [8442]~P99(x84421)+~P1(f775(f775(f233(f857(x84421,a844)),f295(x84421,x84423,x84424)),f295(x84421,x84422,x84425)))+P1(f775(f775(f232(x84421),x84422),x84423))+~P1(f775(f775(f232(x84421),x84423),x84424)) % 186.05/186.63 [8443]~P99(x84431)+~P1(f775(f775(f232(f857(x84431,a844)),f295(x84431,x84433,x84434)),f295(x84431,x84432,x84435)))+P1(f775(f775(f232(x84431),x84432),x84433))+~P1(f775(f775(f232(x84431),x84433),x84434)) % 186.05/186.63 [5902]~P21(x59022,x59025,x59023)+E(x59021,f180(f857(x59022,a844)))+~P1(f775(f63(x59022),x59021))+E(f775(x59023,f775(f775(f302(x59022),x59024),x59021)),f775(f775(x59025,x59024),f775(x59023,x59021))) % 186.05/186.63 [6706]~E(x67061,x67062)+~E(f775(f775(f104(f857(x67063,a844)),x67064),x67065),f180(f857(x67063,a844)))+~P1(f775(f775(f334(x67063),x67062),x67065))+~P1(f775(f775(f334(x67063),x67061),x67064)) % 186.05/186.63 [6793]~P22(x67932,x67935,x67931)+~P1(f775(f63(x67932),x67934))+E(f775(x67931,f775(f775(f302(x67932),x67933),x67934)),f775(f775(f66(x67932,x67932,x67935),x67933),x67934))+P1(f775(f775(f334(x67932),x67933),x67934)) % 186.05/186.63 [6864]~P66(x68642)+~P1(f775(f63(x68641),x68645))+E(f775(f775(f8(x68641,x68642),x68643),f775(f775(f302(x68641),x68644),x68645)),f775(f775(f82(x68642),f775(x68643,x68644)),f775(f775(f8(x68641,x68642),x68643),x68645)))+P1(f775(f775(f334(x68641),x68644),x68645)) % 186.05/186.63 [6866]~P70(x68662)+~P1(f775(f63(x68661),x68665))+E(f775(f775(f11(x68661,x68662),x68663),f775(f775(f302(x68661),x68664),x68665)),f775(f775(f83(x68662),f775(x68663,x68664)),f775(f775(f11(x68661,x68662),x68663),x68665)))+P1(f775(f775(f334(x68661),x68664),x68665)) % 186.05/186.63 [7277]~P85(x72771)+~P1(f775(f63(x72774),x72775))+~P1(f775(f775(f334(x72774),x72773),x72775))+P1(f775(f775(f279(x72771),f775(x72772,x72773)),f775(f775(f11(x72774,x72771),x72772),x72775))) % 186.05/186.63 [7390]~P22(x73902,x73905,x73901)+~P1(f775(f63(x73902),x73904))+E(f775(x73901,f775(f775(f302(x73902),x73903),x73904)),x73903)+~E(f775(f775(f3(f857(x73902,a844)),x73904),f775(f775(f302(x73902),x73903),f180(f857(x73902,a844)))),f180(f857(x73902,a844))) % 186.05/186.63 [7703]~P1(f775(x77031,x77033))+~P1(f775(f775(f187(x77032),x77033),x77035))+~P1(f775(f775(f187(f35(x77031,x77032)),x77035),x77034))+P1(f775(f775(f187(f35(x77031,x77032)),x77033),x77034)) % 186.05/186.63 [7721]~P85(x77211)+~P1(f775(f775(f279(x77211),x77212),x77214))+~P1(f775(f775(f232(a850),x77213),x77215))+P1(f775(f775(f279(x77211),f775(f775(f242(x77211),x77212),x77213)),f775(f775(f242(x77211),x77214),x77215))) % 186.05/186.63 [7755]~P7(x77551)+E(f775(f775(f43(x77551),f775(f775(f83(x77551),x77552),x77553)),f775(f775(f83(x77551),x77554),x77555)),f775(f775(f83(x77551),f775(f775(f43(x77551),x77552),x77554)),f775(f775(f43(x77551),x77553),x77555)))+~P1(f775(f775(f279(x77551),x77555),x77553))+~P1(f775(f775(f279(x77551),x77554),x77552)) % 186.05/186.63 [7759]~P80(x77591)+~P1(f775(f775(f233(x77591),x77593),x77595))+~P1(f775(f775(f233(x77591),x77592),x77594))+P1(f775(f775(f233(x77591),f775(f775(f82(x77591),x77592),x77593)),f775(f775(f82(x77591),x77594),x77595))) % 186.05/186.63 [7760]~P80(x77601)+~P1(f775(f775(f232(x77601),x77602),x77604))+~P1(f775(f775(f233(x77601),x77603),x77605))+P1(f775(f775(f233(x77601),f775(f775(f82(x77601),x77602),x77603)),f775(f775(f82(x77601),x77604),x77605))) % 186.05/186.63 [7761]~P80(x77611)+~P1(f775(f775(f232(x77611),x77613),x77615))+~P1(f775(f775(f233(x77611),x77612),x77614))+P1(f775(f775(f233(x77611),f775(f775(f82(x77611),x77612),x77613)),f775(f775(f82(x77611),x77614),x77615))) % 186.05/186.63 [7762]~P78(x77621)+~P1(f775(f775(f232(x77621),x77623),x77625))+~P1(f775(f775(f232(x77621),x77622),x77624))+P1(f775(f775(f232(x77621),f775(f775(f82(x77621),x77622),x77623)),f775(f775(f82(x77621),x77624),x77625))) % 186.05/186.63 [7763]~P100(x77631)+~P1(f775(f775(f232(x77631),x77633),x77635))+~P1(f775(f775(f232(x77631),x77632),x77634))+P1(f775(f775(f232(x77631),f775(f775(f236(x77631),x77632),x77633)),f775(f775(f236(x77631),x77634),x77635))) % 186.05/186.63 [7764]~P100(x77641)+~P1(f775(f775(f232(x77641),x77643),x77645))+~P1(f775(f775(f232(x77641),x77642),x77644))+P1(f775(f775(f232(x77641),f775(f775(f179(x77641),x77642),x77643)),f775(f775(f179(x77641),x77644),x77645))) % 186.05/186.63 [7765]~P92(x77651)+~P1(f775(f775(f232(x77651),x77653),x77655))+~P1(f775(f775(f232(x77651),x77652),x77654))+P1(f775(f775(f232(x77651),f775(f775(f103(x77651),x77652),x77653)),f775(f775(f103(x77651),x77654),x77655))) % 186.05/186.63 [7766]~P98(x77661)+~P1(f775(f775(f232(x77661),x77663),x77665))+~P1(f775(f775(f232(x77661),x77662),x77664))+P1(f775(f775(f232(x77661),f775(f775(f104(x77661),x77662),x77663)),f775(f775(f104(x77661),x77664),x77665))) % 186.05/186.63 [7767]~P85(x77671)+~P1(f775(f775(f279(x77671),x77673),x77675))+~P1(f775(f775(f279(x77671),x77672),x77674))+P1(f775(f775(f279(x77671),f775(f775(f83(x77671),x77672),x77673)),f775(f775(f83(x77671),x77674),x77675))) % 186.05/186.63 [7900]~P137(x79005)+E(x79001,x79002)+E(x79003,x79004)+~E(f775(f775(f82(x79005),f775(f775(f83(x79005),x79003),x79001)),f775(f775(f83(x79005),x79004),x79002)),f775(f775(f82(x79005),f775(f775(f83(x79005),x79003),x79002)),f775(f775(f83(x79005),x79004),x79001))) % 186.05/186.63 [8038]P31(x80381,x80382,x80383)+~P32(x80381,x80384,x80385)+~P31(x80381,x80382,f829(x80385,x80384,x80381,x80382))+~P1(f775(f775(f334(f849(x80381)),x80383),x80385)) % 186.05/186.63 [8101]~P100(x81014)+~P1(f775(f127(x81011),x81013))+P1(f775(f775(f334(x81011),x81012),f775(f158(x81011),x81013)))+P1(f775(f127(x81011),f775(f775(f138(x81011,x81014,x81015),x81012),x81013))) % 186.05/186.63 [8245]~P66(x82451)+E(f775(f775(f82(x82451),f775(f775(f8(a850,x82451),x82452),f775(f294(a850,x82453),x82454))),f775(f775(f8(a850,x82451),x82452),f775(f294(a850,x82454),x82455))),f775(f775(f8(a850,x82451),x82452),f775(f294(a850,x82453),x82455)))+~P1(f775(f775(f232(a850),x82454),x82455))+~P1(f775(f775(f232(a850),x82453),x82454)) % 186.05/186.63 [8246]~P6(x82461)+E(f775(f775(f3(x82461),f775(f775(f8(a850,x82461),x82462),f775(f294(a850,x82463),x82464))),f775(f775(f8(a850,x82461),x82462),f775(f294(a850,x82463),x82465))),f775(f775(f8(a850,x82461),x82462),f775(f294(a850,x82465),x82464)))+~P1(f775(f775(f232(a850),x82465),x82464))+~P1(f775(f775(f232(a850),x82463),x82465)) % 186.05/186.63 [8565]~P61(x85652)+E(x85651,f2(x85652))+E(x85653,f2(x85652))+E(f775(f775(f283(x85652),f775(f775(f82(x85652),f775(f775(f83(x85652),x85654),x85651)),f775(f775(f83(x85652),x85655),x85653))),f775(f775(f83(x85652),x85653),x85651)),f775(f775(f82(x85652),f775(f775(f283(x85652),x85654),x85653)),f775(f775(f283(x85652),x85655),x85651))) % 186.05/186.63 [8566]~P61(x85662)+E(x85661,f2(x85662))+E(x85663,f2(x85662))+E(f775(f775(f283(x85662),f775(f775(f3(x85662),f775(f775(f83(x85662),x85664),x85661)),f775(f775(f83(x85662),x85665),x85663))),f775(f775(f83(x85662),x85663),x85661)),f775(f775(f3(x85662),f775(f775(f283(x85662),x85664),x85663)),f775(f775(f283(x85662),x85665),x85661))) % 186.05/186.63 [8575]~E(x85752,f775(x85753,x85751))+E(x85751,f523(x85752,x85753,x85754,x85755))+~P29(x85755,x85754,x85753,f239(f857(x85755,a844)))+~P1(f775(f775(f334(x85754),x85752),f775(f303(x85755,x85754,x85753),f239(f857(x85755,a844))))) % 186.05/186.63 [8759]~P110(x87591)+~P1(f775(f775(f233(x87591),f775(f77(x87591),x87592)),x87594))+P1(f775(f775(f233(x87591),f775(f775(f83(x87591),f775(f77(x87591),x87592)),f775(f77(x87591),x87593))),f775(f775(f83(x87591),x87594),x87595)))+~P1(f775(f775(f233(x87591),f775(f77(x87591),x87593)),x87595)) % 186.05/186.63 [8773]~P32(x87731,x87735,x87734)+P31(x87731,x87732,x87733)+P1(f775(f775(f334(f849(x87731)),f829(x87734,x87735,x87731,x87732)),x87735))+~P1(f775(f775(f334(f849(x87731)),x87733),x87734)) % 186.05/186.63 [8853]~P29(x88531,x88533,x88535,x88532)+~P1(f775(f63(x88533),x88534))+P1(f775(f775(f232(a850),f775(f42(x88531),x88532)),f775(f42(x88533),x88534)))+~P1(f775(f775(f232(f857(x88533,a844)),f775(f303(x88531,x88533,x88535),x88532)),x88534)) % 186.05/186.63 [8922]~P66(x89222)+~P29(x89221,x89221,x89224,x89225)+~P1(f775(f63(x89221),x89225))+E(f775(f775(f8(x89221,x89222),f775(f75(x89221,x89222,x89221,x89223),x89224)),x89225),f775(f775(f8(x89221,x89222),x89223),f775(f303(x89221,x89221,x89224),x89225))) % 186.05/186.63 [8923]~P70(x89232)+~P29(x89231,x89231,x89234,x89235)+~P1(f775(f63(x89231),x89235))+E(f775(f775(f11(x89231,x89232),f775(f75(x89231,x89232,x89231,x89233),x89234)),x89235),f775(f775(f11(x89231,x89232),x89233),f775(f303(x89231,x89231,x89234),x89235))) % 186.05/186.63 [9035]~P36(x90351,x90352)+~P1(f775(f775(f334(x90351),x90353),x90354))+~P1(f775(f775(f334(x90351),x90355),x90354))+~P1(f775(f775(f334(f856(x90351,x90351)),f775(f775(f241(x90351,x90351),x90355),f695(x90352,x90351,x90354))),x90352)) % 186.05/186.63 [9068]~P29(x90682,x90683,x90685,x90681)+E(x90681,f180(f857(x90682,a844)))+E(f775(f303(x90683,x90682,f525(x90684,x90683,x90682,x90681)),x90684),x90681)+~P1(f775(f775(f232(f857(x90683,a844)),f775(f303(x90682,x90683,x90685),x90681)),x90684)) % 186.05/186.63 [9510]~P100(x95105)+~P9(x95105)+P1(f775(f775(f334(x95101),f390(x95102,x95103,x95101,x95104,x95105)),x95103))+~P1(f775(f775(f233(x95105),x95104),f775(f775(f46(x95101,x95105),x95103),x95102))) % 186.05/186.63 [9515]~P100(x95151)+~P9(x95151)+P1(f775(f775(f233(x95151),x95152),f775(x95153,f390(x95153,x95154,x95155,x95152,x95151))))+~P1(f775(f775(f233(x95151),x95152),f775(f775(f46(x95155,x95151),x95154),x95153))) % 186.05/186.63 [9584]~P64(x95841)+~P1(f775(f68(x95841,x95841,f83(x95841),x95842,x95843),x95845))+P1(f775(f775(f334(x95841),x95842),x95843))+P1(f775(f68(x95841,x95841,f83(x95841),x95844,f775(f775(f302(x95841),x95842),x95843)),f775(f775(f83(x95841),x95844),x95845))) % 186.05/186.63 [9793]~P66(x97932)+~P1(f775(f63(x97931),x97935))+E(f775(f775(f8(x97931,x97932),f775(f775(f9(x97931,x97932,x97932),f775(f775(f20(x97931,x97932,f857(x97932,x97932)),f775(f775(f10(a844,f857(x97932,f857(x97932,x97932)),x97931),f98(x97932)),f775(a330,x97933))),x97934)),f2(x97932))),x97935),f2(x97932))+P1(f775(f775(f334(x97931),x97933),x97935)) % 186.05/186.63 [9794]~P70(x97942)+~P1(f775(f63(x97941),x97945))+E(f775(f775(f11(x97941,x97942),f775(f775(f9(x97941,x97942,x97942),f775(f775(f20(x97941,x97942,f857(x97942,x97942)),f775(f775(f10(a844,f857(x97942,f857(x97942,x97942)),x97941),f98(x97942)),f775(a330,x97943))),x97944)),f80(x97942))),x97945),f80(x97942))+P1(f775(f775(f334(x97941),x97943),x97945)) % 186.05/186.63 [9795]~P66(x97952)+~P1(f775(f63(x97951),x97955))+E(f775(f775(f8(x97951,x97952),f775(f775(f9(x97951,x97952,x97952),f775(f775(f20(x97951,x97952,f857(x97952,x97952)),f775(f775(f10(a844,f857(x97952,f857(x97952,x97952)),x97951),f98(x97952)),f775(a330,x97953))),x97954)),f2(x97952))),x97955),f775(x97954,x97953))+~P1(f775(f775(f334(x97951),x97953),x97955)) % 186.05/186.63 [9796]~P70(x97962)+~P1(f775(f63(x97961),x97965))+E(f775(f775(f11(x97961,x97962),f775(f775(f9(x97961,x97962,x97962),f775(f775(f20(x97961,x97962,f857(x97962,x97962)),f775(f775(f10(a844,f857(x97962,f857(x97962,x97962)),x97961),f98(x97962)),f775(a330,x97963))),x97964)),f80(x97962))),x97965),f775(x97964,x97963))+~P1(f775(f775(f334(x97961),x97963),x97965)) % 186.05/186.63 [9857]~P66(x98572)+~P1(f775(f63(x98571),x98575))+E(f775(f775(f8(x98571,x98572),f775(f775(f9(x98571,x98572,x98572),f775(f775(f20(x98571,x98572,f857(x98572,x98572)),f775(f775(f10(a844,f857(x98572,f857(x98572,x98572)),x98571),f98(x98572)),f775(f775(f9(x98571,x98571,a844),a330),x98573))),x98574)),f2(x98572))),x98575),f2(x98572))+P1(f775(f775(f334(x98571),x98573),x98575)) % 186.05/186.63 [9858]~P70(x98582)+~P1(f775(f63(x98581),x98585))+E(f775(f775(f11(x98581,x98582),f775(f775(f9(x98581,x98582,x98582),f775(f775(f20(x98581,x98582,f857(x98582,x98582)),f775(f775(f10(a844,f857(x98582,f857(x98582,x98582)),x98581),f98(x98582)),f775(f775(f9(x98581,x98581,a844),a330),x98583))),x98584)),f80(x98582))),x98585),f80(x98582))+P1(f775(f775(f334(x98581),x98583),x98585)) % 186.05/186.63 [9860]~P66(x98602)+~P1(f775(f63(x98601),x98605))+E(f775(f775(f8(x98601,x98602),f775(f775(f9(x98601,x98602,x98602),f775(f775(f20(x98601,x98602,f857(x98602,x98602)),f775(f775(f10(a844,f857(x98602,f857(x98602,x98602)),x98601),f98(x98602)),f775(f775(f9(x98601,x98601,a844),a330),x98603))),x98604)),f2(x98602))),x98605),f775(x98604,x98603))+~P1(f775(f775(f334(x98601),x98603),x98605)) % 186.05/186.63 [9861]~P70(x98612)+~P1(f775(f63(x98611),x98615))+E(f775(f775(f11(x98611,x98612),f775(f775(f9(x98611,x98612,x98612),f775(f775(f20(x98611,x98612,f857(x98612,x98612)),f775(f775(f10(a844,f857(x98612,f857(x98612,x98612)),x98611),f98(x98612)),f775(f775(f9(x98611,x98611,a844),a330),x98613))),x98614)),f80(x98612))),x98615),f775(x98614,x98613))+~P1(f775(f775(f334(x98611),x98613),x98615)) % 186.05/186.63 [7758]~P6(x77582)+~P1(f775(f63(x77581),x77584))+E(f775(f775(f8(x77581,x77582),x77583),f775(f775(f3(f857(x77581,a844)),x77584),f775(f775(f302(x77581),x77585),f180(f857(x77581,a844))))),f775(f775(f8(x77581,x77582),x77583),x77584))+P1(f775(f775(f334(x77581),x77585),x77584)) % 186.05/186.63 [8251]~P121(x82512)+~P1(f775(f63(x82511),x82514))+E(f775(f775(f8(x82511,x82512),x82513),f775(f775(f3(f857(x82511,a844)),x82514),f775(f775(f302(x82511),x82515),f180(f857(x82511,a844))))),f775(f775(f3(x82512),f775(f775(f8(x82511,x82512),x82513),x82514)),f775(x82513,x82515)))+~P1(f775(f775(f334(x82511),x82515),x82514)) % 186.05/186.63 [8252]~P6(x82522)+~P1(f775(f63(x82521),x82524))+E(f775(f775(f8(x82521,x82522),x82523),f775(f775(f3(f857(x82521,a844)),x82524),f775(f775(f302(x82521),x82525),f180(f857(x82521,a844))))),f775(f775(f3(x82522),f775(f775(f8(x82521,x82522),x82523),x82524)),f775(x82523,x82525)))+~P1(f775(f775(f334(x82521),x82525),x82524)) % 186.05/186.63 [8263]~P85(x82631)+~P1(f775(f775(f232(a850),x82633),x82635))+~P1(f775(f775(f279(x82631),f775(f775(f242(x82631),x82632),x82635)),x82634))+P1(f775(f775(f279(x82631),f775(f775(f242(x82631),x82632),x82633)),x82634)) % 186.05/186.63 [8280]~P6(x82801)+~P1(f775(f63(x82802),x82804))+E(f775(f775(f3(x82801),f775(f775(f8(x82802,x82801),x82803),x82804)),f775(f775(f8(x82802,x82801),x82803),x82805)),f775(f775(f8(x82802,x82801),x82803),f775(f775(f3(f857(x82802,a844)),x82804),x82805)))+~P1(f775(f775(f232(f857(x82802,a844)),x82805),x82804)) % 186.05/186.63 [8301]P1(f775(f63(x83011),f775(x83012,x83013)))+~P1(f775(f63(x83014),x83015))+~P1(f775(f775(f334(x83014),x83013),x83015))+~P1(f775(f63(x83011),f775(f775(f46(x83014,f857(x83011,a844)),x83015),x83012))) % 186.05/186.63 [8724]~P12(x87241,x87245,x87244)+~E(f775(f277(x87241,x87241,x87244),f775(f775(f302(x87241),x87242),f180(f857(x87241,a844)))),f775(f277(x87241,x87241,x87244),f775(f775(f302(x87241),x87243),f180(f857(x87241,a844)))))+~P1(f775(f775(f334(x87241),x87243),x87245))+P1(f775(f775(f334(f856(x87241,x87241)),f775(f775(f241(x87241,x87241),x87242),x87243)),x87244)) % 186.05/186.63 [8995]~P1(f775(x89951,x89955))+P1(f775(x89951,f381(x89951,x89952,x89953,x89954)))+P1(f775(x89951,f379(x89951,x89952,x89953,x89954)))+~P1(f775(f775(f334(x89954),x89955),f775(f775(f103(f857(x89954,a844)),x89953),x89952))) % 186.05/186.63 [9156]~P1(f775(x91561,x91565))+P1(f775(x91561,f379(x91561,x91562,x91563,x91564)))+P1(f775(f775(f334(x91564),f381(x91561,x91562,x91563,x91564)),x91562))+~P1(f775(f775(f334(x91564),x91565),f775(f775(f103(f857(x91564,a844)),x91563),x91562))) % 186.05/186.63 [9157]~P1(f775(x91571,x91575))+P1(f775(x91571,f381(x91571,x91572,x91573,x91574)))+P1(f775(f775(f334(x91574),f379(x91571,x91572,x91573,x91574)),x91573))+~P1(f775(f775(f334(x91574),x91575),f775(f775(f103(f857(x91574,a844)),x91573),x91572))) % 186.05/186.63 [9161]P1(f775(x91611,x91612))+~P1(f775(x91611,f385(x91611,x91613,x91614,x91615)))+~P1(f775(x91611,f384(x91611,x91613,x91614,x91615)))+~P1(f775(f775(f334(x91615),x91612),f775(f775(f103(f857(x91615,a844)),x91614),x91613))) % 186.05/186.63 [9194]E(x91941,x91942)+~P1(f775(f775(f334(f856(x91943,x91943)),f775(f775(f241(x91943,x91943),x91941),x91942)),f300(x91943,x91945)))+P1(f775(f775(f334(x91943),x91941),x91944))+~P1(f775(f775(f232(f857(f856(x91943,x91943),a844)),x91945),f775(f775(f248(x91943,x91943),x91944),f775(f18(f857(x91943,a844),x91943),x91944)))) % 186.05/186.63 [9211]P1(f775(x92111,x92112))+~P1(f775(x92111,f384(x92111,x92114,x92115,x92113)))+P1(f775(f775(f334(x92113),f385(x92111,x92114,x92115,x92113)),x92114))+~P1(f775(f775(f334(x92113),x92112),f775(f775(f103(f857(x92113,a844)),x92115),x92114))) % 186.05/186.63 [9212]P1(f775(x92121,x92122))+~P1(f775(x92121,f385(x92121,x92124,x92125,x92123)))+P1(f775(f775(f334(x92123),f384(x92121,x92124,x92125,x92123)),x92125))+~P1(f775(f775(f334(x92123),x92122),f775(f775(f103(f857(x92123,a844)),x92125),x92124))) % 186.05/186.63 [9274]P1(f775(x92741,x92742))+P1(f775(f775(f334(x92743),f385(x92741,x92744,x92745,x92743)),x92744))+P1(f775(f775(f334(x92743),f384(x92741,x92744,x92745,x92743)),x92745))+~P1(f775(f775(f334(x92743),x92742),f775(f775(f103(f857(x92743,a844)),x92745),x92744))) % 186.05/186.63 [9276]~P1(f775(x92762,x92765))+P1(f775(f775(f334(x92761),f381(x92762,x92763,x92764,x92761)),x92763))+P1(f775(f775(f334(x92761),f379(x92762,x92763,x92764,x92761)),x92764))+~P1(f775(f775(f334(x92761),x92765),f775(f775(f103(f857(x92761,a844)),x92764),x92763))) % 186.05/186.63 [9423]~P12(x94231,x94235,x94234)+~P1(f775(f775(f334(x94231),x94233),x94235))+P1(f775(f775(f334(f856(x94231,x94231)),f775(f775(f241(x94231,x94231),x94232),x94233)),x94234))+~P1(f775(f775(f232(f857(x94231,a844)),f775(f277(x94231,x94231,x94234),f775(f775(f302(x94231),x94233),f180(f857(x94231,a844))))),f775(f277(x94231,x94231,x94234),f775(f775(f302(x94231),x94232),f180(f857(x94231,a844)))))) % 186.05/186.63 [9539]~P100(x95395)+~P9(x95395)+P1(f775(f775(f334(x95391),f662(x95392,x95393,x95394,x95391,x95395)),x95394))+~P1(f775(f775(f233(x95395),f775(f775(f47(x95391,x95395),x95394),x95393)),x95392)) % 186.05/186.63 [9571]~P67(x95715)+~P78(x95715)+P1(f775(f775(f334(x95711),f753(x95712,x95713,x95714,x95711,x95715)),f775(f158(x95711),x95714)))+P1(f775(f775(f232(x95715),f775(f155(x95715),f775(f775(f143(x95711,x95715),x95713),x95714))),f775(f155(x95715),f775(f775(f143(x95711,x95715),x95712),x95714)))) % 186.05/186.63 [9666]~P100(x96661)+~P9(x96661)+P1(f775(f775(f233(x96661),f775(x96662,f662(x96663,x96662,x96664,x96665,x96661))),x96663))+~P1(f775(f775(f233(x96661),f775(f775(f47(x96665,x96661),x96664),x96662)),x96663)) % 186.05/186.63 [9810]~P67(x98101)+~P78(x98101)+~P1(f775(f775(f232(x98101),f775(x98103,f753(x98105,x98103,x98104,x98102,x98101))),f775(x98105,f753(x98105,x98103,x98104,x98102,x98101))))+P1(f775(f775(f232(x98101),f775(f155(x98101),f775(f775(f143(x98102,x98101),x98103),x98104))),f775(f155(x98101),f775(f775(f143(x98102,x98101),x98105),x98104)))) % 186.05/186.63 [8583]~P66(x85831)+~P1(f775(f63(x85834),x85835))+~P1(f775(f775(f334(x85834),x85833),x85835))+E(f775(f775(f82(x85831),f775(x85832,x85833)),f775(f775(f8(x85834,x85831),x85832),f775(f775(f3(f857(x85834,a844)),x85835),f775(f775(f302(x85834),x85833),f180(f857(x85834,a844)))))),f775(f775(f8(x85834,x85831),x85832),x85835)) % 186.05/186.63 [8584]~P70(x85841)+~P1(f775(f63(x85844),x85845))+~P1(f775(f775(f334(x85844),x85843),x85845))+E(f775(f775(f83(x85841),f775(x85842,x85843)),f775(f775(f11(x85844,x85841),x85842),f775(f775(f3(f857(x85844,a844)),x85845),f775(f775(f302(x85844),x85843),f180(f857(x85844,a844)))))),f775(f775(f11(x85844,x85841),x85842),x85845)) % 186.05/186.63 [8637]~P22(x86371,x86374,x86375)+~P1(f775(f63(x86371),x86372))+E(f775(f775(f3(f857(x86371,a844)),x86372),f775(f775(f302(x86371),x86373),f180(f857(x86371,a844)))),f180(f857(x86371,a844)))+E(f775(f775(x86374,x86373),f775(x86375,f775(f775(f3(f857(x86371,a844)),x86372),f775(f775(f302(x86371),x86373),f180(f857(x86371,a844)))))),f775(x86375,f775(f775(f302(x86371),x86373),x86372))) % 186.05/186.63 [8970]~P66(x89701)+~P1(f775(f63(x89702),x89705))+~P1(f775(f63(x89702),x89704))+E(f775(f775(f82(x89701),f775(f775(f8(x89702,x89701),x89703),f775(f775(f103(f857(x89702,a844)),x89704),x89705))),f775(f775(f8(x89702,x89701),x89703),f775(f775(f104(f857(x89702,a844)),x89704),x89705))),f775(f775(f82(x89701),f775(f775(f8(x89702,x89701),x89703),x89704)),f775(f775(f8(x89702,x89701),x89703),x89705))) % 186.05/186.63 [8972]~P70(x89721)+~P1(f775(f63(x89722),x89725))+~P1(f775(f63(x89722),x89724))+E(f775(f775(f83(x89721),f775(f775(f11(x89722,x89721),x89723),f775(f775(f103(f857(x89722,a844)),x89724),x89725))),f775(f775(f11(x89722,x89721),x89723),f775(f775(f104(f857(x89722,a844)),x89724),x89725))),f775(f775(f83(x89721),f775(f775(f11(x89722,x89721),x89723),x89724)),f775(f775(f11(x89722,x89721),x89723),x89725))) % 186.05/186.63 [9106]~P6(x91061)+~P1(f775(f63(x91062),x91065))+~P1(f775(f63(x91062),x91064))+E(f775(f775(f3(x91061),f775(f775(f82(x91061),f775(f775(f8(x91062,x91061),x91063),x91064)),f775(f775(f8(x91062,x91061),x91063),x91065))),f775(f775(f8(x91062,x91061),x91063),f775(f775(f104(f857(x91062,a844)),x91064),x91065))),f775(f775(f8(x91062,x91061),x91063),f775(f775(f103(f857(x91062,a844)),x91064),x91065))) % 186.05/186.63 [9288]~P29(x92881,x92882,x92883,x92885)+~P29(x92881,x92882,x92883,x92884)+P29(x92881,x92882,x92883,f775(f775(f103(f857(x92881,a844)),x92884),x92885))+~E(f775(f775(f104(f857(x92882,a844)),f775(f303(x92881,x92882,x92883),f775(f775(f3(f857(x92881,a844)),x92884),x92885))),f775(f303(x92881,x92882,x92883),f775(f775(f3(f857(x92881,a844)),x92885),x92884))),f180(f857(x92882,a844))) % 186.05/186.63 [9395]E(x93951,f2(a1))+~P1(f775(f775(f233(a1),f2(a1)),x93953))+~P1(f775(f56(x93952,x93951),f775(f775(f241(a1,a1),x93954),x93955)))+P1(f775(f56(x93952,f775(f775(f83(a1),x93951),x93953)),f775(f775(f241(a1,a1),f775(f775(f43(a1),x93954),x93953)),f775(f775(f82(a1),f775(f775(f83(a1),x93951),f52(a1,x93954,x93953))),x93955)))) % 186.05/186.63 [9403]~P1(f775(f775(f233(a850),f2(a850)),x94033))+~P1(f775(f775(f233(a850),f2(a850)),x94032))+~P1(f775(f55(x94031,x94032),f775(f775(f241(a850,a850),x94034),x94035)))+P1(f775(f55(x94031,f775(f775(f83(a850),x94032),x94033)),f775(f775(f241(a850,a850),f775(f775(f43(a850),x94034),x94033)),f775(f775(f82(a850),f775(f775(f83(a850),x94032),f52(a850,x94034,x94033))),x94035)))) % 186.05/186.63 [9453]E(f775(f775(f82(a1),f363(x94531,x94532,x94533,x94534,x94535)),f364(x94531,x94532,x94533,x94534,x94535)),x94535)+~P1(f775(f775(f279(a1),x94534),x94533))+~P1(f775(f775(f279(a1),x94534),f775(f775(f82(a1),x94535),x94531)))+P1(f775(f775(f279(a1),x94534),f775(f775(f82(a1),f775(f775(f3(a1),x94535),x94533)),x94531))) % 186.05/186.63 [9454]E(f775(f775(f3(a1),f365(x94541,x94542,x94543,x94544,x94545)),f366(x94541,x94542,x94543,x94544,x94545)),x94545)+~P1(f775(f775(f279(a1),x94544),x94543))+~P1(f775(f775(f279(a1),x94544),f775(f775(f82(a1),x94545),x94541)))+P1(f775(f775(f279(a1),x94544),f775(f775(f82(a1),f775(f775(f82(a1),x94545),x94543)),x94541))) % 186.05/186.63 [9455]~P70(x94551)+~P1(f775(f63(x94552),x94555))+~P1(f775(f63(x94552),x94554))+E(f775(f775(f83(x94551),f775(f775(f775(f67(x94551,x94552,f83(x94551)),x94553),f80(x94551)),f775(f775(f103(f857(x94552,a844)),x94554),x94555))),f775(f775(f775(f67(x94551,x94552,f83(x94551)),x94553),f80(x94551)),f775(f775(f104(f857(x94552,a844)),x94554),x94555))),f775(f775(f83(x94551),f775(f775(f775(f67(x94551,x94552,f83(x94551)),x94553),f80(x94551)),x94554)),f775(f775(f775(f67(x94551,x94552,f83(x94551)),x94553),f80(x94551)),x94555))) % 186.05/186.63 [9457]~E(f775(f775(f159(x94571),x94575),x94572),f775(f775(f159(x94571),x94575),x94573))+P1(f775(f775(f334(f856(f851(x94571),f851(x94571))),f775(f775(f241(f851(x94571),f851(x94571)),x94572),x94573)),f137(x94571,x94574)))+~P1(f775(f775(f233(a850),x94575),f775(f775(f236(a850),f775(f181(f851(x94571)),x94572)),f775(f181(f851(x94571)),x94573))))+~P1(f775(f775(f334(f856(x94571,x94571)),f775(f775(f241(x94571,x94571),f775(f775(f153(x94571),x94572),x94575)),f775(f775(f153(x94571),x94573),x94575))),x94574)) % 186.05/186.63 [9466]E(f775(f775(f82(a1),f367(x94661,x94662,x94663,x94664,x94665)),f368(x94661,x94662,x94663,x94664,x94665)),x94665)+~P1(f775(f775(f279(a1),x94664),x94663))+P1(f775(f775(f279(a1),x94664),f775(f775(f82(a1),x94665),x94661)))+~P1(f775(f775(f279(a1),x94664),f775(f775(f82(a1),f775(f775(f3(a1),x94665),x94663)),x94661))) % 186.05/186.63 [9467]E(f775(f775(f3(a1),f359(x94671,x94672,x94673,x94674,x94675)),f360(x94671,x94672,x94673,x94674,x94675)),x94675)+~P1(f775(f775(f279(a1),x94674),x94673))+P1(f775(f775(f279(a1),x94674),f775(f775(f82(a1),x94675),x94671)))+~P1(f775(f775(f279(a1),x94674),f775(f775(f82(a1),f775(f775(f82(a1),x94675),x94673)),x94671))) % 186.05/186.63 [9548]~P1(f775(f775(f279(a1),x95484),x95483))+P1(f775(f775(f334(a1),f365(x95481,x95482,x95483,x95484,x95485)),x95482))+~P1(f775(f775(f279(a1),x95484),f775(f775(f82(a1),x95485),x95481)))+P1(f775(f775(f279(a1),x95484),f775(f775(f82(a1),f775(f775(f82(a1),x95485),x95483)),x95481))) % 186.05/186.63 [9549]~P1(f775(f775(f279(a1),x95494),x95493))+P1(f775(f775(f334(a1),f363(x95491,x95492,x95493,x95494,x95495)),x95492))+~P1(f775(f775(f279(a1),x95494),f775(f775(f82(a1),x95495),x95491)))+P1(f775(f775(f279(a1),x95494),f775(f775(f82(a1),f775(f775(f3(a1),x95495),x95493)),x95491))) % 186.05/186.63 [9556]~P1(f775(f775(f279(a1),x95564),x95563))+P1(f775(f775(f334(a1),f366(x95561,x95562,x95563,x95564,x95565)),f295(a1,f80(a1),x95563)))+~P1(f775(f775(f279(a1),x95564),f775(f775(f82(a1),x95565),x95561)))+P1(f775(f775(f279(a1),x95564),f775(f775(f82(a1),f775(f775(f82(a1),x95565),x95563)),x95561))) % 186.05/186.63 [9557]~P1(f775(f775(f279(a1),x95574),x95573))+P1(f775(f775(f334(a1),f364(x95571,x95572,x95573,x95574,x95575)),f295(a1,f80(a1),x95573)))+~P1(f775(f775(f279(a1),x95574),f775(f775(f82(a1),x95575),x95571)))+P1(f775(f775(f279(a1),x95574),f775(f775(f82(a1),f775(f775(f3(a1),x95575),x95573)),x95571))) % 186.05/186.63 [9558]~P2(x95585)+~P78(x95585)+P1(f775(f775(f334(x95581),f440(x95582,x95583,x95584,x95581,x95585)),x95584))+P1(f775(f775(f232(x95585),f775(f775(f8(x95581,x95585),x95583),x95584)),f775(f775(f83(x95585),f775(f102(x95585),f775(f42(x95581),x95584))),x95582))) % 186.05/186.63 [9559]~P1(f775(f775(f279(a1),x95594),x95593))+P1(f775(f775(f334(a1),f359(x95591,x95592,x95593,x95594,x95595)),x95592))+P1(f775(f775(f279(a1),x95594),f775(f775(f82(a1),x95595),x95591)))+~P1(f775(f775(f279(a1),x95594),f775(f775(f82(a1),f775(f775(f82(a1),x95595),x95593)),x95591))) % 186.05/186.63 [9560]~P1(f775(f775(f279(a1),x95604),x95603))+P1(f775(f775(f334(a1),f367(x95601,x95602,x95603,x95604,x95605)),x95602))+P1(f775(f775(f279(a1),x95604),f775(f775(f82(a1),x95605),x95601)))+~P1(f775(f775(f279(a1),x95604),f775(f775(f82(a1),f775(f775(f3(a1),x95605),x95603)),x95601))) % 186.05/186.63 [9561]~P1(f775(f775(f279(a1),x95611),x95615))+P1(f775(f775(f334(a1),f360(x95613,x95614,x95615,x95611,x95612)),f295(a1,f80(a1),x95615)))+P1(f775(f775(f279(a1),x95611),f775(f775(f82(a1),x95612),x95613)))+~P1(f775(f775(f279(a1),x95611),f775(f775(f82(a1),f775(f775(f82(a1),x95612),x95615)),x95613))) % 186.05/186.63 [9562]~P1(f775(f775(f279(a1),x95621),x95625))+P1(f775(f775(f334(a1),f368(x95623,x95624,x95625,x95621,x95622)),f295(a1,f80(a1),x95625)))+P1(f775(f775(f279(a1),x95621),f775(f775(f82(a1),x95622),x95623)))+~P1(f775(f775(f279(a1),x95621),f775(f775(f82(a1),f775(f775(f3(a1),x95622),x95625)),x95623))) % 186.05/186.63 [9726]~P2(x97261)+~P78(x97261)+~P1(f775(f775(f232(x97261),f775(x97263,f440(x97265,x97263,x97264,x97262,x97261))),x97265))+P1(f775(f775(f232(x97261),f775(f775(f8(x97262,x97261),x97263),x97264)),f775(f775(f83(x97261),f775(f102(x97261),f775(f42(x97262),x97264))),x97265))) % 186.05/186.63 [8609]E(f775(f775(f125(x86091),x86092),x86093),f775(f775(f125(x86091),x86094),x86095))+~E(f775(f775(f159(x86091),f775(f181(f851(x86091)),x86092)),x86094),x86092)+~E(f775(f775(f125(x86091),f775(f775(f128(x86091),f775(f181(f851(x86091)),x86092)),x86094)),x86095),x86093)+P1(f775(f775(f232(a850),f775(f181(f851(x86091)),x86094)),f775(f181(f851(x86091)),x86092))) % 186.05/186.63 [8722]E(f775(f775(f125(x87221),x87222),x87223),f775(f775(f125(x87221),x87224),x87225))+~E(f775(f775(f159(x87221),f775(f181(f851(x87221)),x87222)),x87224),x87222)+~E(x87223,f775(f775(f125(x87221),f775(f775(f128(x87221),f775(f181(f851(x87221)),x87222)),x87224)),x87225))+~P1(f775(f775(f232(a850),f775(f181(f851(x87221)),x87222)),f775(f181(f851(x87221)),x87224))) % 186.05/186.63 [9878]~P1(f775(x98785,x98784))+~P1(f775(f63(x98782),f775(f256(x98782),x98785)))+P1(f775(f63(x98781),f775(f256(x98781),f775(f775(f9(x98781,x98782,a844),x98783),x98784))))+~P1(f775(f63(x98781),f775(f256(x98781),f775(f775(f10(f857(x98782,a844),a844,x98781),f89(x98782)),f775(f775(f10(f857(x98782,a844),f857(x98782,a844),x98781),f775(f20(x98782,a844,a844),f775(f775(f10(a844,f857(a844,a844),x98782),a331),x98785))),x98783))))) % 186.05/186.63 [7904]~P39(x79042,x79043,x79044,x79046)+~P39(f35(x79041,x79042),x79046,x79044,x79045)+P39(f35(x79041,x79042),x79043,x79044,x79045)+~P1(f775(x79041,x79043)) % 186.05/186.63 [8416]~P23(x84165,x84161,x84166,x84162)+E(f775(f75(x84161,x84161,x84161,f775(x84162,x84163)),f775(x84162,x84164)),f775(f75(x84161,x84161,x84161,f775(x84162,x84164)),f775(x84162,x84163)))+~P1(f775(f63(x84165),x84164))+~P1(f775(f63(x84165),x84163)) % 186.05/186.63 [7814]~P29(x78141,x78142,x78144,x78143)+~E(f775(x78144,x78146),x78145)+E(f775(f79(x78141,x78142,x78143,x78144),x78145),x78146)+~P1(f775(f775(f334(x78141),x78146),x78143)) % 186.05/186.63 [8007]~P24(x80076,x80071,x80074,x80072)+E(f775(f75(x80071,x80071,x80071,f775(x80072,x80073)),f775(x80074,x80075)),f775(x80072,x80073))+~P1(f775(f63(x80076),x80073))+~P1(f775(f775(f334(x80076),x80075),x80073)) % 186.05/186.63 [9144]~P23(x91443,x91441,x91446,x91442)+E(f775(f75(x91441,x91441,x91441,f775(x91442,f775(f775(f3(f857(x91443,a844)),x91444),f775(f775(f302(x91443),x91445),f180(f857(x91443,a844)))))),f775(x91446,x91445)),f775(x91442,x91444))+~P1(f775(f63(x91443),x91444))+~P1(f775(f775(f334(x91443),x91445),x91444)) % 186.05/186.63 [6871]~P7(x68711)+~E(f52(x68711,x68713,x68714),f52(x68711,x68716,x68714))+~E(f52(x68711,x68712,x68714),f52(x68711,x68715,x68714))+E(f52(x68711,f775(f775(f82(x68711),x68712),x68713),x68714),f52(x68711,f775(f775(f82(x68711),x68715),x68716),x68714)) % 186.05/186.63 [6872]~P7(x68721)+~E(f52(x68721,x68723,x68724),f52(x68721,x68726,x68724))+~E(f52(x68721,x68722,x68724),f52(x68721,x68725,x68724))+E(f52(x68721,f775(f775(f83(x68721),x68722),x68723),x68724),f52(x68721,f775(f775(f83(x68721),x68725),x68726),x68724)) % 186.05/186.63 [6873]~P8(x68731)+~E(f52(x68731,x68733,x68734),f52(x68731,x68736,x68734))+~E(f52(x68731,x68732,x68734),f52(x68731,x68735,x68734))+E(f52(x68731,f775(f775(f3(x68731),x68732),x68733),x68734),f52(x68731,f775(f775(f3(x68731),x68735),x68736),x68734)) % 186.05/186.63 [7705]~P20(x77051,x77052,x77053)+~P1(f775(f63(x77051),x77056))+E(f775(f775(f66(x77051,x77052,x77053),x77054),f775(f775(f302(x77051),x77055),x77056)),f775(f775(f66(x77051,x77052,x77053),f775(f775(x77053,x77055),x77054)),x77056))+P1(f775(f775(f334(x77051),x77055),x77056)) % 186.05/186.63 [7772]~P9(x77721)+P1(f775(f775(f232(x77721),x77722),f775(x77723,x77724)))+~P1(f775(f775(f334(x77725),x77724),x77726))+~P1(f775(f775(f232(x77721),x77722),f775(f775(f47(x77725,x77721),x77726),x77723))) % 186.05/186.63 [7932]~P20(x79321,x79322,x79323)+~P1(f775(f63(x79321),x79326))+E(f775(f775(f66(x79321,x79322,x79323),x79324),f775(f775(f302(x79321),x79325),x79326)),f775(f775(x79323,x79325),f775(f775(f66(x79321,x79322,x79323),x79324),x79326)))+P1(f775(f775(f334(x79321),x79325),x79326)) % 186.05/186.63 [8023]~P100(x80233)+~P1(f775(x80232,x80235))+~P18(x80233,f775(f775(f143(x80231,x80233),x80234),x80236))+E(f775(f126(x80231,x80232),f775(f775(f138(x80231,x80233,x80234),x80235),x80236)),f775(f775(f138(x80231,x80233,x80234),x80235),f775(f126(x80231,x80232),x80236))) % 186.05/186.63 [8046]E(x80461,x80462)+E(x80463,f2(a1))+~P1(f775(f56(x80464,x80463),f775(f775(f241(a1,a1),x80465),x80462)))+~P1(f775(f56(x80464,x80463),f775(f775(f241(a1,a1),x80466),x80461))) % 186.05/186.63 [8047]E(x80471,x80472)+E(x80473,f2(a1))+~P1(f775(f56(x80474,x80473),f775(f775(f241(a1,a1),x80472),x80475)))+~P1(f775(f56(x80474,x80473),f775(f775(f241(a1,a1),x80471),x80476))) % 186.05/186.63 [8069]~P23(x80692,x80695,x80696,x80691)+~P1(f775(f63(x80692),x80694))+E(f775(x80691,f775(f775(f302(x80692),x80693),x80694)),f775(f75(x80695,x80695,x80695,f775(x80691,x80694)),f775(x80696,x80693)))+P1(f775(f775(f334(x80692),x80693),x80694)) % 186.05/186.63 [8283]~P24(x82835,x82831,x82836,x82832)+E(f775(f75(x82831,x82831,x82831,f775(x82832,x82833)),f775(x82832,x82834)),f775(x82832,x82833))+~P1(f775(f63(x82835),x82833))+~P1(f775(f775(f232(f857(x82835,a844)),x82834),x82833)) % 186.05/186.63 [9334]~P29(x93341,x93342,x93344,x93343)+~P1(f775(f775(f334(x93342),x93345),f775(f303(x93341,x93342,x93344),x93343)))+P1(f775(f775(f334(x93341),f775(f79(x93341,x93342,x93343,x93344),x93345)),x93346))+~P1(f775(f775(f232(f857(x93341,a844)),x93343),x93346)) % 186.05/186.63 [9677]~P66(x96772)+~E(f495(x96771,x96773,x96775,x96776,x96774,x96772),f496(x96771,x96773,x96775,x96776,x96774,x96772))+~P1(f775(f63(x96774),x96776))+E(f775(f775(f8(x96771,x96772),x96773),f775(f303(x96774,x96771,x96775),x96776)),f775(f775(f8(x96774,x96772),f775(f75(x96771,x96772,x96774,x96773),x96775)),x96776)) % 186.05/186.63 [9706]~P66(x97066)+E(f775(x97061,f495(x97062,x97063,x97061,x97064,x97065,x97066)),f775(x97061,f496(x97062,x97063,x97061,x97064,x97065,x97066)))+E(f775(f775(f8(x97062,x97066),x97063),f775(f303(x97065,x97062,x97061),x97064)),f775(f775(f8(x97065,x97066),f775(f75(x97062,x97066,x97065,x97063),x97061)),x97064))+~P1(f775(f63(x97065),x97064)) % 186.05/186.63 [9760]~P66(x97602)+~E(f775(x97603,f775(x97605,f496(x97601,x97603,x97605,x97606,x97604,x97602))),f2(x97602))+~P1(f775(f63(x97604),x97606))+E(f775(f775(f8(x97601,x97602),x97603),f775(f303(x97604,x97601,x97605),x97606)),f775(f775(f8(x97604,x97602),f775(f75(x97601,x97602,x97604,x97603),x97605)),x97606)) % 186.05/186.63 [9820]~P66(x98202)+~P1(f775(f63(x98204),x98206))+E(f775(f775(f8(x98201,x98202),x98203),f775(f303(x98204,x98201,x98205),x98206)),f775(f775(f8(x98204,x98202),f775(f75(x98201,x98202,x98204,x98203),x98205)),x98206))+P1(f775(f775(f334(x98204),f496(x98201,x98203,x98205,x98206,x98204,x98202)),x98206)) % 186.05/186.63 [9821]~P66(x98212)+~P1(f775(f63(x98214),x98216))+E(f775(f775(f8(x98211,x98212),x98213),f775(f303(x98214,x98211,x98215),x98216)),f775(f775(f8(x98214,x98212),f775(f75(x98211,x98212,x98214,x98213),x98215)),x98216))+P1(f775(f775(f334(x98214),f495(x98211,x98213,x98215,x98216,x98214,x98212)),x98216)) % 186.05/186.63 [9943]~P70(x99431)+~P1(f775(f63(x99432),x99436))+E(f775(f775(f775(f67(x99431,x99432,f83(x99431)),f775(f775(f20(x99432,f857(x99433,a844),x99431),f775(f775(f9(x99432,x99431,f857(f857(x99433,a844),x99431)),f775(f775(f10(f857(x99433,x99431),f857(x99431,f857(f857(x99433,a844),x99431)),x99432),f67(x99431,x99433,f83(x99431))),x99434)),f80(x99431))),x99435)),f80(x99431)),x99436),f775(f775(f775(f67(x99431,f856(x99432,x99433),f83(x99431)),f775(f251(x99432,x99433,x99431),x99434)),f80(x99431)),f775(f775(f248(x99432,x99433),x99436),x99435)))+P1(f775(f775(f334(x99432),f564(x99434,x99435,x99433,x99436,x99432,x99431)),x99436)) % 186.05/186.63 [9959]~P70(x99591)+~P1(f775(f63(x99592),x99596))+E(f775(f775(f775(f67(x99591,x99592,f83(x99591)),f775(f775(f20(x99592,f857(x99593,a844),x99591),f775(f775(f9(x99592,x99591,f857(f857(x99593,a844),x99591)),f775(f775(f10(f857(x99593,x99591),f857(x99591,f857(f857(x99593,a844),x99591)),x99592),f67(x99591,x99593,f83(x99591))),x99594)),f80(x99591))),x99595)),f80(x99591)),x99596),f775(f775(f775(f67(x99591,f856(x99592,x99593),f83(x99591)),f775(f251(x99592,x99593,x99591),x99594)),f80(x99591)),f775(f775(f248(x99592,x99593),x99596),x99595)))+~P1(f775(f63(x99593),f775(x99595,f564(x99594,x99595,x99593,x99596,x99592,x99591)))) % 186.05/186.63 [8198]~P24(x81982,x81985,x81986,x81981)+~P1(f775(f63(x81982),x81984))+~P1(f775(f63(x81982),x81983))+E(f775(x81981,f775(f775(f103(f857(x81982,a844)),x81983),x81984)),f775(f75(x81985,x81985,x81985,f775(x81981,x81983)),f775(x81981,x81984))) % 186.05/186.63 [8418]~P9(x84181)+P1(f775(f775(f232(x84181),f775(x84182,x84183)),x84184))+~P1(f775(f775(f334(x84185),x84183),x84186))+~P1(f775(f775(f232(x84181),f775(f775(f46(x84185,x84181),x84186),x84182)),x84184)) % 186.05/186.63 [8792]~P29(x87922,x87921,x87923,x87926)+E(f775(f775(f3(f857(x87921,a844)),f775(f303(x87922,x87921,x87923),x87924)),f775(f303(x87922,x87921,x87923),x87925)),f775(f303(x87922,x87921,x87923),f775(f775(f3(f857(x87922,a844)),x87924),x87925)))+~P1(f775(f775(f232(f857(x87922,a844)),x87925),x87926))+~P1(f775(f775(f232(f857(x87922,a844)),x87924),x87926)) % 186.05/186.63 [8793]~P29(x87932,x87931,x87933,x87936)+E(f775(f775(f104(f857(x87931,a844)),f775(f303(x87932,x87931,x87933),x87934)),f775(f303(x87932,x87931,x87933),x87935)),f775(f303(x87932,x87931,x87933),f775(f775(f104(f857(x87932,a844)),x87934),x87935)))+~P1(f775(f775(f232(f857(x87932,a844)),x87935),x87936))+~P1(f775(f775(f232(f857(x87932,a844)),x87934),x87936)) % 186.05/186.63 [9037]E(x90371,x90372)+~P53(x90373,x90374,x90375)+~P1(f775(f775(f334(f856(x90373,x90374)),f775(f775(f241(x90373,x90374),x90376),x90372)),x90375))+~P1(f775(f775(f334(f856(x90373,x90374)),f775(f775(f241(x90373,x90374),x90376),x90371)),x90375)) % 186.05/186.63 [9617]~P66(x96171)+~P1(f775(f63(x96173),x96176))+~P1(f775(f63(x96172),x96175))+E(f775(f775(f82(x96171),f775(f775(f8(x96172,x96171),f775(f75(f858(x96172,x96173),x96171,x96172,x96174),f304(x96172,x96173))),x96175)),f775(f775(f8(x96173,x96171),f775(f75(f858(x96172,x96173),x96171,x96173,x96174),f313(x96173,x96172))),x96176)),f775(f775(f8(f858(x96172,x96173),x96171),x96174),f314(x96172,x96173,x96175,x96176))) % 186.05/186.63 [9756]~P64(x97561)+~E(f775(x97563,f631(x97564,x97566,x97563,x97565,x97562,x97561)),f775(x97566,f631(x97564,x97566,x97563,x97565,x97562,x97561)))+~P1(f775(f63(x97562),x97565))+E(f775(f775(f775(f67(x97561,x97562,f83(x97561)),x97563),x97564),x97565),f775(f775(f775(f67(x97561,x97562,f83(x97561)),x97566),x97564),x97565)) % 186.05/186.63 [9817]~P64(x98171)+~P1(f775(f63(x98172),x98175))+E(f775(f775(f775(f67(x98171,x98172,f83(x98171)),x98173),x98174),x98175),f775(f775(f775(f67(x98171,x98172,f83(x98171)),x98176),x98174),x98175))+P1(f775(f775(f334(x98172),f631(x98174,x98173,x98176,x98175,x98172,x98171)),x98175)) % 186.05/186.63 [8622]~P64(x86221)+~P1(f775(f63(x86222),x86226))+P1(f775(f775(f334(x86222),x86225),x86226))+E(f775(f775(f775(f67(x86221,x86222,f83(x86221)),x86223),x86224),f775(f775(f302(x86222),x86225),x86226)),f775(f775(f83(x86221),f775(x86223,x86225)),f775(f775(f775(f67(x86221,x86222,f83(x86221)),x86223),x86224),x86226))) % 186.05/186.63 [8666]~P12(x86661,x86666,x86663)+~P16(x86661,f857(x86662,a844),x86663,x86665)+~P1(f775(f775(f334(x86661),x86664),x86666))+E(f775(f775(f46(x86661,f857(x86662,a844)),f775(f277(x86661,x86661,x86663),f775(f775(f302(x86661),x86664),f180(f857(x86661,a844))))),x86665),f775(x86665,x86664)) % 186.05/186.63 [8774]~P20(x87743,x87744,x87741)+~P1(f775(f63(x87743),x87746))+~P1(f775(f775(f334(x87743),x87742),x87746))+E(f775(f775(x87741,x87742),f775(f775(f66(x87743,x87744,x87741),x87745),f775(f775(f3(f857(x87743,a844)),x87746),f775(f775(f302(x87743),x87742),f180(f857(x87743,a844)))))),f775(f775(f66(x87743,x87744,x87741),x87745),x87746)) % 186.05/186.63 [9047]~P23(x90473,x90471,x90476,x90472)+~P1(f775(f63(x90473),x90475))+~P1(f775(f63(x90473),x90474))+E(f775(f75(x90471,x90471,x90471,f775(x90472,f775(f775(f103(f857(x90473,a844)),x90474),x90475))),f775(x90472,f775(f775(f104(f857(x90473,a844)),x90474),x90475))),f775(f75(x90471,x90471,x90471,f775(x90472,x90474)),f775(x90472,x90475))) % 186.05/186.63 [9354]~E(x93543,f775(f775(f148(x93541,x93542),x93545),x93546))+P1(f775(f775(f334(f856(f851(x93541),f851(x93541))),f775(f775(f241(f851(x93541),f851(x93541)),x93542),x93543)),f146(x93541,x93544)))+~P1(f775(f775(f233(a850),x93545),f775(f181(f851(x93541)),x93542)))+~P1(f775(f775(f334(f856(x93541,x93541)),f775(f775(f241(x93541,x93541),f775(f775(f153(x93541),x93542),x93545)),x93546)),x93544)) % 186.05/186.63 [9836]~P66(x98362)+~P1(f775(f63(x98361),x98366))+P1(f775(f775(f334(x98361),f563(x98364,x98365,x98363,x98366,x98361,x98362)),x98366))+E(f775(f775(f8(x98361,x98362),f775(f775(f20(x98361,f857(x98363,a844),x98362),f775(f775(f10(f857(x98363,x98362),f857(f857(x98363,a844),x98362),x98361),f8(x98363,x98362)),x98364)),x98365)),x98366),f775(f775(f8(f856(x98361,x98363),x98362),f775(f251(x98361,x98363,x98362),x98364)),f775(f775(f248(x98361,x98363),x98366),x98365))) % 186.05/186.63 [9837]~P70(x98372)+~P1(f775(f63(x98371),x98376))+P1(f775(f775(f334(x98371),f556(x98374,x98375,x98373,x98376,x98371,x98372)),x98376))+E(f775(f775(f11(x98371,x98372),f775(f775(f20(x98371,f857(x98373,a844),x98372),f775(f775(f10(f857(x98373,x98372),f857(f857(x98373,a844),x98372),x98371),f11(x98373,x98372)),x98374)),x98375)),x98376),f775(f775(f11(f856(x98371,x98373),x98372),f775(f251(x98371,x98373,x98372),x98374)),f775(f775(f248(x98371,x98373),x98376),x98375))) % 186.05/186.63 [9876]~P66(x98762)+~P1(f775(f63(x98761),x98766))+~P1(f775(f63(x98763),f775(x98765,f563(x98764,x98765,x98763,x98766,x98761,x98762))))+E(f775(f775(f8(x98761,x98762),f775(f775(f20(x98761,f857(x98763,a844),x98762),f775(f775(f10(f857(x98763,x98762),f857(f857(x98763,a844),x98762),x98761),f8(x98763,x98762)),x98764)),x98765)),x98766),f775(f775(f8(f856(x98761,x98763),x98762),f775(f251(x98761,x98763,x98762),x98764)),f775(f775(f248(x98761,x98763),x98766),x98765))) % 186.05/186.63 [9877]~P70(x98772)+~P1(f775(f63(x98771),x98776))+~P1(f775(f63(x98773),f775(x98775,f556(x98774,x98775,x98773,x98776,x98771,x98772))))+E(f775(f775(f11(x98771,x98772),f775(f775(f20(x98771,f857(x98773,a844),x98772),f775(f775(f10(f857(x98773,x98772),f857(f857(x98773,a844),x98772),x98771),f11(x98773,x98772)),x98774)),x98775)),x98776),f775(f775(f11(f856(x98771,x98773),x98772),f775(f251(x98771,x98773,x98772),x98774)),f775(f775(f248(x98771,x98773),x98776),x98775))) % 186.05/186.63 [9859]~P70(x98592)+~P1(f775(f63(x98591),x98596))+P1(f775(f775(f334(x98591),x98593),x98596))+E(f775(f775(f11(x98591,x98592),f775(f775(f9(x98591,x98592,x98592),f775(f775(f20(x98591,x98592,f857(x98592,x98592)),f775(f775(f10(a844,f857(x98592,f857(x98592,x98592)),x98591),f98(x98592)),f775(f775(f9(x98591,x98591,a844),a330),x98593))),x98594)),x98595)),x98596),f775(f775(f242(x98592),x98595),f775(f42(x98591),x98596))) % 186.05/186.63 [9864]~P70(x98642)+~P1(f775(f63(x98641),x98646))+~P1(f775(f775(f334(x98641),x98643),x98646))+E(f775(f775(f11(x98641,x98642),f775(f775(f9(x98641,x98642,x98642),f775(f775(f20(x98641,x98642,f857(x98642,x98642)),f775(f775(f10(a844,f857(x98642,f857(x98642,x98642)),x98641),f98(x98642)),f775(f775(f9(x98641,x98641,a844),a330),x98643))),x98644)),x98645)),x98646),f775(f775(f83(x98642),f775(x98644,x98643)),f775(f775(f242(x98642),x98645),f775(f775(f3(a850),f775(f42(x98641),x98646)),f80(a850))))) % 186.05/186.63 [9930]~P1(f775(f63(x99301),x99305))+~P1(f775(f63(x99302),x99303))+P1(f775(f775(f334(x99302),f586(x99306,x99304,x99303,x99302,x99305,x99301)),x99303))+E(f775(f775(f8(x99301,a850),f775(f775(f10(f857(x99302,a844),a850,x99301),f42(x99302)),f775(f775(f10(f857(x99302,a844),f857(x99302,a844),x99301),f256(x99302)),f775(f775(f10(f857(x99302,a844),f857(x99302,a844),x99301),f775(f20(x99302,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99302),a331),f775(f775(f9(x99302,f857(x99302,a844),a844),f334(x99302)),x99303)))),x99304)))),x99305),f775(f775(f83(a850),x99306),f775(f42(x99302),x99303))) % 186.05/186.63 [9931]~P1(f775(f63(x99311),x99315))+~P1(f775(f63(x99312),x99313))+P1(f775(f775(f334(x99312),f587(x99316,x99314,x99313,x99312,x99315,x99311)),x99313))+E(f775(f775(f8(x99311,a850),f775(f775(f10(f857(x99312,a844),a850,x99311),f42(x99312)),f775(f775(f10(f857(x99312,a844),f857(x99312,a844),x99311),f256(x99312)),f775(f775(f10(f857(x99312,a844),f857(x99312,a844),x99311),f775(f20(x99312,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99312),a331),f775(f775(f9(x99312,f857(x99312,a844),a844),f334(x99312)),x99313)))),x99314)))),x99315),f775(f775(f8(x99312,a850),x99316),x99313)) % 186.05/186.63 [9965]~P1(f775(f63(x99652),x99653))+~P1(f775(f63(x99651),x99655))+~E(f775(f42(x99651),f775(f256(x99651),f775(f775(f20(x99651,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99651),a331),f775(f775(f9(x99651,f857(x99651,a844),a844),f334(x99651)),x99655))),f775(f775(f9(x99651,x99652,a844),x99654),f586(x99656,x99654,x99653,x99652,x99655,x99651))))),x99656)+E(f775(f775(f8(x99651,a850),f775(f775(f10(f857(x99652,a844),a850,x99651),f42(x99652)),f775(f775(f10(f857(x99652,a844),f857(x99652,a844),x99651),f256(x99652)),f775(f775(f10(f857(x99652,a844),f857(x99652,a844),x99651),f775(f20(x99652,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99652),a331),f775(f775(f9(x99652,f857(x99652,a844),a844),f334(x99652)),x99653)))),x99654)))),x99655),f775(f775(f83(a850),x99656),f775(f42(x99652),x99653))) % 186.05/186.63 [9967]~P1(f775(f63(x99672),x99673))+~P1(f775(f63(x99671),x99675))+~E(f775(f42(x99671),f775(f256(x99671),f775(f775(f20(x99671,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99671),a331),f775(f775(f9(x99671,f857(x99671,a844),a844),f334(x99671)),x99675))),f775(f775(f9(x99671,x99672,a844),x99674),f587(x99676,x99674,x99673,x99672,x99675,x99671))))),f775(x99676,f587(x99676,x99674,x99673,x99672,x99675,x99671)))+E(f775(f775(f8(x99671,a850),f775(f775(f10(f857(x99672,a844),a850,x99671),f42(x99672)),f775(f775(f10(f857(x99672,a844),f857(x99672,a844),x99671),f256(x99672)),f775(f775(f10(f857(x99672,a844),f857(x99672,a844),x99671),f775(f20(x99672,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99672),a331),f775(f775(f9(x99672,f857(x99672,a844),a844),f334(x99672)),x99673)))),x99674)))),x99675),f775(f775(f8(x99672,a850),x99676),x99673)) % 186.05/186.63 [9616]E(x96161,x96162)+~P20(x96163,x96164,x96165)+~P1(f775(f68(x96163,x96164,x96165,x96166,x96167),x96162))+~P1(f775(f68(x96163,x96164,x96165,x96166,x96167),x96161)) % 186.05/186.63 [9426]P1(f775(x94261,x94262))+~P1(f775(f775(f334(x94267),x94262),f775(x94266,x94264)))+~P1(f775(x94261,f387(x94261,x94266,x94265,x94263,x94267)))+~P1(f775(f775(f334(x94263),x94264),x94265)) % 186.05/186.63 [9851]~P20(x98517,x98516,x98511)+E(f775(f775(x98511,x98512),f664(x98512,x98513,x98514,x98515,x98511,x98516,x98517)),x98513)+~P1(f775(f68(x98517,x98516,x98511,x98515,x98514),x98513))+~P1(f775(f775(f334(x98517),x98512),x98514)) % 186.05/186.63 [9915]~P20(x99151,x99152,x99153)+~P1(f775(f68(x99151,x99152,x99153,x99154,x99155),x99157))+P1(f775(f68(x99151,x99152,x99153,x99154,f775(f775(f3(f857(x99151,a844)),x99155),f775(f775(f302(x99151),x99156),f180(f857(x99151,a844))))),f664(x99156,x99157,x99155,x99154,x99153,x99152,x99151)))+~P1(f775(f775(f334(x99151),x99156),x99155)) % 186.05/186.63 [9330]~P64(x93301)+~P29(x93305,x93302,x93306,x93307)+~P1(f775(f63(x93305),x93307))+E(f775(f775(f775(f67(x93301,x93302,f83(x93301)),x93303),x93304),f775(f303(x93305,x93302,x93306),x93307)),f775(f775(f775(f67(x93301,x93305,f83(x93301)),f775(f75(x93302,x93301,x93305,x93303),x93306)),x93304),x93307)) % 186.05/186.63 [9448]~E(f775(f775(f302(x94481),x94485),x94486),f775(f775(f302(x94481),x94482),x94483))+~P1(f775(f68(x94481,x94481,x94484,x94482,x94483),x94487))+P1(f775(f775(f334(x94481),x94482),x94483))+P1(f775(f64(x94481,x94484,f775(f775(f302(x94481),x94485),x94486)),x94487)) % 186.05/186.63 [9527]P1(f775(x95271,x95272))+~P1(f775(f775(f334(x95273),x95272),f775(x95274,x95277)))+~P1(f775(f775(f334(x95276),x95277),x95275))+P1(f775(f775(f334(x95273),f387(x95271,x95274,x95275,x95276,x95273)),f775(f775(f46(x95276,f857(x95273,a844)),x95275),x95274))) % 186.05/186.63 [9540]~P29(x95402,x95401,x95405,x95404)+~P29(x95401,x95403,x95406,f775(f303(x95402,x95401,x95405),x95404))+E(f775(f775(f75(x95401,x95402,x95403,f79(x95402,x95401,x95404,x95405)),f79(x95401,x95403,f775(f303(x95402,x95401,x95405),x95404),x95406)),x95407),f775(f79(x95402,x95403,x95404,f775(f75(x95401,x95403,x95402,x95406),x95405)),x95407))+~P1(f775(f775(f334(x95403),x95407),f775(f303(x95401,x95403,x95406),f775(f303(x95402,x95401,x95405),x95404)))) % 186.05/186.63 [9852]~P20(x98527,x98526,x98521)+E(f775(f775(x98521,x98522),f692(x98523,x98524,x98522,x98525,x98521,x98526,x98527)),x98523)+P1(f775(f775(f334(x98527),x98522),x98524))+~P1(f775(f68(x98527,x98526,x98521,x98525,f775(f775(f302(x98527),x98522),x98524)),x98523)) % 186.05/186.63 [9914]~P20(x99141,x99144,x99145)+P1(f775(f68(x99141,x99144,x99145,x99146,x99143),f692(x99147,x99143,x99142,x99146,x99145,x99144,x99141)))+P1(f775(f775(f334(x99141),x99142),x99143))+~P1(f775(f68(x99141,x99144,x99145,x99146,f775(f775(f302(x99141),x99142),x99143)),x99147)) % 186.05/186.63 [9599]E(x95991,f2(a1))+~P1(f775(f56(x95993,x95991),f775(f775(f241(a1,a1),x95995),x95997)))+~P1(f775(f56(x95992,x95991),f775(f775(f241(a1,a1),x95994),x95996)))+P1(f775(f56(f775(f775(f82(a1),x95992),x95993),x95991),f775(f775(f241(a1,a1),f775(f775(f82(a1),f775(f775(f82(a1),x95994),x95995)),f775(f775(f43(a1),f775(f775(f82(a1),x95996),x95997)),x95991))),f52(a1,f775(f775(f82(a1),x95996),x95997),x95991)))) % 186.05/186.63 [9601]~P1(f775(f775(f233(a850),f2(a850)),x96013))+~P1(f775(f55(x96012,x96013),f775(f775(f241(a850,a850),x96015),x96017)))+~P1(f775(f55(x96011,x96013),f775(f775(f241(a850,a850),x96014),x96016)))+P1(f775(f55(f775(f775(f82(a850),x96011),x96012),x96013),f775(f775(f241(a850,a850),f775(f775(f82(a850),f775(f775(f82(a850),x96014),x96015)),f775(f775(f43(a850),f775(f775(f82(a850),x96016),x96017)),x96013))),f52(a850,f775(f775(f82(a850),x96016),x96017),x96013)))) % 186.05/186.63 [9964]~P66(x99642)+~P1(f775(f63(x99643),x99645))+~P1(f775(f63(x99641),x99647))+E(f775(f775(f8(x99641,x99642),f775(f775(f20(x99641,f857(x99643,a844),x99642),f775(f775(f10(f857(x99643,x99642),f857(f857(x99643,a844),x99642),x99641),f8(x99643,x99642)),x99644)),f775(f775(f10(f857(x99643,a844),f857(x99643,a844),x99641),f256(x99643)),f775(f775(f10(f857(x99643,a844),f857(x99643,a844),x99641),f775(f20(x99643,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99643),a331),f775(f775(f9(x99643,f857(x99643,a844),a844),f334(x99643)),x99645)))),x99646)))),x99647),f775(f775(f8(x99643,x99642),f775(f775(f20(x99643,f857(x99641,a844),x99642),f775(f775(f10(f857(x99641,x99642),f857(f857(x99641,a844),x99642),x99643),f8(x99641,x99642)),f775(f9(x99641,x99643,x99642),x99644))),f775(f775(f10(f857(x99641,a844),f857(x99641,a844),x99643),f256(x99641)),f775(f775(f10(f857(x99641,a844),f857(x99641,a844),x99643),f775(f20(x99641,a844,a844),f775(f775(f10(a844,f857(a844,a844),x99641),a331),f775(f775(f9(x99641,f857(x99641,a844),a844),f334(x99641)),x99647)))),f775(f9(x99641,x99643,a844),x99646))))),x99645)) % 186.05/186.63 [9486]~P26(x94867,x94866,x94861,x94868,x94862,x94864)+E(f775(f775(x94861,f775(x94862,x94863)),f775(x94864,x94865)),f775(x94864,x94865))+~P1(f775(f63(x94866),x94865))+~P1(f775(f775(f334(x94866),x94863),x94865)) % 186.05/186.63 [9490]~P17(x94906,x94901,x94902,x94908,x94903,x94904)+~P12(x94906,x94907,x94908)+P16(x94901,x94902,x94903,f775(x94904,x94905))+~P1(f775(f775(f334(x94906),x94905),x94907)) % 186.05/186.63 [7732]~P39(x77324,x77325,x77326,x77323)+~P31(x77328,x77326,f775(f775(f775(f93(x77328),x77327),x77324),x77321))+P1(f775(f775(x77321,x77322),x77323))+~P1(f775(f775(x77327,x77322),x77325)) % 186.05/186.63 [9134]~P23(x91347,x91341,x91348,x91343)+~P1(f775(f63(x91347),x91345))+~P1(f775(f63(x91347),x91344))+E(f775(f75(x91341,x91341,x91342,f775(x91343,x91344)),f775(f75(x91341,x91341,x91342,f775(x91343,x91345)),x91346)),f775(f75(x91341,x91341,x91342,f775(x91343,x91345)),f775(f75(x91341,x91341,x91342,f775(x91343,x91344)),x91346))) % 186.05/186.63 [9201]~P29(x92012,x92012,x92015,x92016)+~P25(x92013,x92012,x92017,x92018,x92011)+~P1(f775(f63(x92012),x92016))+E(f775(f775(x92011,f775(f75(x92012,x92013,x92012,x92014),x92015)),x92016),f775(f775(x92011,x92014),f775(f303(x92012,x92012,x92015),x92016))) % 186.05/186.63 [9488]~P27(x94887,x94882,x94885,x94888,x94886,x94881)+~P1(f775(f63(x94882),x94884))+E(f775(x94881,f775(f775(f302(x94882),x94883),x94884)),f775(f775(x94885,f775(x94886,x94883)),f775(x94881,x94884)))+P1(f775(f775(f334(x94882),x94883),x94884)) % 186.05/186.63 [9495]~P26(x94956,x94955,x94951,x94957,x94958,x94952)+E(f775(f775(x94951,f775(x94952,x94953)),f775(x94952,x94954)),f775(x94952,x94954))+~P1(f775(f63(x94955),x94954))+~P1(f775(f775(f232(f857(x94955,a844)),x94953),x94954)) % 186.05/186.63 [9121]P1(f775(f775(f334(f856(f851(x91211),f851(x91211))),f775(f775(f241(f851(x91211),f851(x91211)),x91212),x91213)),f146(x91211,x91214)))+~E(x91213,f775(f775(f125(x91211),x91215),f775(f775(f140(x91211),x91216),x91217)))+~E(x91212,f775(f775(f125(x91211),x91215),f775(f775(f140(x91211),x91218),x91217)))+~P1(f775(f775(f334(f856(x91211,x91211)),f775(f775(f241(x91211,x91211),x91218),x91216)),x91214)) % 186.05/186.63 [9491]~P26(x94916,x94912,x94915,x94917,x94918,x94911)+~P1(f775(f63(x94912),x94914))+~P1(f775(f63(x94912),x94913))+E(f775(x94911,f775(f775(f103(f857(x94912,a844)),x94913),x94914)),f775(f775(x94915,f775(x94911,x94913)),f775(x94911,x94914))) % 186.05/186.63 [10004]~P29(x100044,x100042,x100045,x100048)+E(f775(f775(f47(x100041,f857(x100042,a844)),x100043),f775(f775(f10(f857(x100044,a844),f857(x100042,a844),x100041),f303(x100044,x100042,x100045)),x100046)),f775(f303(x100044,x100042,x100045),f775(f775(f47(x100041,f857(x100044,a844)),x100043),x100046)))+~P1(f775(f775(f334(x100041),x100047),x100043))+P1(f775(f775(f334(x100041),f679(x100047,x100046,x100043,x100041,x100048,x100045,x100042,x100044)),x100043)) % 186.05/186.63 [10022]~P29(x100224,x100222,x100225,x100227)+E(f775(f775(f47(x100221,f857(x100222,a844)),x100223),f775(f775(f10(f857(x100224,a844),f857(x100222,a844),x100221),f303(x100224,x100222,x100225)),x100226)),f775(f303(x100224,x100222,x100225),f775(f775(f47(x100221,f857(x100224,a844)),x100223),x100226)))+~P1(f775(f775(f334(x100221),x100228),x100223))+~P1(f775(f775(f232(f857(x100224,a844)),f775(x100226,f679(x100228,x100226,x100223,x100221,x100227,x100225,x100222,x100224))),x100227)) % 186.05/186.63 [9545]~P27(x95457,x95455,x95451,x95458,x95452,x95454)+~P1(f775(f63(x95455),x95456))+~P1(f775(f775(f334(x95455),x95453),x95456))+E(f775(f775(x95451,f775(x95452,x95453)),f775(x95454,f775(f775(f3(f857(x95455,a844)),x95456),f775(f775(f302(x95455),x95453),f180(f857(x95455,a844)))))),f775(x95454,x95456)) % 186.05/186.63 [9554]~P27(x95546,x95543,x95541,x95547,x95548,x95542)+~P1(f775(f63(x95543),x95545))+~P1(f775(f63(x95543),x95544))+E(f775(f775(x95541,f775(x95542,f775(f775(f103(f857(x95543,a844)),x95544),x95545))),f775(x95542,f775(f775(f104(f857(x95543,a844)),x95544),x95545))),f775(f775(x95541,f775(x95542,x95544)),f775(x95542,x95545))) % 186.05/186.63 [9636]P41(x96361,x96362,x96363,x96364,x96365,f775(f775(x96363,x96366),x96367))+~P41(x96361,x96362,x96363,x96364,f775(f775(f3(f857(x96361,a844)),x96365),f775(f775(f302(x96361),x96368),f180(f857(x96361,a844)))),x96369)+~E(f775(f775(x96363,x96366),x96367),f775(f775(x96363,x96368),x96369))+~P1(f775(f775(f334(x96361),x96368),x96365)) % 186.05/186.63 [10033]P28(x100331,x100332,f775(f775(f302(f849(x100331)),f775(f775(f775(f93(x100331),f775(x100333,f426(x100334,x100335,x100336,x100337,x100333,x100332,x100331,x100338,x100339))),f775(x100337,f426(x100334,x100335,x100336,x100337,x100333,x100332,x100331,x100338,x100339))),f775(x100336,f426(x100334,x100335,x100336,x100337,x100333,x100332,x100331,x100338,x100339)))),f180(f857(f849(x100331),a844))))+~P1(f775(f63(x100339),x100338))+~P28(x100331,x100332,f775(f303(x100339,f849(x100331),f775(f775(f20(x100339,f857(x100331,f857(a847,a844)),f849(x100331)),f775(f775(f20(x100339,a845,f857(f857(x100331,f857(a847,a844)),f849(x100331))),f775(f775(f10(f857(x100331,f857(a847,a844)),f857(a845,f857(f857(x100331,f857(a847,a844)),f849(x100331))),x100339),f93(x100331)),x100333)),x100337)),x100336)),x100338))+P28(x100331,x100332,f775(f303(x100339,f849(x100331),f775(f775(f20(x100339,f857(x100331,f857(a847,a844)),f849(x100331)),f775(f775(f20(x100339,a845,f857(f857(x100331,f857(a847,a844)),f849(x100331))),f775(f775(f10(f857(x100331,f857(a847,a844)),f857(a845,f857(f857(x100331,f857(a847,a844)),f849(x100331))),x100339),f93(x100331)),x100335)),x100337)),x100334)),x100338)) % 186.05/186.63 [10034]~P28(x100341,x100342,f775(f775(f302(f849(x100341)),f775(f775(f775(f93(x100341),f775(x100344,f426(x100346,x100344,x100348,x100345,x100349,x100342,x100341,x100347,x100343))),f775(x100345,f426(x100346,x100344,x100348,x100345,x100349,x100342,x100341,x100347,x100343))),f775(x100346,f426(x100346,x100344,x100348,x100345,x100349,x100342,x100341,x100347,x100343)))),f180(f857(f849(x100341),a844))))+~P1(f775(f63(x100343),x100347))+~P28(x100341,x100342,f775(f303(x100343,f849(x100341),f775(f775(f20(x100343,f857(x100341,f857(a847,a844)),f849(x100341)),f775(f775(f20(x100343,a845,f857(f857(x100341,f857(a847,a844)),f849(x100341))),f775(f775(f10(f857(x100341,f857(a847,a844)),f857(a845,f857(f857(x100341,f857(a847,a844)),f849(x100341))),x100343),f93(x100341)),x100349)),x100345)),x100348)),x100347))+P28(x100341,x100342,f775(f303(x100343,f849(x100341),f775(f775(f20(x100343,f857(x100341,f857(a847,a844)),f849(x100341)),f775(f775(f20(x100343,a845,f857(f857(x100341,f857(a847,a844)),f849(x100341))),f775(f775(f10(f857(x100341,f857(a847,a844)),f857(a845,f857(f857(x100341,f857(a847,a844)),f849(x100341))),x100343),f93(x100341)),x100344)),x100345)),x100346)),x100347)) % 186.05/186.63 [9578]~P17(x95786,x95787,x95788,x95789,x957810,x95781)+E(f775(f775(x95781,x95782),x95783),f775(f775(x95781,x95784),x95785))+~P1(f775(f775(f334(f856(x95787,x95787)),f775(f775(f241(x95787,x95787),x95783),x95785)),x957810))+~P1(f775(f775(f334(f856(x95786,x95786)),f775(f775(f241(x95786,x95786),x95782),x95784)),x95789)) % 186.05/186.63 [6800]E(x68001,x68002)+~P1(f775(f775(f232(a1),f2(a1)),x68002))+~P1(f775(f775(f232(a1),f2(a1)),x68001))+~P1(f775(f775(f279(a1),x68002),x68001))+~P1(f775(f775(f279(a1),x68001),x68002)) % 186.05/186.63 [9203]~P93(x92032)+E(x92031,f180(f857(x92032,a844)))+~P1(f775(f63(x92032),x92031))+P1(f775(f775(f334(x92032),f15(x92032,x92031)),x92031))+~P1(f775(f775(f334(x92032),f775(f775(f103(x92032),f443(x92031,x92032)),f444(x92031,x92032))),f775(f775(f302(x92032),f443(x92031,x92032)),f775(f775(f302(x92032),f444(x92031,x92032)),f180(f857(x92032,a844)))))) % 186.05/186.63 [9206]~P93(x92062)+E(x92061,f180(f857(x92062,a844)))+~P1(f775(f63(x92062),x92061))+P1(f775(f775(f334(x92062),f12(x92062,x92061)),x92061))+~P1(f775(f775(f334(x92062),f775(f775(f104(x92062),f516(x92061,x92062)),f518(x92061,x92062))),f775(f775(f302(x92062),f516(x92061,x92062)),f775(f775(f302(x92062),f518(x92061,x92062)),f180(f857(x92062,a844)))))) % 186.05/186.63 [9234]~P64(x92342)+E(x92341,f180(f857(x92342,a844)))+~P1(f775(f63(x92342),x92341))+P1(f775(f775(f334(x92342),f775(f65(x92342,f83(x92342)),x92341)),x92341))+~P1(f775(f775(f334(x92342),f775(f775(f83(x92342),f565(x92341,x92342)),f566(x92341,x92342))),f775(f775(f302(x92342),f565(x92341,x92342)),f775(f775(f302(x92342),f566(x92341,x92342)),f180(f857(x92342,a844)))))) % 186.05/186.63 [9240]~P100(x92402)+E(x92401,f180(f857(x92402,a844)))+~P1(f775(f63(x92402),x92401))+P1(f775(f775(f334(x92402),f13(x92402,f179(x92402),x92401)),x92401))+~P1(f775(f775(f334(x92402),f775(f775(f179(x92402),f452(x92401,x92402)),f455(x92401,x92402))),f775(f775(f302(x92402),f452(x92401,x92402)),f775(f775(f302(x92402),f455(x92401,x92402)),f180(f857(x92402,a844)))))) % 186.05/186.63 [9241]~P100(x92412)+E(x92411,f180(f857(x92412,a844)))+~P1(f775(f63(x92412),x92411))+P1(f775(f775(f334(x92412),f14(x92412,f236(x92412),x92411)),x92411))+~P1(f775(f775(f334(x92412),f775(f775(f236(x92412),f456(x92411,x92412)),f457(x92411,x92412))),f775(f775(f302(x92412),f456(x92411,x92412)),f775(f775(f302(x92412),f457(x92411,x92412)),f180(f857(x92412,a844)))))) % 186.05/186.63 [6412]~P81(x64122)+E(x64121,f2(x64122))+~E(f775(f775(f82(x64122),x64123),x64121),f2(x64122))+~P1(f775(f775(f232(x64122),f2(x64122)),x64123))+~P1(f775(f775(f232(x64122),f2(x64122)),x64121)) % 186.05/186.63 [6413]~P81(x64132)+E(x64131,f2(x64132))+~E(f775(f775(f82(x64132),x64131),x64133),f2(x64132))+~P1(f775(f775(f232(x64132),f2(x64132)),x64133))+~P1(f775(f775(f232(x64132),f2(x64132)),x64131)) % 186.05/186.63 [7133]~P100(x71331)+E(f17(x71331,x71332),x71333)+~P1(f775(f63(x71331),x71332))+~P1(f775(f775(f232(x71331),x71333),f630(x71333,x71332,x71331)))+~P1(f775(f775(f334(x71331),x71333),x71332)) % 186.05/186.63 [7168]~P100(x71681)+~P18(x71681,x71682)+~P18(x71681,x71683)+P18(x71681,f775(f775(f125(x71681),x71682),x71683))+P1(f775(f775(f334(x71681),f765(x71683,x71682,x71681)),f775(f158(x71681),x71682))) % 186.05/186.63 [7169]~P100(x71691)+~P18(x71691,x71692)+~P18(x71691,x71693)+P18(x71691,f775(f775(f125(x71691),x71692),x71693))+P1(f775(f775(f334(x71691),f766(x71693,x71692,x71691)),f775(f158(x71691),x71693))) % 186.05/186.63 [7235]~P100(x72351)+E(f16(x72351,x72352),x72353)+~P1(f775(f63(x72351),x72352))+P1(f775(f775(f334(x72351),f633(x72353,x72352,x72351)),x72352))+~P1(f775(f775(f334(x72351),x72353),x72352)) % 186.05/186.63 [7236]~P100(x72361)+E(f17(x72361,x72362),x72363)+~P1(f775(f63(x72361),x72362))+P1(f775(f775(f334(x72361),f630(x72363,x72362,x72361)),x72362))+~P1(f775(f775(f334(x72361),x72363),x72362)) % 186.05/186.63 [7835]~P100(x78351)+E(f16(x78351,x78352),x78353)+~P1(f775(f63(x78351),x78352))+~P1(f775(f775(f334(x78351),x78353),x78352))+~P1(f775(f775(f232(x78351),f633(x78353,x78352,x78351)),x78353)) % 186.05/186.63 [8149]~P100(x81491)+~P18(x81491,x81492)+~P18(x81491,x81493)+P18(x81491,f775(f775(f125(x81491),x81492),x81493))+~P1(f775(f775(f232(x81491),f765(x81493,x81492,x81491)),f766(x81493,x81492,x81491))) % 186.05/186.63 [8878]~P93(x88782)+E(x88781,f180(f857(x88782,a844)))+~E(f775(f775(f103(x88782),f775(x88783,f474(x88781,x88783,x88782))),f775(x88783,f477(x88781,x88783,x88782))),f775(x88783,f775(f775(f103(x88782),f474(x88781,x88783,x88782)),f477(x88781,x88783,x88782))))+E(f15(x88782,f775(f303(x88782,x88782,x88783),x88781)),f775(x88783,f15(x88782,x88781)))+~P1(f775(f63(x88782),x88781)) % 186.05/186.63 [8879]~P100(x88792)+E(x88791,f180(f857(x88792,a844)))+~E(f775(f775(f179(x88792),f775(x88793,f465(x88791,x88793,x88792))),f775(x88793,f470(x88791,x88793,x88792))),f775(x88793,f775(f775(f179(x88792),f465(x88791,x88793,x88792)),f470(x88791,x88793,x88792))))+E(f16(x88792,f775(f303(x88792,x88792,x88793),x88791)),f775(x88793,f16(x88792,x88791)))+~P1(f775(f63(x88792),x88791)) % 186.05/186.63 [8880]~P100(x88802)+E(x88801,f180(f857(x88802,a844)))+~E(f775(f775(f236(x88802),f775(x88803,f475(x88801,x88803,x88802))),f775(x88803,f476(x88801,x88803,x88802))),f775(x88803,f775(f775(f236(x88802),f475(x88801,x88803,x88802)),f476(x88801,x88803,x88802))))+E(f17(x88802,f775(f303(x88802,x88802,x88803),x88801)),f775(x88803,f17(x88802,x88801)))+~P1(f775(f63(x88802),x88801)) % 186.05/186.63 [8881]~P93(x88812)+E(x88811,f180(f857(x88812,a844)))+~E(f775(f775(f104(x88812),f775(x88813,f530(x88811,x88813,x88812))),f775(x88813,f532(x88811,x88813,x88812))),f775(x88813,f775(f775(f104(x88812),f530(x88811,x88813,x88812)),f532(x88811,x88813,x88812))))+E(f12(x88812,f775(f303(x88812,x88812,x88813),x88811)),f775(x88813,f12(x88812,x88811)))+~P1(f775(f63(x88812),x88811)) % 186.05/186.63 [8945]~P100(x89452)+E(x89451,f180(f857(x89452,a844)))+~E(f775(f775(f179(x89452),f775(x89453,f466(x89451,x89453,x89452))),f775(x89453,f467(x89451,x89453,x89452))),f775(x89453,f775(f775(f179(x89452),f466(x89451,x89453,x89452)),f467(x89451,x89453,x89452))))+E(f13(x89452,f179(x89452),f775(f303(x89452,x89452,x89453),x89451)),f775(x89453,f13(x89452,f179(x89452),x89451)))+~P1(f775(f63(x89452),x89451)) % 186.05/186.63 [8946]~P100(x89462)+E(x89461,f180(f857(x89462,a844)))+~E(f775(f775(f236(x89462),f775(x89463,f468(x89461,x89463,x89462))),f775(x89463,f469(x89461,x89463,x89462))),f775(x89463,f775(f775(f236(x89462),f468(x89461,x89463,x89462)),f469(x89461,x89463,x89462))))+E(f14(x89462,f236(x89462),f775(f303(x89462,x89462,x89463),x89461)),f775(x89463,f14(x89462,f236(x89462),x89461)))+~P1(f775(f63(x89462),x89461)) % 186.05/186.63 [6429]~P64(x64292)+E(x64291,f180(f857(x64292,a844)))+~P1(f775(f63(x64292),x64291))+E(f775(f65(x64292,f83(x64292)),f775(f775(f302(x64292),x64293),x64291)),f775(f775(f83(x64292),x64293),f775(f65(x64292,f83(x64292)),x64291)))+P1(f775(f775(f334(x64292),x64293),x64291)) % 186.05/186.63 [6971]~P100(x69712)+E(f775(f775(f236(x69712),f17(x69712,x69711)),f17(x69712,x69713)),f17(x69712,x69713))+E(x69711,f180(f857(x69712,a844)))+~P1(f775(f63(x69712),x69713))+~P1(f775(f775(f232(f857(x69712,a844)),x69711),x69713)) % 186.05/186.63 [6972]~P100(x69722)+E(f775(f775(f179(x69722),f16(x69722,x69721)),f16(x69722,x69723)),f16(x69722,x69723))+E(x69721,f180(f857(x69722,a844)))+~P1(f775(f63(x69722),x69723))+~P1(f775(f775(f232(f857(x69722,a844)),x69721),x69723)) % 186.05/186.63 [6973]~P93(x69732)+E(f775(f775(f103(x69732),f15(x69732,x69731)),f15(x69732,x69733)),f15(x69732,x69733))+E(x69731,f180(f857(x69732,a844)))+~P1(f775(f63(x69732),x69733))+~P1(f775(f775(f232(f857(x69732,a844)),x69731),x69733)) % 186.05/186.63 [6974]~P93(x69742)+E(f775(f775(f104(x69742),f12(x69742,x69741)),f12(x69742,x69743)),f12(x69742,x69743))+E(x69741,f180(f857(x69742,a844)))+~P1(f775(f63(x69742),x69743))+~P1(f775(f775(f232(f857(x69742,a844)),x69741),x69743)) % 186.05/186.63 [7291]~P100(x72912)+E(x72911,f180(f857(x72912,a844)))+~P1(f775(f63(x72912),x72913))+P1(f775(f775(f232(x72912),f16(x72912,x72911)),f16(x72912,x72913)))+~P1(f775(f775(f232(f857(x72912,a844)),x72911),x72913)) % 186.05/186.63 [7292]~P100(x72922)+E(x72921,f180(f857(x72922,a844)))+~P1(f775(f63(x72922),x72923))+P1(f775(f775(f232(x72922),f17(x72922,x72923)),f17(x72922,x72921)))+~P1(f775(f775(f232(f857(x72922,a844)),x72921),x72923)) % 186.05/186.63 [7354]~P93(x73541)+E(f15(x73541,x73542),x73543)+~P1(f775(f63(x73541),x73542))+~E(f775(f775(f3(f857(x73541,a844)),x73542),f775(f775(f302(x73541),x73543),f180(f857(x73541,a844)))),f180(f857(x73541,a844)))+~P1(f775(f775(f334(x73541),x73543),x73542)) % 186.05/186.63 [7355]~P100(x73551)+E(f16(x73551,x73552),x73553)+~P1(f775(f63(x73551),x73552))+~E(f775(f775(f3(f857(x73551,a844)),x73552),f775(f775(f302(x73551),x73553),f180(f857(x73551,a844)))),f180(f857(x73551,a844)))+~P1(f775(f775(f334(x73551),x73553),x73552)) % 186.05/186.63 [7356]~P100(x73561)+E(f17(x73561,x73562),x73563)+~P1(f775(f63(x73561),x73562))+~E(f775(f775(f3(f857(x73561,a844)),x73562),f775(f775(f302(x73561),x73563),f180(f857(x73561,a844)))),f180(f857(x73561,a844)))+~P1(f775(f775(f334(x73561),x73563),x73562)) % 186.05/186.63 [7357]~P93(x73571)+E(f12(x73571,x73572),x73573)+~P1(f775(f63(x73571),x73572))+~E(f775(f775(f3(f857(x73571,a844)),x73572),f775(f775(f302(x73571),x73573),f180(f857(x73571,a844)))),f180(f857(x73571,a844)))+~P1(f775(f775(f334(x73571),x73573),x73572)) % 186.05/186.63 [7457]~P100(x74571)+E(f13(x74571,f179(x74571),x74572),x74573)+~P1(f775(f63(x74571),x74572))+~E(f775(f775(f3(f857(x74571,a844)),x74572),f775(f775(f302(x74571),x74573),f180(f857(x74571,a844)))),f180(f857(x74571,a844)))+~P1(f775(f775(f334(x74571),x74573),x74572)) % 186.05/186.63 [7458]~P100(x74581)+E(f14(x74581,f236(x74581),x74582),x74583)+~P1(f775(f63(x74581),x74582))+~E(f775(f775(f3(f857(x74581,a844)),x74582),f775(f775(f302(x74581),x74583),f180(f857(x74581,a844)))),f180(f857(x74581,a844)))+~P1(f775(f775(f334(x74581),x74583),x74582)) % 186.05/186.63 [7495]~P100(x74952)+E(x74951,f180(f857(x74952,a844)))+~P1(f775(f63(x74952),x74951))+~P1(f775(f775(f233(x74952),x74953),f547(x74953,x74951,x74952)))+P1(f775(f775(f233(x74952),x74953),f775(f65(x74952,f236(x74952)),x74951))) % 186.05/186.63 [7496]~P100(x74962)+E(x74961,f180(f857(x74962,a844)))+~P1(f775(f63(x74962),x74961))+~P1(f775(f775(f232(x74962),x74963),f548(x74963,x74961,x74962)))+P1(f775(f775(f232(x74962),x74963),f775(f65(x74962,f236(x74962)),x74961))) % 186.05/186.63 [7497]~P98(x74972)+E(x74971,f180(f857(x74972,a844)))+~P1(f775(f63(x74972),x74971))+~P1(f775(f775(f232(x74972),x74973),f549(x74973,x74971,x74972)))+P1(f775(f775(f232(x74972),x74973),f775(f65(x74972,f104(x74972)),x74971))) % 186.05/186.63 [7585]~P98(x75852)+E(x75851,f180(f857(x75852,a844)))+~P1(f775(f63(x75852),x75851))+P1(f775(f775(f334(x75852),f549(x75853,x75851,x75852)),x75851))+P1(f775(f775(f232(x75852),x75853),f775(f65(x75852,f104(x75852)),x75851))) % 186.05/186.63 [7586]~P100(x75862)+E(x75861,f180(f857(x75862,a844)))+~P1(f775(f63(x75862),x75861))+P1(f775(f775(f334(x75862),f548(x75863,x75861,x75862)),x75861))+P1(f775(f775(f232(x75862),x75863),f775(f65(x75862,f236(x75862)),x75861))) % 186.05/186.63 [7587]~P100(x75872)+E(x75871,f180(f857(x75872,a844)))+~P1(f775(f63(x75872),x75871))+P1(f775(f775(f334(x75872),f547(x75873,x75871,x75872)),x75871))+P1(f775(f775(f233(x75872),x75873),f775(f65(x75872,f236(x75872)),x75871))) % 186.05/186.63 [7707]~P100(x77072)+E(x77071,f180(f857(x77072,a844)))+E(f775(f775(f236(x77072),f14(x77072,f236(x77072),x77071)),f14(x77072,f236(x77072),x77073)),f14(x77072,f236(x77072),x77073))+~P1(f775(f63(x77072),x77073))+~P1(f775(f775(f232(f857(x77072,a844)),x77071),x77073)) % 186.05/186.63 [7708]~P100(x77082)+E(x77081,f180(f857(x77082,a844)))+E(f775(f775(f179(x77082),f13(x77082,f179(x77082),x77081)),f13(x77082,f179(x77082),x77083)),f13(x77082,f179(x77082),x77083))+~P1(f775(f63(x77082),x77083))+~P1(f775(f775(f232(f857(x77082,a844)),x77081),x77083)) % 186.05/186.63 [7910]~E(f676(x79101,x79103,x79102),f677(x79101,x79103,x79102))+~E(f775(f42(x79102),f678(x79101,x79103,x79102)),x79101)+E(f775(f775(f83(a850),x79101),f775(f42(f857(x79102,a844)),x79103)),f775(f42(x79102),f44(f857(x79102,a844),x79103)))+~P1(f775(f63(x79102),f44(f857(x79102,a844),x79103)))+~P1(f775(f63(f857(x79102,a844)),x79103)) % 186.05/186.63 [8085]~P100(x80852)+E(x80851,f180(f857(x80852,a844)))+~P1(f775(f63(x80852),x80853))+P1(f775(f775(f232(x80852),f775(f65(x80852,f236(x80852)),x80853)),f775(f65(x80852,f236(x80852)),x80851)))+~P1(f775(f775(f232(f857(x80852,a844)),x80851),x80853)) % 186.05/186.63 [8389]~E(f676(x83891,x83893,x83892),f677(x83891,x83893,x83892))+E(f775(f775(f83(a850),x83891),f775(f42(f857(x83892,a844)),x83893)),f775(f42(x83892),f44(f857(x83892,a844),x83893)))+P1(f775(f775(f334(f857(x83892,a844)),f678(x83891,x83893,x83892)),x83893))+~P1(f775(f63(x83892),f44(f857(x83892,a844),x83893)))+~P1(f775(f63(f857(x83892,a844)),x83893)) % 186.05/186.63 [8413]~E(f775(f42(x84132),f678(x84131,x84133,x84132)),x84131)+E(f775(f775(f83(a850),x84131),f775(f42(f857(x84132,a844)),x84133)),f775(f42(x84132),f44(f857(x84132,a844),x84133)))+P1(f775(f775(f334(f857(x84132,a844)),f677(x84131,x84133,x84132)),x84133))+~P1(f775(f63(x84132),f44(f857(x84132,a844),x84133)))+~P1(f775(f63(f857(x84132,a844)),x84133)) % 186.05/186.63 [8414]~E(f775(f42(x84142),f678(x84141,x84143,x84142)),x84141)+E(f775(f775(f83(a850),x84141),f775(f42(f857(x84142,a844)),x84143)),f775(f42(x84142),f44(f857(x84142,a844),x84143)))+P1(f775(f775(f334(f857(x84142,a844)),f676(x84141,x84143,x84142)),x84143))+~P1(f775(f63(x84142),f44(f857(x84142,a844),x84143)))+~P1(f775(f63(f857(x84142,a844)),x84143)) % 186.05/186.63 [8444]~E(f775(f42(x84442),f678(x84441,x84443,x84442)),x84441)+~E(f775(f775(f104(f857(x84442,a844)),f677(x84441,x84443,x84442)),f676(x84441,x84443,x84442)),f180(f857(x84442,a844)))+E(f775(f775(f83(a850),x84441),f775(f42(f857(x84442,a844)),x84443)),f775(f42(x84442),f44(f857(x84442,a844),x84443)))+~P1(f775(f63(f857(x84442,a844)),x84443))+~P1(f775(f63(x84442),f44(f857(x84442,a844),x84443))) % 186.05/186.63 [8670]E(f775(f775(f83(a850),x86701),f775(f42(f857(x86702,a844)),x86703)),f775(f42(x86702),f44(f857(x86702,a844),x86703)))+P1(f775(f775(f334(f857(x86702,a844)),f678(x86701,x86703,x86702)),x86703))+P1(f775(f775(f334(f857(x86702,a844)),f677(x86701,x86703,x86702)),x86703))+~P1(f775(f63(f857(x86702,a844)),x86703))+~P1(f775(f63(x86702),f44(f857(x86702,a844),x86703))) % 186.05/186.63 [8671]E(f775(f775(f83(a850),x86711),f775(f42(f857(x86712,a844)),x86713)),f775(f42(x86712),f44(f857(x86712,a844),x86713)))+P1(f775(f775(f334(f857(x86712,a844)),f678(x86711,x86713,x86712)),x86713))+P1(f775(f775(f334(f857(x86712,a844)),f676(x86711,x86713,x86712)),x86713))+~P1(f775(f63(f857(x86712,a844)),x86713))+~P1(f775(f63(x86712),f44(f857(x86712,a844),x86713))) % 186.05/186.63 [8696]~E(f775(f775(f104(f857(x86962,a844)),f677(x86961,x86963,x86962)),f676(x86961,x86963,x86962)),f180(f857(x86962,a844)))+E(f775(f775(f83(a850),x86961),f775(f42(f857(x86962,a844)),x86963)),f775(f42(x86962),f44(f857(x86962,a844),x86963)))+~P1(f775(f63(f857(x86962,a844)),x86963))+P1(f775(f775(f334(f857(x86962,a844)),f678(x86961,x86963,x86962)),x86963))+~P1(f775(f63(x86962),f44(f857(x86962,a844),x86963))) % 186.05/186.63 [8924]~P91(x89242)+E(x89241,f180(f857(x89242,a844)))+~E(f775(f775(f83(x89242),f775(x89243,f567(x89241,x89243,x89242))),f775(x89243,f568(x89241,x89243,x89242))),f775(x89243,f775(f775(f83(x89242),f567(x89241,x89243,x89242)),f568(x89241,x89243,x89242))))+~P1(f775(f63(x89242),x89241))+E(f775(f65(x89242,f83(x89242)),f775(f303(x89242,x89242,x89243),x89241)),f775(x89243,f775(f65(x89242,f83(x89242)),x89241))) % 186.05/186.63 [9791]P1(f775(f775(x97911,x97912),x97913))+P1(f775(f775(f233(a1),f827(x97911,x97913,x97912)),f828(x97911,x97913,x97912)))+P1(f775(f775(f232(a1),f828(x97911,x97913,x97912)),f2(a1)))+P1(f775(f775(x97911,f827(x97911,x97913,x97912)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f828(x97911,x97913,x97912))))+~P1(f775(f321(f856(a1,a1),a62),f775(f775(f241(a1,a1),x97912),x97913))) % 186.05/186.63 [9797]P1(f775(f775(x97971,x97972),x97973))+P1(f775(f775(f232(a1),f826(x97971,x97973,x97972)),f2(a1)))+P1(f775(f775(x97971,f825(x97971,x97973,x97972)),f775(f775(f83(a1),f775(f106(a1),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f826(x97971,x97973,x97972))))+P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),f825(x97971,x97973,x97972)),f826(x97971,x97973,x97972))))+~P1(f775(f321(f856(a1,a1),a59),f775(f775(f241(a1,a1),x97972),x97973))) % 186.05/186.63 [7880]~P110(x78801)+~P1(f775(f775(f232(x78801),x78802),f80(x78801)))+~P1(f775(f775(f232(x78801),f2(x78801)),x78802))+~P1(f775(f775(f232(x78801),f2(x78801)),x78803))+P1(f775(f775(f232(x78801),f775(f775(f83(x78801),x78802),x78803)),x78803)) % 186.05/186.63 [7881]~P110(x78811)+~P1(f775(f775(f232(x78811),x78813),f80(x78811)))+~P1(f775(f775(f232(x78811),f2(x78811)),x78813))+~P1(f775(f775(f232(x78811),f2(x78811)),x78812))+P1(f775(f775(f232(x78811),f775(f775(f83(x78811),x78812),x78813)),x78812)) % 186.05/186.63 [8230]~P100(x82302)+E(x82301,f180(f857(x82302,a844)))+~P1(f775(f63(x82302),x82301))+P1(f775(f775(f334(x82302),f552(x82303,x82301,x82302)),x82301))+~P1(f775(f775(f232(x82302),f775(f65(x82302,f236(x82302)),x82301)),x82303)) % 186.05/186.63 [8231]~P100(x82312)+E(x82311,f180(f857(x82312,a844)))+~P1(f775(f63(x82312),x82311))+P1(f775(f775(f334(x82312),f553(x82313,x82311,x82312)),x82311))+~P1(f775(f775(f233(x82312),f775(f65(x82312,f236(x82312)),x82311)),x82313)) % 186.05/186.63 [8232]~P100(x82322)+E(x82321,f180(f857(x82322,a844)))+~P1(f775(f63(x82322),x82321))+P1(f775(f775(f233(x82322),f553(x82323,x82321,x82322)),x82323))+~P1(f775(f775(f233(x82322),f775(f65(x82322,f236(x82322)),x82321)),x82323)) % 186.05/186.63 [8233]~P100(x82332)+E(x82331,f180(f857(x82332,a844)))+~P1(f775(f63(x82332),x82331))+P1(f775(f775(f232(x82332),f552(x82333,x82331,x82332)),x82333))+~P1(f775(f775(f232(x82332),f775(f65(x82332,f236(x82332)),x82331)),x82333)) % 186.05/186.63 [8318]~P1(f775(x83181,x83183))+P1(f775(x83181,f352(x83181,x83182)))+P1(f775(x83181,f351(x83181,x83182)))+~P1(f775(f775(f233(a1),f2(a1)),x83182))+P1(f775(x83181,f775(f775(f3(a1),f351(x83181,x83182)),f775(f775(f83(a1),f353(x83181,x83182)),x83182)))) % 186.05/186.63 [8536]~P1(f775(x85361,x85363))+P1(f775(x85361,f351(x85361,x85362)))+~P1(f775(f775(f233(a1),f2(a1)),x85362))+P1(f775(f775(f334(a1),f352(x85361,x85362)),f295(a1,f80(a1),x85362)))+P1(f775(x85361,f775(f775(f3(a1),f351(x85361,x85362)),f775(f775(f83(a1),f353(x85361,x85362)),x85362)))) % 186.05/186.63 [8714]~P1(f775(x87141,x87143))+~P1(f775(x87141,f351(x87141,x87142)))+P1(f775(x87141,f352(x87141,x87142)))+~P1(f775(f775(f233(a1),f2(a1)),x87142))+~P1(f775(x87141,f775(f775(f3(a1),f351(x87141,x87142)),f775(f775(f83(a1),f353(x87141,x87142)),x87142)))) % 186.05/186.63 [8817]~P1(f775(x88171,x88173))+~P1(f775(x88171,f351(x88171,x88172)))+~P1(f775(f775(f233(a1),f2(a1)),x88172))+P1(f775(f775(f334(a1),f352(x88171,x88172)),f295(a1,f80(a1),x88172)))+~P1(f775(x88171,f775(f775(f3(a1),f351(x88171,x88172)),f775(f775(f83(a1),f353(x88171,x88172)),x88172)))) % 186.05/186.63 [8633]~P93(x86331)+~P1(f775(f63(x86331),x86332))+E(f775(f775(f3(f857(x86331,a844)),x86332),f775(f775(f302(x86331),x86333),f180(f857(x86331,a844)))),f180(f857(x86331,a844)))+~P1(f775(f775(f334(x86331),x86333),x86332))+E(f775(f775(f103(x86331),x86333),f15(x86331,f775(f775(f3(f857(x86331,a844)),x86332),f775(f775(f302(x86331),x86333),f180(f857(x86331,a844)))))),f15(x86331,x86332)) % 186.05/186.63 [8634]~P100(x86341)+~P1(f775(f63(x86341),x86342))+E(f775(f775(f3(f857(x86341,a844)),x86342),f775(f775(f302(x86341),x86343),f180(f857(x86341,a844)))),f180(f857(x86341,a844)))+~P1(f775(f775(f334(x86341),x86343),x86342))+E(f775(f775(f179(x86341),x86343),f16(x86341,f775(f775(f3(f857(x86341,a844)),x86342),f775(f775(f302(x86341),x86343),f180(f857(x86341,a844)))))),f16(x86341,x86342)) % 186.05/186.63 [8635]~P100(x86351)+~P1(f775(f63(x86351),x86352))+E(f775(f775(f3(f857(x86351,a844)),x86352),f775(f775(f302(x86351),x86353),f180(f857(x86351,a844)))),f180(f857(x86351,a844)))+~P1(f775(f775(f334(x86351),x86353),x86352))+E(f775(f775(f236(x86351),x86353),f17(x86351,f775(f775(f3(f857(x86351,a844)),x86352),f775(f775(f302(x86351),x86353),f180(f857(x86351,a844)))))),f17(x86351,x86352)) % 186.05/186.63 [8636]~P93(x86361)+~P1(f775(f63(x86361),x86362))+E(f775(f775(f3(f857(x86361,a844)),x86362),f775(f775(f302(x86361),x86363),f180(f857(x86361,a844)))),f180(f857(x86361,a844)))+~P1(f775(f775(f334(x86361),x86363),x86362))+E(f775(f775(f104(x86361),x86363),f12(x86361,f775(f775(f3(f857(x86361,a844)),x86362),f775(f775(f302(x86361),x86363),f180(f857(x86361,a844)))))),f12(x86361,x86362)) % 186.05/186.63 [8691]~P100(x86911)+~P1(f775(f63(x86911),x86912))+E(f775(f775(f3(f857(x86911,a844)),x86912),f775(f775(f302(x86911),x86913),f180(f857(x86911,a844)))),f180(f857(x86911,a844)))+~P1(f775(f775(f334(x86911),x86913),x86912))+E(f775(f775(f179(x86911),x86913),f13(x86911,f179(x86911),f775(f775(f3(f857(x86911,a844)),x86912),f775(f775(f302(x86911),x86913),f180(f857(x86911,a844)))))),f13(x86911,f179(x86911),x86912)) % 186.05/186.63 [8692]~P100(x86921)+~P1(f775(f63(x86921),x86922))+E(f775(f775(f3(f857(x86921,a844)),x86922),f775(f775(f302(x86921),x86923),f180(f857(x86921,a844)))),f180(f857(x86921,a844)))+~P1(f775(f775(f334(x86921),x86923),x86922))+E(f775(f775(f236(x86921),x86923),f14(x86921,f236(x86921),f775(f775(f3(f857(x86921,a844)),x86922),f775(f775(f302(x86921),x86923),f180(f857(x86921,a844)))))),f14(x86921,f236(x86921),x86922)) % 186.05/186.63 [8702]~P100(x87021)+~P1(f775(f63(x87021),x87023))+~P1(f775(f63(x87021),x87022))+E(f775(f775(f104(f857(x87021,a844)),x87022),x87023),f180(f857(x87021,a844)))+E(f775(f775(f236(x87021),f17(x87021,f775(f775(f103(f857(x87021,a844)),x87022),x87023))),f17(x87021,f775(f775(f104(f857(x87021,a844)),x87022),x87023))),f775(f775(f236(x87021),f17(x87021,x87022)),f17(x87021,x87023))) % 186.05/186.63 [8703]~P100(x87031)+~P1(f775(f63(x87031),x87033))+~P1(f775(f63(x87031),x87032))+E(f775(f775(f104(f857(x87031,a844)),x87032),x87033),f180(f857(x87031,a844)))+E(f775(f775(f179(x87031),f16(x87031,f775(f775(f103(f857(x87031,a844)),x87032),x87033))),f16(x87031,f775(f775(f104(f857(x87031,a844)),x87032),x87033))),f775(f775(f179(x87031),f16(x87031,x87032)),f16(x87031,x87033))) % 186.05/186.63 [8704]~P93(x87041)+~P1(f775(f63(x87041),x87043))+~P1(f775(f63(x87041),x87042))+E(f775(f775(f104(f857(x87041,a844)),x87042),x87043),f180(f857(x87041,a844)))+E(f775(f775(f103(x87041),f15(x87041,f775(f775(f103(f857(x87041,a844)),x87042),x87043))),f15(x87041,f775(f775(f104(f857(x87041,a844)),x87042),x87043))),f775(f775(f103(x87041),f15(x87041,x87042)),f15(x87041,x87043))) % 186.05/186.63 [8705]~P93(x87051)+~P1(f775(f63(x87051),x87053))+~P1(f775(f63(x87051),x87052))+E(f775(f775(f104(f857(x87051,a844)),x87052),x87053),f180(f857(x87051,a844)))+E(f775(f775(f104(x87051),f12(x87051,f775(f775(f103(f857(x87051,a844)),x87052),x87053))),f12(x87051,f775(f775(f104(f857(x87051,a844)),x87052),x87053))),f775(f775(f104(x87051),f12(x87051,x87052)),f12(x87051,x87053))) % 186.05/186.63 [8898]~P100(x88981)+~P1(f775(f63(x88981),x88983))+~P1(f775(f63(x88981),x88982))+E(f775(f775(f104(f857(x88981,a844)),x88982),x88983),f180(f857(x88981,a844)))+E(f775(f775(f236(x88981),f14(x88981,f236(x88981),f775(f775(f103(f857(x88981,a844)),x88982),x88983))),f14(x88981,f236(x88981),f775(f775(f104(f857(x88981,a844)),x88982),x88983))),f775(f775(f236(x88981),f14(x88981,f236(x88981),x88982)),f14(x88981,f236(x88981),x88983))) % 186.05/186.63 [8899]~P100(x88991)+~P1(f775(f63(x88991),x88993))+~P1(f775(f63(x88991),x88992))+E(f775(f775(f104(f857(x88991,a844)),x88992),x88993),f180(f857(x88991,a844)))+E(f775(f775(f179(x88991),f13(x88991,f179(x88991),f775(f775(f103(f857(x88991,a844)),x88992),x88993))),f13(x88991,f179(x88991),f775(f775(f104(f857(x88991,a844)),x88992),x88993))),f775(f775(f179(x88991),f13(x88991,f179(x88991),x88992)),f13(x88991,f179(x88991),x88993))) % 186.05/186.63 [9633]~P117(x96333)+E(x96331,x96332)+~P1(f775(f775(f232(x96333),f2(x96333)),x96332))+~P1(f775(f775(f232(x96333),f2(x96333)),x96331))+~E(f775(f775(f242(x96333),x96331),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)))),f775(f775(f242(x96333),x96332),f775(f106(a850),f775(f775(f82(a1),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99)),f775(f775(f3(a1),f775(f775(f82(a1),a85),a85)),a99))))) % 186.05/186.63 [6577]P142(x65771,x65772)+~P142(x65771,x65773)+~P39(a861,x65773,x65774,x65772)+~P31(a843,x65774,f773(x65774))+~P1(f775(a859,x65773)) % 186.05/186.63 [5751]~P7(x57512)+E(x57511,f2(x57512))+~E(f775(f775(f43(x57512),x57513),x57511),x57514)+E(x57513,f775(f775(f83(x57512),x57514),x57511))+~P1(f775(f775(f279(x57512),x57511),x57513)) % 186.05/186.63 [5752]~P7(x57522)+E(x57521,f2(x57522))+~E(x57523,f775(f775(f83(x57522),x57524),x57521))+E(f775(f775(f43(x57522),x57523),x57521),x57524)+~P1(f775(f775(f279(x57522),x57521),x57523)) % 186.05/186.63 [6216]E(f404(x62161,x62162,x62163),x62164)+E(f775(x62161,x62164),f2(a850))+~E(f775(f775(f8(x62163,a850),x62161),x62162),f80(a850))+~P1(f775(f63(x62163),x62162))+~P1(f775(f775(f334(x62163),x62164),x62162)) % 186.05/186.63 [6284]E(f406(x62841,x62842,x62843),x62844)+E(f775(x62841,x62844),f2(a850))+~E(f775(f775(f8(x62843,a850),x62841),x62842),f775(a114,f2(a850)))+~P1(f775(f63(x62843),x62842))+~P1(f775(f775(f334(x62843),x62844),x62842)) % 186.05/186.63 [6398]~P100(x63981)+~P9(x63981)+P1(f775(f775(f233(x63981),x63982),f44(x63981,x63983)))+~P1(f775(f775(f233(x63981),x63982),x63984))+~P1(f775(f775(f334(x63981),x63984),x63983)) % 186.05/186.63 [6576]~P100(x65761)+~P9(x65761)+~P1(f775(f775(f233(x65761),x65764),x65763))+P1(f775(f775(f233(x65761),f45(x65761,x65762)),x65763))+~P1(f775(f775(f334(x65761),x65764),x65762)) % 186.05/186.63 [6734]P142(x67341,x67342)+~P142(x67341,x67344)+~P39(a861,x67344,x67343,x67342)+~P1(f775(a859,x67344))+P1(f775(f775(f334(f849(a843)),f773(x67343)),a860)) % 186.05/186.63 [6854]~P117(x68543)+E(x68541,x68542)+~E(f775(f775(f242(x68543),x68541),f775(a114,x68544)),f775(f775(f242(x68543),x68542),f775(a114,x68544)))+~P1(f775(f775(f232(x68543),f2(x68543)),x68542))+~P1(f775(f775(f232(x68543),f2(x68543)),x68541)) % 186.05/186.63 [7065]~E(f409(x70652,x70653,x70651,x70654),x70654)+~E(f775(x70652,x70654),f80(a850))+E(f775(f775(f8(x70651,a850),x70652),x70653),f80(a850))+~P1(f775(f63(x70651),x70653))+~P1(f775(f775(f334(x70651),x70654),x70653)) % 186.05/186.63 [7072]~P85(x70724)+~P127(x70724)+E(f775(x70721,f451(x70721,x70722,x70723,x70724)),f2(x70724))+~E(f775(f775(f11(x70723,x70724),x70721),x70722),f2(x70724))+~P1(f775(f63(x70723),x70722)) % 186.05/186.63 [7155]~E(f408(x71552,x71553,x71551,x71554),x71554)+~E(f775(x71552,x71554),f775(a114,f2(a850)))+E(f775(f775(f8(x71551,a850),x71552),x71553),f775(a114,f2(a850)))+~P1(f775(f63(x71551),x71553))+~P1(f775(f775(f334(x71551),x71554),x71553)) % 186.05/186.63 [7920]~E(f775(x79202,x79204),f80(a850))+~E(f775(x79202,f409(x79202,x79203,x79201,x79204)),f2(a850))+E(f775(f775(f8(x79201,a850),x79202),x79203),f80(a850))+~P1(f775(f63(x79201),x79203))+~P1(f775(f775(f334(x79201),x79204),x79203)) % 186.05/186.63 [7965]~E(f775(x79652,x79654),f775(a114,f2(a850)))+~E(f775(x79652,f408(x79652,x79653,x79651,x79654)),f2(a850))+E(f775(f775(f8(x79651,a850),x79652),x79653),f775(a114,f2(a850)))+~P1(f775(f63(x79651),x79653))+~P1(f775(f775(f334(x79651),x79654),x79653)) % 186.05/186.63 [8044]~P136(x80442)+~P112(x80442)+~P1(f775(x80441,x80444))+~P1(f775(f775(f279(x80442),x80443),f775(f775(f82(x80442),x80444),f2(x80442))))+P1(f775(x80441,f775(f775(f83(x80442),x80443),f840(x80443,x80441,x80442)))) % 186.05/186.63 [8539]E(x85391,x85392)+E(f775(f775(f82(a1),f433(x85393,x85392,x85394,x85391)),f434(x85393,x85392,x85394,x85391)),x85391)+~E(f775(f775(f3(a1),x85391),x85394),x85392)+~P1(f775(f775(f233(a1),f2(a1)),x85394))+~P1(f775(f775(f334(a1),x85392),x85393)) % 186.05/186.63 [8540]E(x85401,x85402)+E(f775(f775(f3(a1),f423(x85403,x85402,x85404,x85401)),f424(x85403,x85402,x85404,x85401)),x85401)+~E(f775(f775(f82(a1),x85401),x85404),x85402)+~P1(f775(f775(f233(a1),f2(a1)),x85404))+~P1(f775(f775(f334(a1),x85402),x85403)) % 186.05/186.63 [8701]E(f775(x87011,f818(x87012,x87011,x87013,x87014)),x87012)+P1(f775(f775(f232(a850),x87014),f819(x87012,x87011,x87013,x87014)))+~P1(f775(f775(f232(a1),x87012),f775(x87011,x87013)))+~P1(f775(f775(f233(a850),x87014),x87013))+~P1(f775(f775(f232(a1),f775(x87011,x87014)),x87012)) % 186.05/186.63 [8718]~P85(x87184)+~P127(x87184)+~E(f775(f775(f11(x87181,x87184),x87182),x87183),f2(x87184))+~P1(f775(f63(x87181),x87183))+P1(f775(f775(f334(x87181),f451(x87182,x87183,x87181,x87184)),x87183)) % 186.05/186.63 [8751]~E(f775(x87512,x87514),f80(a850))+E(f775(f775(f8(x87511,a850),x87512),x87513),f80(a850))+~P1(f775(f63(x87511),x87513))+~P1(f775(f775(f334(x87511),x87514),x87513))+P1(f775(f775(f334(x87511),f409(x87512,x87513,x87511,x87514)),x87513)) % 186.05/186.63 [8760]E(x87601,x87602)+~E(f775(f775(f82(a1),x87602),x87604),x87601)+~P1(f775(f775(f233(a1),f2(a1)),x87604))+~P1(f775(f775(f334(a1),x87601),x87603))+P1(f775(f775(f334(a1),f423(x87603,x87601,x87604,x87602)),x87603)) % 186.05/186.63 [8761]E(x87611,x87612)+~E(f775(f775(f3(a1),x87612),x87614),x87611)+~P1(f775(f775(f233(a1),f2(a1)),x87614))+~P1(f775(f775(f334(a1),x87611),x87613))+P1(f775(f775(f334(a1),f433(x87613,x87611,x87614,x87612)),x87613)) % 186.05/186.63 [8763]~E(f775(x87632,x87634),f775(a114,f2(a850)))+E(f775(f775(f8(x87631,a850),x87632),x87633),f775(a114,f2(a850)))+~P1(f775(f63(x87631),x87633))+~P1(f775(f775(f334(x87631),x87634),x87633))+P1(f775(f775(f334(x87631),f408(x87632,x87633,x87631,x87634)),x87633)) % 186.05/186.63 [8767]P57(x87672,x87673,x87674,x87671)+E(x87671,f180(f857(x87672,a844)))+~P1(f775(f63(x87672),x87674))+~P1(f775(f63(x87672),x87671))+P1(f775(f775(f334(x87672),f537(x87671,x87674,x87673,x87672)),x87674)) % 186.05/186.63 [8830]E(x88301,x88302)+~E(f775(f775(f82(a1),x88302),x88304),x88301)+~P1(f775(f775(f233(a1),f2(a1)),x88304))+~P1(f775(f775(f334(a1),x88301),x88303))+P1(f775(f775(f334(a1),f424(x88303,x88301,x88304,x88302)),f295(a1,f80(a1),x88304))) % 186.05/186.63 [8831]E(x88311,x88312)+~E(f775(f775(f3(a1),x88312),x88314),x88311)+~P1(f775(f775(f233(a1),f2(a1)),x88314))+~P1(f775(f775(f334(a1),x88311),x88313))+P1(f775(f775(f334(a1),f434(x88313,x88311,x88314,x88312)),f295(a1,f80(a1),x88314))) % 186.05/186.63 [8904]P1(f775(f775(f232(a850),x89041),f818(x89042,x89043,x89044,x89041)))+~P1(f775(f775(f232(a1),x89042),f775(x89043,x89044)))+P1(f775(f775(f232(a850),x89041),f819(x89042,x89043,x89044,x89041)))+~P1(f775(f775(f233(a850),x89041),x89044))+~P1(f775(f775(f232(a1),f775(x89043,x89041)),x89042)) % 186.05/186.63 [9011]E(f775(x90111,f818(x90112,x90111,x90113,x90114)),x90112)+~P1(f775(f775(f232(a1),x90112),f775(x90111,x90113)))+P1(f775(f775(f233(a850),f819(x90112,x90111,x90113,x90114)),x90113))+~P1(f775(f775(f233(a850),x90114),x90113))+~P1(f775(f775(f232(a1),f775(x90111,x90114)),x90112)) % 186.05/186.63 [9116]~P1(f775(f775(f279(a850),x91164),x91161))+~P1(f775(f775(f279(a850),x91164),x91163))+~P1(f775(f775(f279(a850),x91162),x91161))+P1(f775(f775(f279(a850),x91161),x91162))+P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x91163,x91162)),f282(a850,f279(a850),x91164,x91161))) % 186.05/186.63 [9117]~P1(f775(f775(f279(a850),x91172),x91171))+~P1(f775(f775(f279(a850),x91173),x91174))+~P1(f775(f775(f279(a850),x91172),x91174))+P1(f775(f775(f279(a850),x91171),x91172))+P1(f775(f775(f233(f857(a850,a844)),f282(a850,f279(a850),x91171,x91173)),f282(a850,f279(a850),x91172,x91174))) % 186.05/186.63 [9128]~P1(f775(f775(f232(a1),x91282),f775(x91283,x91284)))+P1(f775(f775(f232(a850),x91281),f819(x91282,x91283,x91284,x91281)))+P1(f775(f775(f232(a850),f818(x91282,x91283,x91284,x91281)),x91284))+~P1(f775(f775(f233(a850),x91281),x91284))+~P1(f775(f775(f232(a1),f775(x91283,x91281)),x91282)) % 186.05/186.63 [9129]~P1(f775(f775(f232(a1),x91292),f775(x91293,x91294)))+P1(f775(f775(f232(a850),x91291),f818(x91292,x91293,x91294,x91291)))+P1(f775(f775(f233(a850),f819(x91292,x91293,x91294,x91291)),x91294))+~P1(f775(f775(f233(a850),x91291),x91294))+~P1(f775(f775(f232(a1),f775(x91293,x91291)),x91292)) % 186.05/186.63 [9216]~P1(f775(f775(f232(a1),x92161),f775(x92162,x92163)))+P1(f775(f775(f232(a850),f818(x92161,x92162,x92163,x92164)),x92163))+~P1(f775(f775(f233(a850),x92164),x92163))+~P1(f775(f775(f232(a1),f775(x92162,x92164)),x92161))+P1(f775(f775(f233(a850),f819(x92161,x92162,x92163,x92164)),x92163)) % 186.05/186.63 [9300]E(x93001,f180(f857(x93002,a844)))+~P1(f775(f63(x93002),x93004))+~P1(f775(f63(x93002),x93001))+P1(f775(f775(f334(f856(f857(x93002,a844),f857(x93002,a844))),f775(f775(f241(f857(x93002,a844),f857(x93002,a844)),x93004),x93001)),f324(x93002,x93003)))+P1(f775(f775(f334(x93002),f539(x93003,x93001,x93004,x93002)),x93004)) % 186.05/186.63 [9301]E(x93011,f180(f857(x93012,a844)))+~P1(f775(f63(x93012),x93014))+~P1(f775(f63(x93012),x93011))+P1(f775(f775(f334(f856(f857(x93012,a844),f857(x93012,a844))),f775(f775(f241(f857(x93012,a844),f857(x93012,a844)),x93014),x93011)),f324(x93012,x93013)))+P1(f775(f775(f334(x93012),f624(x93013,x93011,x93014,x93012)),x93014)) % 186.05/186.63 [9944]E(f775(x99441,f818(x99442,x99441,x99443,x99444)),x99442)+~P1(f775(f775(f232(a1),x99442),f775(x99441,x99443)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x99441,f775(f775(f82(a850),f819(x99442,x99441,x99443,x99444)),f80(a850)))),f775(x99441,f819(x99442,x99441,x99443,x99444))))),f80(a1)))+~P1(f775(f775(f233(a850),x99444),x99443))+~P1(f775(f775(f232(a1),f775(x99441,x99444)),x99442)) % 186.05/186.63 [9945]~P1(f775(f775(f232(a1),x99452),f775(x99453,x99454)))+P1(f775(f775(f232(a850),x99451),f818(x99452,x99453,x99454,x99451)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x99453,f775(f775(f82(a850),f819(x99452,x99453,x99454,x99451)),f80(a850)))),f775(x99453,f819(x99452,x99453,x99454,x99451))))),f80(a1)))+~P1(f775(f775(f233(a850),x99451),x99454))+~P1(f775(f775(f232(a1),f775(x99453,x99451)),x99452)) % 186.05/186.63 [9946]~P1(f775(f775(f232(a1),x99461),f775(x99462,x99463)))+~P1(f775(f775(f232(a1),f775(f77(a1),f775(f775(f3(a1),f775(x99462,f775(f775(f82(a850),f819(x99461,x99462,x99463,x99464)),f80(a850)))),f775(x99462,f819(x99461,x99462,x99463,x99464))))),f80(a1)))+~P1(f775(f775(f233(a850),x99464),x99463))+~P1(f775(f775(f232(a1),f775(x99462,x99464)),x99461))+P1(f775(f775(f232(a850),f818(x99461,x99462,x99463,x99464)),x99463)) % 186.05/186.63 [7123]~P62(x71231)+P1(f775(f775(f233(x71231),x71232),f2(x71231)))+~P1(f775(f775(f233(x71231),x71233),f2(x71231)))+P1(f775(f775(f233(x71231),f2(x71231)),x71232))+P1(f775(f775(f233(x71231),x71233),f775(f775(f283(x71231),x71234),x71232))) % 186.05/186.63 [7124]~P62(x71241)+P1(f775(f775(f233(x71241),x71242),f2(x71241)))+~P1(f775(f775(f232(x71241),x71243),f2(x71241)))+P1(f775(f775(f233(x71241),f2(x71241)),x71242))+P1(f775(f775(f232(x71241),x71243),f775(f775(f283(x71241),x71244),x71242))) % 186.05/186.63 [7395]~P62(x73951)+P1(f775(f775(f233(x73951),x73952),f2(x73951)))+P1(f775(f775(f233(x73951),x73953),f2(x73951)))+P1(f775(f775(f233(x73951),f2(x73951)),x73953))+~P1(f775(f775(f233(x73951),x73952),f775(f775(f283(x73951),x73954),x73953))) % 186.05/186.63 [7396]~P62(x73961)+P1(f775(f775(f233(x73961),x73962),f2(x73961)))+P1(f775(f775(f232(x73961),x73963),f2(x73961)))+P1(f775(f775(f233(x73961),f2(x73961)),x73962))+~P1(f775(f775(f232(x73961),x73963),f775(f775(f283(x73961),x73964),x73962))) % 186.05/186.63 [7515]E(x75151,x75152)+~E(f775(f775(f153(x75153),x75154),x75151),f775(f775(f153(x75153),x75154),x75152))+~P1(f775(f127(x75153),x75154))+~P1(f775(f775(f233(a850),x75152),f775(f181(f851(x75153)),x75154)))+~P1(f775(f775(f233(a850),x75151),f775(f181(f851(x75153)),x75154))) % 186.05/186.63 [7882]~P62(x78821)+~P1(f775(f775(f233(x78821),x78823),f2(x78821)))+P1(f775(f775(f233(x78821),f2(x78821)),x78822))+~P1(f775(f775(f233(x78821),x78824),f775(f775(f83(x78821),x78823),x78822)))+P1(f775(f775(f233(x78821),x78823),f775(f775(f283(x78821),x78824),x78822))) % 186.05/186.63 [7883]~P62(x78831)+~P1(f775(f775(f232(x78831),x78833),f2(x78831)))+P1(f775(f775(f233(x78831),f2(x78831)),x78832))+~P1(f775(f775(f232(x78831),x78834),f775(f775(f83(x78831),x78833),x78832)))+P1(f775(f775(f232(x78831),x78833),f775(f775(f283(x78831),x78834),x78832))) % 186.05/186.63 [7884]~P62(x78841)+~P1(f775(f775(f233(x78841),x78842),f2(x78841)))+P1(f775(f775(f233(x78841),f2(x78841)),x78842))+~P1(f775(f775(f233(x78841),x78844),f775(f775(f83(x78841),x78843),x78842)))+P1(f775(f775(f233(x78841),x78843),f775(f775(f283(x78841),x78844),x78842))) % 186.05/186.63 [7885]~P62(x78851)+~P1(f775(f775(f233(x78851),x78852),f2(x78851)))+P1(f775(f775(f233(x78851),f2(x78851)),x78852))+~P1(f775(f775(f233(x78851),x78854),f775(f775(f283(x78851),x78853),x78852)))+P1(f775(f775(f233(x78851),x78853),f775(f775(f83(x78851),x78854),x78852))) % 186.05/186.63 [7886]~P62(x78861)+~P1(f775(f775(f233(x78861),x78862),f2(x78861)))+P1(f775(f775(f233(x78861),f2(x78861)),x78862))+~P1(f775(f775(f232(x78861),x78864),f775(f775(f83(x78861),x78863),x78862)))+P1(f775(f775(f232(x78861),x78863),f775(f775(f283(x78861),x78864),x78862))) % 186.05/186.63 [7887]~P62(x78871)+~P1(f775(f775(f233(x78871),x78872),f2(x78871)))+P1(f775(f775(f233(x78871),f2(x78871)),x78872))+~P1(f775(f775(f232(x78871),x78874),f775(f775(f283(x78871),x78873),x78872)))+P1(f775(f775(f232(x78871),x78873),f775(f775(f83(x78871),x78874),x78872))) % 186.05/186.63 [8012]~P7(x80121)+~P1(f775(f775(f279(x80121),x80123),x80124))+~P1(f775(f775(f279(x80121),x80123),x80122))+~P1(f775(f775(f279(x80121),x80122),x80124))+P1(f775(f775(f279(x80121),f775(f775(f43(x80121),x80122),x80123)),f775(f775(f43(x80121),x80124),x80123))) % 186.05/186.63 [8027]~P100(x80271)+~P18(x80271,x80272)+~P1(f775(f775(f232(a850),x80273),x80274))+P1(f775(f775(f232(x80271),f775(f775(f153(x80271),x80272),x80273)),f775(f775(f153(x80271),x80272),x80274)))+~P1(f775(f775(f233(a850),x80274),f775(f181(f851(x80271)),x80272))) % 186.05/186.63 [8077]~P117(x80771)+~P1(f775(f775(f233(x80771),x80772),f80(x80771)))+~P1(f775(f775(f233(x80771),f2(x80771)),x80772))+~P1(f775(f775(f233(a850),x80774),x80773))+P1(f775(f775(f233(x80771),f775(f775(f242(x80771),x80772),x80773)),f775(f775(f242(x80771),x80772),x80774))) % 186.05/186.63 [8078]~P117(x80781)+~P1(f775(f775(f232(x80781),x80782),f80(x80781)))+~P1(f775(f775(f232(x80781),f2(x80781)),x80782))+~P1(f775(f775(f232(a850),x80784),x80783))+P1(f775(f775(f232(x80781),f775(f775(f242(x80781),x80782),x80783)),f775(f775(f242(x80781),x80782),x80784))) % 186.05/186.63 [8079]~P117(x80791)+~P1(f775(f775(f232(x80791),f2(x80791)),x80792))+~P1(f775(f775(f233(a850),f2(a850)),x80793))+~P1(f775(f775(f233(x80791),x80792),x80794))+P1(f775(f775(f233(x80791),f775(f775(f242(x80791),x80792),x80793)),f775(f775(f242(x80791),x80794),x80793))) % 186.05/186.63 [8097]~P100(x80971)+~P18(x80971,f775(f142(x80971),x80972))+~P1(f775(f775(f232(a850),x80974),x80973))+P1(f775(f775(f232(x80971),f775(f775(f153(x80971),x80972),x80973)),f775(f775(f153(x80971),x80972),x80974)))+~P1(f775(f775(f233(a850),x80973),f775(f181(f851(x80971)),x80972))) % 186.05/186.63 [8325]~P7(x83251)+P1(f775(f775(f279(x83251),x83252),x83253))+~P1(f775(f775(f279(x83251),x83254),x83253))+~P1(f775(f775(f279(x83251),x83254),x83252))+~P1(f775(f775(f279(x83251),f775(f775(f43(x83251),x83252),x83254)),f775(f775(f43(x83251),x83253),x83254))) % 186.05/186.63 [8342]~P63(x83421)+~P1(f775(f775(f233(x83421),x83422),f2(x83421)))+~P1(f775(f775(f233(x83421),x83423),x83424))+~P1(f775(f775(f233(x83421),f2(x83421)),f775(f775(f83(x83421),x83423),x83424)))+P1(f775(f775(f233(x83421),f775(f775(f283(x83421),x83422),x83423)),f775(f775(f283(x83421),x83422),x83424))) % 186.05/186.63 [8343]~P62(x83431)+~P1(f775(f775(f232(x83431),x83432),f2(x83431)))+~P1(f775(f775(f232(x83431),x83433),x83434))+~P1(f775(f775(f233(x83431),f2(x83431)),f775(f775(f83(x83431),x83433),x83434)))+P1(f775(f775(f232(x83431),f775(f775(f283(x83431),x83432),x83433)),f775(f775(f283(x83431),x83432),x83434))) % 186.05/186.63 [8353]~P63(x83531)+~P1(f775(f775(f233(x83531),x83534),x83533))+~P1(f775(f775(f233(x83531),f2(x83531)),x83532))+~P1(f775(f775(f233(x83531),f2(x83531)),f775(f775(f83(x83531),x83533),x83534)))+P1(f775(f775(f233(x83531),f775(f775(f283(x83531),x83532),x83533)),f775(f775(f283(x83531),x83532),x83534))) % 186.05/186.63 [8354]~P63(x83541)+~P1(f775(f775(f232(x83541),x83544),x83543))+~P1(f775(f775(f232(x83541),f2(x83541)),x83542))+~P1(f775(f775(f233(x83541),f2(x83541)),f775(f775(f83(x83541),x83543),x83544)))+P1(f775(f775(f232(x83541),f775(f775(f283(x83541),x83542),x83543)),f775(f775(f283(x83541),x83542),x83544))) % 186.05/186.63 [8462]P1(f775(x84621,x84622))+~P1(f775(f63(x84624),x84622))+P1(f775(x84621,f486(x84621,x84623,x84622,x84624)))+~P1(f775(x84621,f180(f857(x84624,a844))))+~P1(f775(f775(f232(f857(x84624,a844)),x84622),x84623)) % 186.05/186.63 [8470]P1(f775(x84701,x84702))+P1(f775(f63(x84703),f486(x84701,x84704,x84702,x84703)))+~P1(f775(f63(x84703),x84702))+~P1(f775(x84701,f180(f857(x84703,a844))))+~P1(f775(f775(f232(f857(x84703,a844)),x84702),x84704)) % 186.05/186.63 [8698]E(f775(f775(f82(a1),f436(x86981,x86982,x86983,x86984)),f437(x86981,x86982,x86983,x86984)),x86984)+~P1(f775(f775(f233(a1),f2(a1)),x86983))+~P1(f775(f775(f233(a1),x86982),x86984))+~P1(f775(f775(f334(a1),x86982),x86981))+P1(f775(f775(f233(a1),x86982),f775(f775(f3(a1),x86984),x86983))) % 186.05/186.63 [8884]~P1(f775(f775(f233(a1),f2(a1)),x88843))+~P1(f775(f775(f233(a1),x88842),x88844))+~P1(f775(f775(f334(a1),x88842),x88841))+P1(f775(f775(f334(a1),f436(x88841,x88842,x88843,x88844)),x88841))+P1(f775(f775(f233(a1),x88842),f775(f775(f3(a1),x88844),x88843))) % 186.05/186.63 [8897]P1(f775(x88971,x88972))+~P1(f775(f63(x88973),x88972))+P1(f775(f775(f334(x88973),f487(x88971,x88974,x88972,x88973)),x88974))+~P1(f775(x88971,f180(f857(x88973,a844))))+~P1(f775(f775(f232(f857(x88973,a844)),x88972),x88974)) % 186.05/186.63 [8914]E(f775(f775(f82(a1),f428(x89141,x89142,x89143,x89144)),f429(x89141,x89142,x89143,x89144)),x89144)+~P1(f775(f775(f233(a1),f2(a1)),x89143))+~P1(f775(f775(f232(a1),x89142),x89144))+P1(f775(f775(f232(a1),x89142),f775(f775(f3(a1),x89144),x89143)))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x89142),f80(a1))),x89141)) % 186.05/186.63 [8961]~P1(f775(f775(f233(a1),f2(a1)),x89613))+~P1(f775(f775(f233(a1),x89611),x89612))+~P1(f775(f775(f334(a1),x89611),x89614))+P1(f775(f775(f334(a1),f437(x89614,x89611,x89613,x89612)),f295(a1,f80(a1),x89613)))+P1(f775(f775(f233(a1),x89611),f775(f775(f3(a1),x89612),x89613))) % 186.05/186.63 [9054]~P1(f775(f775(f233(a1),f2(a1)),x90543))+~P1(f775(f775(f232(a1),x90542),x90544))+P1(f775(f775(f334(a1),f428(x90541,x90542,x90543,x90544)),x90541))+P1(f775(f775(f232(a1),x90542),f775(f775(f3(a1),x90544),x90543)))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x90542),f80(a1))),x90541)) % 186.05/186.63 [9092]~P1(f775(f775(f233(a1),f2(a1)),x90923))+~P1(f775(f775(f232(a1),x90921),x90922))+P1(f775(f775(f334(a1),f429(x90924,x90921,x90923,x90922)),f295(a1,f80(a1),x90923)))+P1(f775(f775(f232(a1),x90921),f775(f775(f3(a1),x90922),x90923)))+~P1(f775(f775(f334(a1),f775(f775(f3(a1),x90921),f80(a1))),x90924)) % 186.05/186.63 [9303]P1(f775(x93031,x93032))+~P1(f775(f775(f334(x93033),f487(x93031,x93034,x93032,x93033)),f486(x93031,x93034,x93032,x93033)))+~P1(f775(f63(x93033),x93032))+~P1(f775(x93031,f180(f857(x93033,a844))))+~P1(f775(f775(f232(f857(x93033,a844)),x93032),x93034)) % 186.05/186.63 [9507]P1(f775(x95071,x95072))+~P1(f775(f63(x95073),x95072))+~P1(f775(x95071,f775(f775(f302(x95073),f487(x95071,x95074,x95072,x95073)),f486(x95071,x95074,x95072,x95073))))+~P1(f775(x95071,f180(f857(x95073,a844))))+~P1(f775(f775(f232(f857(x95073,a844)),x95072),x95074)) % 186.05/186.63 [9826]~P99(x98263)+~P52(a850,x98263,f775(f775(f20(a850,f857(a850,a844),f857(a850,a844)),f775(f775(f10(f857(a850,f857(a844,a844)),f857(f857(a850,a844),f857(a850,a844)),a850),f20(a850,a844,a844)),f775(f775(f10(f857(a850,a844),f857(a850,f857(a844,a844)),a850),f775(f10(a844,f857(a844,a844),a850),a331)),f279(a850)))),f775(f775(f10(f857(a850,a844),f857(a850,a844),a850),f775(f10(a844,a844,a850),a328)),f775(f9(a850,a850,a844),f279(a850)))),x98264)+P1(f775(f775(f233(x98263),f775(x98264,x98262)),f775(x98264,x98261)))+~P1(f775(f775(f279(a850),x98262),x98261))+P1(f775(f775(f279(a850),x98261),x98262)) % 186.05/186.63 [7654]~P62(x76541)+P1(f775(f775(f233(x76541),x76542),f2(x76541)))+P1(f775(f775(f233(x76541),f2(x76541)),x76542))+~P1(f775(f775(f233(x76541),f2(x76541)),x76544))+P1(f775(f775(f233(x76541),f775(f775(f283(x76541),x76543),x76542)),x76544)) % 186.05/186.63 [7655]~P62(x76551)+P1(f775(f775(f233(x76551),x76552),f2(x76551)))+~P1(f775(f775(f232(x76551),f2(x76551)),x76554))+P1(f775(f775(f233(x76551),f2(x76551)),x76552))+P1(f775(f775(f232(x76551),f775(f775(f283(x76551),x76553),x76552)),x76554)) % 186.05/186.63 [7938]~P1(f775(f775(f232(a1),x79384),f2(a1)))+~E(x79382,f775(f775(f82(a1),f775(f775(f83(a1),x79381),x79383)),x79384))+P1(f775(f775(f233(a1),f2(a1)),x79381))+~P1(f775(f775(f233(a1),x79381),x79384))+P1(f775(f56(x79382,x79381),f775(f775(f241(a1,a1),x79383),x79384))) % 186.05/186.63 [7975]~P1(f775(x79751,x79754))+P1(f775(x79751,f807(x79752,x79751,x79753)))+~P1(f775(f775(f233(a1),f2(a1)),x79753))+~P1(f775(f775(f232(a1),f2(a1)),x79752))+P1(f775(x79751,f775(f775(f82(a1),x79754),f775(f775(f83(a1),x79752),x79753)))) % 186.05/186.63 [7976]~P1(f775(x79761,x79764))+P1(f775(x79761,f812(x79762,x79761,x79763)))+~P1(f775(f775(f233(a1),f2(a1)),x79763))+~P1(f775(f775(f232(a1),f2(a1)),x79762))+P1(f775(x79761,f775(f775(f3(a1),x79764),f775(f775(f83(a1),x79762),x79763)))) % 186.05/186.63 [7977]~P62(x79771)+P1(f775(f775(f233(x79771),x79772),f2(x79771)))+P1(f775(f775(f233(x79771),f2(x79771)),x79772))+P1(f775(f775(f233(x79771),f2(x79771)),x79773))+~P1(f775(f775(f233(x79771),f775(f775(f283(x79771),x79774),x79772)),x79773)) % 186.05/186.63 [7978]~P62(x79781)+P1(f775(f775(f233(x79781),x79782),f2(x79781)))+P1(f775(f775(f233(x79781),f2(x79781)),x79782))+P1(f775(f775(f232(x79781),f2(x79781)),x79783))+~P1(f775(f775(f232(x79781),f775(f775(f283(x79781),x79784),x79782)),x79783)) % 186.05/186.63 [8022]~E(x80221,f775(f775(f82(a1),f775(f775(f83(a1),x80222),x80223)),x80224))+~P1(f775(f775(f233(a1),f2(a1)),x80222))+~P1(f775(f775(f232(a1),f2(a1)),x80224))+~P1(f775(f775(f233(a1),x80224),x80222))+P1(f775(f56(x80221,x80222),f775(f775(f241(a1,a1),x80223),x80224))) % 186.05/186.63 [8139]~P62(x81391)+P1(f775(f775(f233(x81391),x81392),f2(x81391)))+~P1(f775(f775(f233(x81391),f2(x81391)),x81394))+~P1(f775(f775(f233(x81391),x81393),f775(f775(f83(x81391),x81394),x81392)))+P1(f775(f775(f233(x81391),f775(f775(f283(x81391),x81393),x81392)),x81394)) % 186.05/186.63 [8140]~P62(x81401)+P1(f775(f775(f233(x81401),x81402),f2(x81401)))+~P1(f775(f775(f232(x81401),f2(x81401)),x81404))+~P1(f775(f775(f232(x81401),x81403),f775(f775(f83(x81401),x81404),x81402)))+P1(f775(f775(f232(x81401),f775(f775(f283(x81401),x81403),x81402)),x81404)) % 186.05/186.63 [8218]~P62(x82181)+P1(f775(f775(f233(x82181),x82182),f2(x82181)))+~P1(f775(f775(f233(x82181),x82183),f2(x82181)))+P1(f775(f775(f233(x82181),x82183),f775(f775(f283(x82181),x82184),x82182)))+~P1(f775(f775(f233(x82181),f775(f775(f83(x82181),x82183),x82182)),x82184)) % 186.05/186.63 [8219]~P62(x82191)+P1(f775(f775(f233(x82191),x82192),f2(x82191)))+~P1(f775(f775(f232(x82191),x82193),f2(x82191)))+P1(f775(f775(f232(x82191),x82193),f775(f775(f283(x82191),x82194),x82192)))+~P1(f775(f775(f232(x82191),f775(f775(f83(x82191),x82193),x82192)),x82194)) % 186.05/186.63 [8378]~P62(x83781)+~P1(f775(f775(f233(x83781),x83782),f2(x83781)))+P1(f775(f775(f233(x83781),f2(x83781)),x83782))+~P1(f775(f775(f233(x83781),f775(f775(f283(x83781),x83784),x83782)),x83783))+P1(f775(f775(f233(x83781),f775(f775(f83(x83781),x83783),x83782)),x83784)) % 186.05/186.63 [8379]~P62(x83791)+~P1(f775(f775(f233(x83791),x83792),f2(x83791)))+P1(f775(f775(f233(x83791),f2(x83791)),x83792))+~P1(f775(f775(f233(x83791),f775(f775(f83(x83791),x83794),x83792)),x83793))+P1(f775(f775(f233(x83791),f775(f775(f283(x83791),x83793),x83792)),x83794)) % 186.05/186.63 [8380]~P62(x83801)+~P1(f775(f775(f233(x83801),x83802),f2(x83801)))+P1(f775(f775(f233(x83801),f2(x83801)),x83802))+~P1(f775(f775(f232(x83801),f775(f775(f283(x83801),x83804),x83802)),x83803))+P1(f775(f775(f232(x83801),f775(f775(f83(x83801),x83803),x83802)),x83804)) % 186.05/186.63 [8381]~P62(x83811)+~P1(f775(f775(f233(x83811),x83812),f2(x83811)))+P1(f775(f775(f233(x83811),f2(x83811)),x83812))+~P1(f775(f775(f232(x83811),f775(f775(f83(x83811),x83814),x83812)),x83813))+P1(f775(f775(f232(x83811),f775(f775(f283(x83811),x83813),x83812)),x83814)) % 186.05/186.63 [8400]~P62(x84001)+~P1(f775(f775(f233(x84001),f2(x84001)),x84004))+P1(f775(f775(f233(x84001),f2(x84001)),x84002))+~P1(f775(f775(f233(x84001),f775(f775(f83(x84001),x84004),x84002)),x84003))+P1(f775(f775(f233(x84001),f775(f775(f283(x84001),x84003),x84002)),x84004)) % 186.05/186.63 [8401]~P62(x84011)+~P1(f775(f775(f232(x84011),f2(x84011)),x84014))+P1(f775(f775(f233(x84011),f2(x84011)),x84012))+~P1(f775(f775(f232(x84011),f775(f775(f83(x84011),x84014),x84012)),x84013))+P1(f775(f775(f232(x84011),f775(f775(f283(x84011),x84013),x84012)),x84014)) % 186.05/186.63 [8478]~P62(x84781)+~P1(f775(f775(f233(x84781),x84784),f2(x84781)))+~P1(f775(f775(f233(x84781),x84783),f775(f775(f83(x84781),x84782),x84784)))+P1(f775(f775(f233(x84781),x84782),f775(f775(f283(x84781),x84783),x84784)))+~P1(f775(f775(f233(x84781),f775(f775(f83(x84781),x84782),x84784)),x84783)) % 186.05/186.63 [8479]~P62(x84791)+~P1(f775(f775(f233(x84791),x84792),f2(x84791)))+~P1(f775(f775(f233(x84791),x84793),f775(f775(f83(x84791),x84792),x84794)))+P1(f775(f775(f233(x84791),x84792),f775(f775(f283(x84791),x84793),x84794)))+~P1(f775(f775(f233(x84791),f775(f775(f83(x84791),x84792),x84794)),x84793)) % 186.05/186.63 [8480]~P62(x84801)+~P1(f775(f775(f233(x84801),x84804),f2(x84801)))+~P1(f775(f775(f232(x84801),x84803),f775(f775(f83(x84801),x84802),x84804)))+P1(f775(f775(f232(x84801),x84802),f775(f775(f283(x84801),x84803),x84804)))+~P1(f775(f775(f232(x84801),f775(f775(f83(x84801),x84802),x84804)),x84803)) % 186.05/186.63 [8481]~P62(x84811)+~P1(f775(f775(f232(x84811),x84812),f2(x84811)))+~P1(f775(f775(f232(x84811),x84813),f775(f775(f83(x84811),x84812),x84814)))+P1(f775(f775(f232(x84811),x84812),f775(f775(f283(x84811),x84813),x84814)))+~P1(f775(f775(f232(x84811),f775(f775(f83(x84811),x84812),x84814)),x84813)) % 186.05/186.63 [8580]~P62(x85801)+~P1(f775(f775(f233(x85801),x85803),f2(x85801)))+~P1(f775(f775(f233(x85801),x85802),f775(f775(f83(x85801),x85804),x85803)))+~P1(f775(f775(f233(x85801),f775(f775(f83(x85801),x85804),x85803)),x85802))+P1(f775(f775(f233(x85801),f775(f775(f283(x85801),x85802),x85803)),x85804)) % 186.05/186.63 [8581]~P62(x85811)+~P1(f775(f775(f233(x85811),x85813),f2(x85811)))+~P1(f775(f775(f232(x85811),x85812),f775(f775(f83(x85811),x85814),x85813)))+~P1(f775(f775(f232(x85811),f775(f775(f83(x85811),x85814),x85813)),x85812))+P1(f775(f775(f232(x85811),f775(f775(f283(x85811),x85812),x85813)),x85814)) % 186.05/186.63 [8595]~P62(x85951)+~P1(f775(f775(f233(x85951),f2(x85951)),x85954))+~P1(f775(f775(f233(x85951),x85952),f775(f775(f83(x85951),x85954),x85953)))+~P1(f775(f775(f233(x85951),f775(f775(f83(x85951),x85954),x85953)),x85952))+P1(f775(f775(f233(x85951),f775(f775(f283(x85951),x85952),x85953)),x85954)) % 186.05/186.63 [8596]~P62(x85961)+~P1(f775(f775(f232(x85961),f2(x85961)),x85964))+~P1(f775(f775(f232(x85961),x85962),f775(f775(f83(x85961),x85964),x85963)))+~P1(f775(f775(f232(x85961),f775(f775(f83(x85961),x85964),x85963)),x85962))+P1(f775(f775(f232(x85961),f775(f775(f283(x85961),x85962),x85963)),x85964)) % 186.05/186.63 [8753]E(f775(f775(f3(a1),f438(x87531,x87532,x87533,x87534)),f439(x87531,x87532,x87533,x87534)),x87534)+~P1(f775(f775(f233(a1),f2(a1)),x87533))+~P1(f775(f775(f334(a1),x87532),x87531))+~P1(f775(f775(f233(a1),x87534),x87532))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x87534),x87533)),x87532)) % 186.05/186.63 [8814]~P1(f775(x88141,x88142))+~P1(f775(f775(f233(a1),f2(a1)),x88144))+~P1(f775(f775(f232(a1),f2(a1)),x88143))+~P1(f775(x88141,f775(f775(f82(a1),f807(x88143,x88141,x88144)),x88144)))+P1(f775(x88141,f775(f775(f82(a1),x88142),f775(f775(f83(a1),x88143),x88144)))) % 186.05/186.63 [8815]~P1(f775(x88151,x88152))+~P1(f775(f775(f233(a1),f2(a1)),x88154))+~P1(f775(f775(f232(a1),f2(a1)),x88153))+~P1(f775(x88151,f775(f775(f3(a1),f812(x88153,x88151,x88154)),x88154)))+P1(f775(x88151,f775(f775(f3(a1),x88152),f775(f775(f83(a1),x88153),x88154)))) % 186.05/186.63 [8954]~P1(f775(f775(f233(a1),f2(a1)),x89543))+~P1(f775(f775(f334(a1),x89542),x89541))+~P1(f775(f775(f233(a1),x89544),x89542))+P1(f775(f775(f334(a1),f438(x89541,x89542,x89543,x89544)),x89541))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x89544),x89543)),x89542)) % 186.05/186.63 [8974]E(f775(f775(f3(a1),f431(x89741,x89742,x89743,x89744)),f432(x89741,x89742,x89743,x89744)),x89744)+~P1(f775(f775(f233(a1),f2(a1)),x89743))+~P1(f775(f775(f232(a1),x89744),x89742))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x89742),f80(a1))),x89741))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x89744),x89743)),x89742)) % 186.05/186.63 [9006]~P1(f775(f775(f233(a1),f2(a1)),x90062))+~P1(f775(f775(f334(a1),x90063),x90064))+~P1(f775(f775(f233(a1),x90061),x90063))+P1(f775(f775(f334(a1),f439(x90064,x90063,x90062,x90061)),f295(a1,f80(a1),x90062)))+P1(f775(f775(f233(a1),f775(f775(f82(a1),x90061),x90062)),x90063)) % 186.05/186.63 [9085]~P1(f775(f775(f233(a1),f2(a1)),x90853))+~P1(f775(f775(f232(a1),x90854),x90852))+P1(f775(f775(f334(a1),f431(x90851,x90852,x90853,x90854)),x90851))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x90852),f80(a1))),x90851))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x90854),x90853)),x90852)) % 186.05/186.63 [9124]~P1(f775(f775(f233(a1),f2(a1)),x91242))+~P1(f775(f775(f232(a1),x91241),x91243))+P1(f775(f775(f334(a1),f432(x91244,x91243,x91242,x91241)),f295(a1,f80(a1),x91242)))+~P1(f775(f775(f334(a1),f775(f775(f82(a1),x91243),f80(a1))),x91244))+P1(f775(f775(f232(a1),f775(f775(f82(a1),x91241),x91242)),x91243)) % 186.05/186.63 [9390]~P36(x93901,x93903)+~P30(x93901,x93904)+P36(x93901,f775(f775(f103(f857(f856(x93901,x93901),a844)),x93902),x93903))+~P1(f775(f775(f232(f857(f856(x93901,x93901),a844)),x93902),f775(f240(f857(f856(x93901,x93901),a844),f857(f856(x93901,x93901),a844)),x93904)))+~P1(f775(f775(f232(f857(f856(x93901,x93901),a844)),x93903),f775(f250(f857(f856(x93901,x93901),a844),f857(f856(x93901,x93901),a844)),x93904))) % 186.05/186.63 [9658]~E(f775(f708(x96581,x96584,x96583,x96582),f712(x96581,x96584,x96583,x96582)),f183(f851(a842)))+P1(f775(f775(f233(a1),f711(x96581,x96584,x96583,x96582)),f712(x96581,x96584,x96583,x96582)))+P1(f775(f775(f775(x96581,x96582),x96583),x96584))+P1(f775(f775(f775(x96581,f708(x96581,x96584,x96583,x96582)),f711(x96581,x96584,x96583,x96582)),f775(f775(f82(a1),f712(x96581,x96584,x96583,x96582)),f80(a1))))+~P1(f775(f321(f856(f857(a1,f854(f851(a842))),f856(a1,a1)),a311),f775(f775(f241(f857(a1,f854(f851(a842))),f856(a1,a1)),x96582),f775(f775(f241(a1,a1),x96583),x96584)))) % 186.05/186.63 [9759]~P22(x97592,x97594,x97593)+E(x97591,f180(f857(x97592,a844)))+~P1(f775(f63(x97592),x97591))+P1(f775(f775(f334(x97592),f775(x97593,x97591)),x97591))+~P1(f775(f775(f334(x97592),f775(f775(x97594,f458(x97591,x97593,x97594,x97592)),f459(x97591,x97593,x97594,x97592))),f775(f775(f302(x97592),f458(x97591,x97593,x97594,x97592)),f775(f775(f302(x97592),f459(x97591,x97593,x97594,x97592)),f180(f857(x97592,a844)))))) % 186.05/186.63 [9310]~P53(x93101,x93101,x93104)+P1(f775(f775(f334(f856(x93101,x93101)),f775(f775(f241(x93101,x93101),x93102),x93103)),f300(x93101,x93104)))+P1(f775(f775(f334(f856(x93101,x93101)),f775(f775(f241(x93101,x93101),x93103),x93102)),f300(x93101,x93104)))+~P1(f775(f775(f334(f856(x93101,x93101)),f775(f775(f241(x93101,x93101),x93105),x93102)),f300(x93101,x93104)))+~P1(f775(f775(f334(f856(x93101,x93101)),f775(f775(f241(x93101,x93101),x93105),x93103)),f300(x93101,x93104))) % 186.05/186.63 [5490]E(x54901,f2(a850))+~E(f775(f42(x54902),x54905),x54901)+E(f775(f42(x54902),x54903),f775(a114,x54901))+~E(x54903,f775(f775(f302(x54902),x54904),x54905))+P1(f775(f775(f334(x54902),x54904),x54905)) % 186.05/186.63 [5611]~P61(x56112)+E(x56111,f2(x56112))+E(x56113,f2(x56112))+~E(f775(f775(f283(x56112),x56114),x56113),f775(f775(f283(x56112),x56115),x56111))+E(f775(f775(f83(x56112),x56114),x56111),f775(f775(f83(x56112),x56115),x56113)) % 186.05/186.63 [5612]~P61(x56122)+E(x56121,f2(x56122))+E(x56123,f2(x56122))+~E(f775(f775(f83(x56122),x56124),x56123),f775(f775(f83(x56122),x56125),x56121))+E(f775(f775(f283(x56122),x56124),x56121),f775(f775(f283(x56122),x56125),x56123)) % 186.05/186.63 [5685]~E(f775(f42(x56851),x56855),x56853)+~E(x56855,f180(f857(x56851,a844)))+E(f775(f42(x56851),x56852),f775(a114,x56853))+~E(x56852,f775(f775(f302(x56851),x56854),x56855))+P1(f775(f775(f334(x56851),x56854),x56855)) % 186.05/186.63 [5912]~P85(x59122)+~E(f775(x59123,x59125),f2(x59122))+E(f775(f775(f11(x59121,x59122),x59123),x59124),f2(x59122))+~P1(f775(f63(x59121),x59124))+~P1(f775(f775(f334(x59121),x59125),x59124)) % 186.05/186.63 [6297]~P100(x62973)+E(x62971,x62972)+~E(f775(f294(x62973,x62974),x62971),f775(f294(x62973,x62975),x62972))+~P1(f775(f775(f233(x62973),x62975),x62972))+~P1(f775(f775(f233(x62973),x62974),x62971)) % 186.05/186.63 [6298]~P100(x62983)+E(x62981,x62982)+~E(f775(f294(x62983,x62981),x62984),f775(f294(x62983,x62982),x62985))+~P1(f775(f775(f233(x62983),x62982),x62985))+~P1(f775(f775(f233(x62983),x62981),x62984)) % 186.05/186.63 [7409]~P100(x74091)+~P18(x74091,f775(f775(f125(x74091),x74094),x74095))+~P1(f775(f775(f334(x74091),x74093),f775(f158(x74091),x74095)))+~P1(f775(f775(f334(x74091),x74092),f775(f158(x74091),x74094)))+P1(f775(f775(f232(x74091),x74092),x74093)) % 186.05/186.63 [8512]~P99(x85121)+~P1(f775(f775(f233(f857(x85121,a844)),f295(x85121,x85125,x85122)),f295(x85121,x85124,x85123)))+~P1(f775(f775(f232(x85121),x85125),x85122))+P1(f775(f775(f233(x85121),x85122),x85123))+P1(f775(f775(f233(x85121),x85124),x85125)) % 186.05/186.63 [9803]~P21(x98032,x98035,x98033)+E(x98031,f180(f857(x98032,a844)))+~E(f775(f775(x98035,f775(x98034,f576(x98031,x98034,x98033,x98035,x98032))),f775(x98034,f577(x98031,x98034,x98033,x98035,x98032))),f775(x98034,f775(f775(x98035,f576(x98031,x98034,x98033,x98035,x98032)),f577(x98031,x98034,x98033,x98035,x98032))))+E(f775(x98033,f775(f303(x98032,x98032,x98034),x98031)),f775(x98034,f775(x98033,x98031)))+~P1(f775(f63(x98032),x98031)) % 186.05/186.63 [6294]~P22(x62942,x62945,x62943)+E(x62941,f180(f857(x62942,a844)))+~P1(f775(f63(x62942),x62941))+E(f775(x62943,f775(f775(f302(x62942),x62944),x62941)),f775(f775(x62945,x62944),f775(x62943,x62941)))+P1(f775(f775(f334(x62942),x62944),x62941)) % 186.05/186.63 [7146]~P21(x71462,x71463,x71464)+E(f775(f775(x71463,f775(x71464,x71461)),f775(x71464,x71465)),f775(x71464,x71465))+E(x71461,f180(f857(x71462,a844)))+~P1(f775(f63(x71462),x71465))+~P1(f775(f775(f232(f857(x71462,a844)),x71461),x71465)) % 186.05/186.63 [7550]~P22(x75504,x75505,x75501)+E(f775(x75501,x75502),x75503)+~P1(f775(f63(x75504),x75502))+~E(f775(f775(f3(f857(x75504,a844)),x75502),f775(f775(f302(x75504),x75503),f180(f857(x75504,a844)))),f180(f857(x75504,a844)))+~P1(f775(f775(f334(x75504),x75503),x75502)) % 186.05/186.63 [7697]E(x76971,x76972)+~E(f775(f181(f851(x76973)),x76972),f775(f181(f851(x76974)),x76975))+~E(f775(f181(f851(x76973)),x76971),f775(f181(f851(x76974)),x76975))+~E(f166(x76974,x76973,f775(f775(f167(x76974,x76973),x76975),x76971)),f166(x76974,x76973,f775(f775(f167(x76974,x76973),x76975),x76972)))+~P1(f775(f127(x76974),x76975)) % 186.05/186.63 [8435]~P70(x84351)+~P112(x84351)+~P1(f775(f63(x84352),x84355))+P1(f775(f775(f279(x84351),f775(f775(f11(x84352,x84351),x84353),x84354)),f775(f775(f11(x84352,x84351),x84353),x84355)))+~P1(f775(f775(f232(f857(x84352,a844)),x84354),x84355)) % 186.05/186.63 [8485]E(x84851,x84852)+~P12(x84853,x84854,x84855)+E(f775(f775(f104(f857(x84853,a844)),x84851),x84852),f180(f857(x84853,a844)))+~P1(f775(f775(f334(f857(x84853,a844)),x84852),f775(f775(f61(x84853),x84854),x84855)))+~P1(f775(f775(f334(f857(x84853,a844)),x84851),f775(f775(f61(x84853),x84854),x84855))) % 186.05/186.63 [9188]~P66(x91882)+~E(f775(x91883,f478(x91883,x91884,x91885,x91881,x91882)),f2(x91882))+E(f775(f775(f8(x91881,x91882),x91883),x91884),f775(f775(f8(x91881,x91882),x91883),x91885))+~P1(f775(f63(x91881),x91885))+~P1(f775(f775(f232(f857(x91881,a844)),x91884),x91885)) % 186.05/186.63 [9189]~P66(x91892)+~E(f775(x91893,f481(x91893,x91894,x91895,x91891,x91892)),f2(x91892))+E(f775(f775(f8(x91891,x91892),x91893),x91894),f775(f775(f8(x91891,x91892),x91893),x91895))+~P1(f775(f63(x91891),x91895))+~P1(f775(f775(f232(f857(x91891,a844)),x91894),x91895)) % 186.05/186.63 [9190]~P70(x91902)+~E(f775(x91903,f479(x91903,x91904,x91905,x91901,x91902)),f80(x91902))+E(f775(f775(f11(x91901,x91902),x91903),x91904),f775(f775(f11(x91901,x91902),x91903),x91905))+~P1(f775(f63(x91901),x91905))+~P1(f775(f775(f232(f857(x91901,a844)),x91904),x91905)) % 186.05/186.63 [9191]~P70(x91912)+~E(f775(x91913,f480(x91913,x91914,x91915,x91911,x91912)),f80(x91912))+E(f775(f775(f11(x91911,x91912),x91913),x91914),f775(f775(f11(x91911,x91912),x91913),x91915))+~P1(f775(f63(x91911),x91915))+~P1(f775(f775(f232(f857(x91911,a844)),x91914),x91915)) % 186.05/186.63 [9641]~P81(x96411)+~P1(f775(f63(x96412),x96415))+~P1(f775(f775(f232(x96411),f2(x96411)),f775(x96413,f441(x96413,x96414,x96415,x96412,x96411))))+P1(f775(f775(f232(x96411),f775(f775(f8(x96412,x96411),x96413),x96414)),f775(f775(f8(x96412,x96411),x96413),x96415)))+~P1(f775(f775(f232(f857(x96412,a844)),x96414),x96415)) % 186.05/186.63 [7406]E(x74061,f2(a850))+P1(f775(x74062,x74063))+~E(x74064,f775(f775(f82(a850),f775(f775(f83(a850),x74061),x74063)),x74065))+~P1(f775(f775(f233(a850),x74065),x74061))+~P1(f775(x74062,f775(f775(f43(a850),x74064),x74061))) % 186.05/186.63 [7489]E(x74891,f2(a850))+P1(f775(x74892,x74893))+~P1(f775(x74892,f52(a850,x74894,x74891)))+~E(x74894,f775(f775(f82(a850),f775(f775(f83(a850),x74891),x74895)),x74893))+~P1(f775(f775(f233(a850),x74893),x74891)) % 186.05/186.63 [7785]~P61(x77853)+E(f775(x77851,x77852),f2(x77853))+~P1(f775(f63(x77854),x77855))+E(f775(f775(f11(x77854,x77853),x77851),f775(f775(f3(f857(x77854,a844)),x77855),f775(f775(f302(x77854),x77852),f180(f857(x77854,a844))))),f775(f775(f11(x77854,x77853),x77851),x77855))+P1(f775(f775(f334(x77854),x77852),x77855)) % 186.05/186.63 [8179]~P66(x81791)+~P1(f775(f63(x81792),x81795))+~P1(f775(f63(x81792),x81794))+~E(f775(f775(f104(f857(x81792,a844)),x81794),x81795),f180(f857(x81792,a844)))+E(f775(f775(f82(x81791),f775(f775(f8(x81792,x81791),x81793),x81794)),f775(f775(f8(x81792,x81791),x81793),x81795)),f775(f775(f8(x81792,x81791),x81793),f775(f775(f103(f857(x81792,a844)),x81794),x81795))) % 186.05/186.63 [8181]~P70(x81811)+~P1(f775(f63(x81812),x81815))+~P1(f775(f63(x81812),x81814))+~E(f775(f775(f104(f857(x81812,a844)),x81814),x81815),f180(f857(x81812,a844)))+E(f775(f775(f83(x81811),f775(f775(f11(x81812,x81811),x81813),x81814)),f775(f775(f11(x81812,x81811),x81813),x81815)),f775(f775(f11(x81812,x81811),x81813),f775(f775(f103(f857(x81812,a844)),x81814),x81815))) % 186.05/186.63 [8271]~P61(x82713)+E(f775(x82711,x82712),f2(x82713))+~P1(f775(f63(x82714),x82715))+E(f775(f775(f11(x82714,x82713),x82711),f775(f775(f3(f857(x82714,a844)),x82715),f775(f775(f302(x82714),x82712),f180(f857(x82714,a844))))),f775(f775(f283(x82713),f775(f775(f11(x82714,x82713),x82711),x82715)),f775(x82711,x82712)))+~P1(f775(f775(f334(x82714),x82712),x82715)) % 186.05/186.63 [8936]~P12(x89361,x89365,x89364)+~E(f775(f775(f61(x89361),f775(f775(f302(x89361),x89362),f180(f857(x89361,a844)))),x89364),f775(f775(f61(x89361),f775(f775(f302(x89361),x89363),f180(f857(x89361,a844)))),x89364))+~P1(f775(f775(f334(x89361),x89363),x89365))+~P1(f775(f775(f334(x89361),x89362),x89365))+P1(f775(f775(f334(f856(x89361,x89361)),f775(f775(f241(x89361,x89361),x89362),x89363)),x89364)) % 186.05/186.63 [8953]~P12(x89531,x89535,x89533)+E(f775(f775(f61(x89531),f775(f775(f302(x89531),x89532),f180(f857(x89531,a844)))),x89533),f775(f775(f61(x89531),f775(f775(f302(x89531),x89534),f180(f857(x89531,a844)))),x89533))+~P1(f775(f775(f334(x89531),x89534),x89535))+~P1(f775(f775(f334(x89531),x89532),x89535))+~P1(f775(f775(f334(f856(x89531,x89531)),f775(f775(f241(x89531,x89531),x89532),x89534)),x89533)) % 186.05/186.63 [9215]~P70(x92151)+~P1(f775(f63(x92152),x92155))+~P1(f775(f63(x92152),x92154))+~E(f775(f775(f104(f857(x92152,a844)),x92154),x92155),f180(f857(x92152,a844)))+E(f775(f775(f83(x92151),f775(f775(f775(f67(x92151,x92152,f83(x92151)),x92153),f80(x92151)),x92154)),f775(f775(f775(f67(x92151,x92152,f83(x92151)),x92153),f80(x92151)),x92155)),f775(f775(f775(f67(x92151,x92152,f83(x92151)),x92153),f80(x92151)),f775(f775(f103(f857(x92152,a844)),x92154),x92155))) % 186.05/186.63 [9225]~P66(x92251)+~E(f775(x92253,f510(x92253,x92255,x92254,x92252,x92251)),f2(x92251))+~P1(f775(f63(x92252),x92254))+~P1(f775(f63(x92252),x92255))+E(f775(f775(f82(x92251),f775(f775(f8(x92252,x92251),x92253),x92254)),f775(f775(f8(x92252,x92251),x92253),x92255)),f775(f775(f8(x92252,x92251),x92253),f775(f775(f103(f857(x92252,a844)),x92254),x92255))) % 186.05/186.63 [9226]~P66(x92261)+~E(f775(x92263,f514(x92263,x92265,x92264,x92262,x92261)),f2(x92261))+~P1(f775(f63(x92262),x92264))+~P1(f775(f63(x92262),x92265))+E(f775(f775(f82(x92261),f775(f775(f8(x92262,x92261),x92263),x92264)),f775(f775(f8(x92262,x92261),x92263),x92265)),f775(f775(f8(x92262,x92261),x92263),f775(f775(f103(f857(x92262,a844)),x92264),x92265))) % 186.05/186.63 [9227]~P70(x92271)+~E(f775(x92273,f511(x92273,x92275,x92274,x92272,x92271)),f80(x92271))+~P1(f775(f63(x92272),x92274))+~P1(f775(f63(x92272),x92275))+E(f775(f775(f83(x92271),f775(f775(f11(x92272,x92271),x92273),x92274)),f775(f775(f11(x92272,x92271),x92273),x92275)),f775(f775(f11(x92272,x92271),x92273),f775(f775(f103(f857(x92272,a844)),x92274),x92275))) % 186.05/186.63 [9228]~P70(x92281)+~E(f775(x92283,f513(x92283,x92285,x92284,x92282,x92281)),f80(x92281))+~P1(f775(f63(x92282),x92284))+~P1(f775(f63(x92282),x92285))+E(f775(f775(f83(x92281),f775(f775(f11(x92282,x92281),x92283),x92284)),f775(f775(f11(x92282,x92281),x92283),x92285)),f775(f775(f11(x92282,x92281),x92283),f775(f775(f103(f857(x92282,a844)),x92284),x92285))) % 186.05/186.63 [9432]~P70(x94321)+~E(f775(x94323,f531(x94323,x94325,x94324,x94322,x94321)),f80(x94321))+~P1(f775(f63(x94322),x94324))+~P1(f775(f63(x94322),x94325))+E(f775(f775(f83(x94321),f775(f775(f775(f67(x94321,x94322,f83(x94321)),x94323),f80(x94321)),x94324)),f775(f775(f775(f67(x94321,x94322,f83(x94321)),x94323),f80(x94321)),x94325)),f775(f775(f775(f67(x94321,x94322,f83(x94321)),x94323),f80(x94321)),f775(f775(f103(f857(x94322,a844)),x94324),x94325))) % 186.05/186.63 [9533]~P66(x95332)+E(f775(f775(f8(x95331,x95332),x95333),x95334),f775(f775(f8(x95331,x95332),x95333),x95335))+~P1(f775(f63(x95331),x95335))+~P1(f775(f775(f232(f857(x95331,a844)),x95334),x95335))+P1(f775(f775(f334(x95331),f478(x95333,x95334,x95335,x95331,x95332)),f775(f775(f3(f857(x95331,a844)),x95335),x95334))) % 186.05/186.63 [9534]~P66(x95342)+E(f775(f775(f8(x95341,x95342),x95343),x95344),f775(f775(f8(x95341,x95342),x95343),x95345))+~P1(f775(f63(x95341),x95345))+~P1(f775(f775(f232(f857(x95341,a844)),x95344),x95345))+P1(f775(f775(f334(x95341),f481(x95343,x95344,x95345,x95341,x95342)),f775(f775(f3(f857(x95341,a844)),x95345),x95344))) % 186.05/186.63 [9535]~P70(x95352)+E(f775(f775(f11(x95351,x95352),x95353),x95354),f775(f775(f11(x95351,x95352),x95353),x95355))+~P1(f775(f63(x95351),x95355))+~P1(f775(f775(f232(f857(x95351,a844)),x95354),x95355))+P1(f775(f775(f334(x95351),f479(x95353,x95354,x95355,x95351,x95352)),f775(f775(f3(f857(x95351,a844)),x95355),x95354))) % 186.05/186.63 [9536]~P70(x95362)+E(f775(f775(f11(x95361,x95362),x95363),x95364),f775(f775(f11(x95361,x95362),x95363),x95365))+~P1(f775(f63(x95361),x95365))+~P1(f775(f775(f232(f857(x95361,a844)),x95364),x95365))+P1(f775(f775(f334(x95361),f480(x95363,x95364,x95365,x95361,x95362)),f775(f775(f3(f857(x95361,a844)),x95365),x95364))) % 186.05/186.63 [9550]~P66(x95501)+~P1(f775(f63(x95502),x95504))+~P1(f775(f63(x95502),x95505))+E(f775(f775(f82(x95501),f775(f775(f8(x95502,x95501),x95503),x95504)),f775(f775(f8(x95502,x95501),x95503),x95505)),f775(f775(f8(x95502,x95501),x95503),f775(f775(f103(f857(x95502,a844)),x95504),x95505)))+P1(f775(f775(f334(x95502),f510(x95503,x95505,x95504,x95502,x95501)),f775(f775(f104(f857(x95502,a844)),x95504),x95505))) % 186.05/186.63 [9551]~P66(x95511)+~P1(f775(f63(x95512),x95514))+~P1(f775(f63(x95512),x95515))+E(f775(f775(f82(x95511),f775(f775(f8(x95512,x95511),x95513),x95514)),f775(f775(f8(x95512,x95511),x95513),x95515)),f775(f775(f8(x95512,x95511),x95513),f775(f775(f103(f857(x95512,a844)),x95514),x95515)))+P1(f775(f775(f334(x95512),f514(x95513,x95515,x95514,x95512,x95511)),f775(f775(f104(f857(x95512,a844)),x95514),x95515))) % 186.05/186.63 [9552]~P70(x95521)+~P1(f775(f63(x95522),x95524))+~P1(f775(f63(x95522),x95525))+E(f775(f775(f83(x95521),f775(f775(f11(x95522,x95521),x95523),x95524)),f775(f775(f11(x95522,x95521),x95523),x95525)),f775(f775(f11(x95522,x95521),x95523),f775(f775(f103(f857(x95522,a844)),x95524),x95525)))+P1(f775(f775(f334(x95522),f511(x95523,x95525,x95524,x95522,x95521)),f775(f775(f104(f857(x95522,a844)),x95524),x95525))) % 186.05/186.63 [9553]~P70(x95531)+~P1(f775(f63(x95532),x95534))+~P1(f775(f63(x95532),x95535))+E(f775(f775(f83(x95531),f775(f775(f11(x95532,x95531),x95533),x95534)),f775(f775(f11(x95532,x95531),x95533),x95535)),f775(f775(f11(x95532,x95531),x95533),f775(f775(f103(f857(x95532,a844)),x95534),x95535)))+P1(f775(f775(f334(x95532),f513(x95533,x95535,x95534,x95532,x95531)),f775(f775(f104(f857(x95532,a844)),x95534),x95535))) % 186.05/186.63 [9565]~P81(x95655)+~P1(f775(f63(x95651),x95654))+P1(f775(f775(f232(x95655),f775(f775(f8(x95651,x95655),x95652),x95653)),f775(f775(f8(x95651,x95655),x95652),x95654)))+~P1(f775(f775(f232(f857(x95651,a844)),x95653),x95654))+P1(f775(f775(f334(x95651),f441(x95652,x95653,x95654,x95651,x95655)),f775(f775(f3(f857(x95651,a844)),x95654),x95653))) % 186.05/186.63 [9607]~P70(x96071)+~P1(f775(f63(x96072),x96074))+~P1(f775(f63(x96072),x96075))+E(f775(f775(f83(x96071),f775(f775(f775(f67(x96071,x96072,f83(x96071)),x96073),f80(x96071)),x96074)),f775(f775(f775(f67(x96071,x96072,f83(x96071)),x96073),f80(x96071)),x96075)),f775(f775(f775(f67(x96071,x96072,f83(x96071)),x96073),f80(x96071)),f775(f775(f103(f857(x96072,a844)),x96074),x96075)))+P1(f775(f775(f334(x96072),f531(x96073,x96075,x96074,x96072,x96071)),f775(f775(f104(f857(x96072,a844)),x96074),x96075))) % 186.05/186.63 [8662]~P22(x86621,x86624,x86625)+~P1(f775(f63(x86621),x86622))+E(f775(f775(f3(f857(x86621,a844)),x86622),f775(f775(f302(x86621),x86623),f180(f857(x86621,a844)))),f180(f857(x86621,a844)))+~P1(f775(f775(f334(x86621),x86623),x86622))+E(f775(f775(x86624,x86623),f775(x86625,f775(f775(f3(f857(x86621,a844)),x86622),f775(f775(f302(x86621),x86623),f180(f857(x86621,a844)))))),f775(x86625,x86622)) % 186.05/186.63 [8729]~P22(x87291,x87294,x87295)+~P1(f775(f63(x87291),x87293))+~P1(f775(f63(x87291),x87292))+E(f775(f775(f104(f857(x87291,a844)),x87292),x87293),f180(f857(x87291,a844)))+E(f775(f775(x87294,f775(x87295,f775(f775(f103(f857(x87291,a844)),x87292),x87293))),f775(x87295,f775(f775(f104(f857(x87291,a844)),x87292),x87293))),f775(f775(x87294,f775(x87295,x87292)),f775(x87295,x87293))) % 186.05/186.63 [9230]~P1(f775(f775(f232(a1),x92304),f2(a1)))+~P1(f775(f775(f233(a1),x92303),x92305))+P1(f775(f775(f232(a1),x92301),x92302))+~P1(f775(f775(f233(a1),x92303),x92304))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),f775(f775(f83(a1),x92303),x92302)),x92305)),f775(f775(f82(a1),f775(f775(f83(a1),x92303),x92301)),x92304))) % 186.05/186.63 [9232]~P1(f775(f775(f232(a1),f2(a1)),x92325))+P1(f775(f775(f232(a1),x92321),x92322))+~P1(f775(f775(f233(a1),x92323),x92324))+~P1(f775(f775(f233(a1),x92325),x92324))+~P1(f775(f775(f232(a1),f775(f775(f82(a1),f775(f775(f83(a1),x92324),x92321)),x92325)),f775(f775(f82(a1),f775(f775(f83(a1),x92324),x92322)),x92323))) % 186.05/186.63 [9345]~P61(x93455)+E(f775(x93451,f512(x93451,x93452,x93453,x93454,x93455)),f2(x93455))+~P1(f775(f63(x93454),x93453))+~P1(f775(f63(x93454),x93452))+E(f775(f775(f283(x93455),f775(f775(f83(x93455),f775(f775(f11(x93454,x93455),x93451),x93453)),f775(f775(f11(x93454,x93455),x93451),x93452))),f775(f775(f11(x93454,x93455),x93451),f775(f775(f104(f857(x93454,a844)),x93453),x93452))),f775(f775(f11(x93454,x93455),x93451),f775(f775(f103(f857(x93454,a844)),x93453),x93452))) % 186.05/186.63 [9600]~P61(x96001)+~P1(f775(f63(x96002),x96004))+~P1(f775(f63(x96002),x96005))+E(f775(f775(f283(x96001),f775(f775(f83(x96001),f775(f775(f11(x96002,x96001),x96003),x96004)),f775(f775(f11(x96002,x96001),x96003),x96005))),f775(f775(f11(x96002,x96001),x96003),f775(f775(f104(f857(x96002,a844)),x96004),x96005))),f775(f775(f11(x96002,x96001),x96003),f775(f775(f103(f857(x96002,a844)),x96004),x96005)))+P1(f775(f775(f334(x96002),f512(x96003,x96005,x96004,x96002,x96001)),f775(f775(f104(f857(x96002,a844)),x96004),x96005))) % 186.05/186.63 [8973]E(f775(f775(f125(x89731),x89732),x89733),f775(f775(f125(x89731),x89734),x89735))+~E(f775(f775(f159(x89731),f775(f181(f851(x89731)),x89734)),x89732),x89734)+~E(f775(f775(f159(x89731),f775(f181(f851(x89731)),x89732)),x89734),x89732)+~E(x89735,f775(f775(f125(x89731),f775(f775(f128(x89731),f775(f181(f851(x89731)),x89734)),x89732)),x89733))+~E(f775(f775(f125(x89731),f775(f775(f128(x89731),f775(f181(f851(x89731)),x89732)),x89734)),x89735),x89733) % 186.05/186.63 [9343]~P100(x93432)+E(f775(f775(f138(x93431,x93432,x93433),x93434),f151(x93431,x93434,x93435)),x93435)+~P18(x93432,f775(f775(f143(x93431,x93432),x93433),x93435))+~P1(f775(f775(f334(x93431),x93434),f775(f158(x93431),x93435)))+~E(f775(f131(x93431),f775(f126(x93431,f775(f775(f10(x93432,a844,x93431),f775(a330,f775(x93433,x93434))),x93433)),x93435)),x93434) % 186.05/186.63 [9655]~P64(x96551)+~P1(f775(f68(x96551,x96551,f83(x96551),x96552,x96553),x96555))+~P1(f775(f775(f334(x96551),x96554),x96553))+P1(f775(f775(f334(x96551),x96552),x96553))+P1(f775(f68(x96551,x96551,f83(x96551),x96554,f775(f775(f302(x96551),x96552),f775(f775(f3(f857(x96551,a844)),x96553),f775(f775(f302(x96551),x96554),f180(f857(x96551,a844)))))),x96555)) % 186.05/186.63 [7153]E(x71531,x71532)+~P29(x71534,x71535,x71533,x71536)+~E(f775(x71533,x71531),f775(x71533,x71532))+~P1(f775(f775(f334(x71534),x71532),x71536))+~P1(f775(f775(f334(x71534),x71531),x71536)) % 186.05/186.63 [6392]~P137(x63924)+E(x63921,x63922)+~E(x63925,x63926)+E(x63923,f2(x63924))+~E(f775(f775(f82(x63924),x63925),f775(f775(f83(x63924),x63923),x63921)),f775(f775(f82(x63924),x63926),f775(f775(f83(x63924),x63923),x63922))) % 186.05/186.63 [7469]~P100(x74691)+~P9(x74691)+~P1(f775(f775(f233(x74691),x74692),f775(x74695,x74696)))+~P1(f775(f775(f334(x74693),x74696),x74694))+P1(f775(f775(f233(x74691),x74692),f775(f775(f46(x74693,x74691),x74694),x74695))) % 186.05/186.63 [9818]~P85(x98186)+~P1(f775(f63(x98181),x98185))+P1(f775(f775(f334(x98181),f632(x98182,x98183,x98184,x98185,x98181,x98186)),x98184))+P1(f775(f775(f279(x98186),f775(f775(f11(x98181,x98186),x98183),x98184)),f775(f775(f11(x98181,x98186),x98182),x98185)))+~P1(f775(f775(f232(f857(x98181,a844)),x98184),x98185)) % 186.05/186.63 [9941]~P85(x99411)+~P1(f775(f63(x99412),x99416))+~P1(f775(f775(f279(x99411),f775(x99413,f632(x99415,x99413,x99414,x99416,x99412,x99411))),f775(x99415,f632(x99415,x99413,x99414,x99416,x99412,x99411))))+P1(f775(f775(f279(x99411),f775(f775(f11(x99412,x99411),x99413),x99414)),f775(f775(f11(x99412,x99411),x99415),x99416)))+~P1(f775(f775(f232(f857(x99412,a844)),x99414),x99416)) % 186.05/186.63 [8150]~P100(x81501)+~P9(x81501)+~P1(f775(f775(f233(x81501),f775(x81504,x81506)),x81505))+~P1(f775(f775(f334(x81502),x81506),x81503))+P1(f775(f775(f233(x81501),f775(f775(f47(x81502,x81501),x81503),x81504)),x81505)) % 186.05/186.63 [8407]~P23(x84072,x84075,x84076,x84071)+~P1(f775(f63(x84072),x84074))+~P1(f775(f63(x84072),x84073))+~E(f775(f775(f104(f857(x84072,a844)),x84073),x84074),f180(f857(x84072,a844)))+E(f775(x84071,f775(f775(f103(f857(x84072,a844)),x84073),x84074)),f775(f75(x84075,x84075,x84075,f775(x84071,x84073)),f775(x84071,x84074))) % 186.05/186.63 [9060]~P112(x90601)+~P108(x90601)+~P1(f775(f775(f279(x90601),x90602),x90605))+~P1(f775(f775(f279(x90601),x90602),f775(f775(f82(x90601),x90603),x90606)))+P1(f775(f775(f279(x90601),x90602),f775(f775(f82(x90601),f775(f775(f3(x90601),x90603),f775(f775(f83(x90601),x90604),x90605))),x90606))) % 186.05/186.63 [9220]~P112(x92201)+~P108(x92201)+~P1(f775(f775(f279(x92201),x92202),x92205))+P1(f775(f775(f279(x92201),x92202),f775(f775(f82(x92201),x92203),x92204)))+~P1(f775(f775(f279(x92201),x92202),f775(f775(f82(x92201),f775(f775(f3(x92201),x92203),f775(f775(f83(x92201),x92206),x92205))),x92204))) % 186.05/186.63 [8700]E(x87001,x87002)+~P55(x87004,x87005,x87006,x87003,x87007)+~E(f775(x87003,x87001),f775(x87003,x87002))+~P1(f775(f775(f334(x87005),x87002),x87007))+~P1(f775(f775(f334(x87005),x87001),x87007)) % 186.05/186.63 [9949]~P12(x99491,x99497,x99496)+~P16(x99491,f857(x99495,a844),x99496,x99494)+P1(f775(f775(f334(x99491),f509(x99492,x99493,x99494,x99495,x99496,x99497,x99491)),x99497))+~P1(f775(f775(f334(f857(x99491,a844)),x99493),f775(f775(f61(x99491),x99497),x99496)))+P1(f775(f775(f334(f857(x99495,a844)),f775(f775(f46(x99491,f857(x99495,a844)),x99493),x99494)),x99492)) % 186.05/186.63 [9996]~P12(x99962,x99966,x99967)+~P16(x99962,f857(x99961,a844),x99967,x99964)+~P1(f775(f775(f334(f857(x99962,a844)),x99963),f775(f775(f61(x99962),x99966),x99967)))+~P1(f775(f775(f334(f857(x99961,a844)),f775(x99964,f509(x99965,x99963,x99964,x99961,x99967,x99966,x99962))),x99965))+P1(f775(f775(f334(f857(x99961,a844)),f775(f775(f46(x99962,f857(x99961,a844)),x99963),x99964)),x99965)) % 186.05/186.63 [8317]~P70(x83172)+~P29(x83171,x83175,x83178,x83174)+~E(x83173,f775(f75(x83175,x83172,x83171,x83176),x83178))+~E(x83177,f775(f303(x83171,x83175,x83178),x83174))+E(f775(f775(f11(x83171,x83172),x83173),x83174),f775(f775(f11(x83175,x83172),x83176),x83177)) % 186.05/186.63 [9999]~P70(x99992)+~P29(x99995,x99991,x99998,x99997)+~E(f775(x99996,f535(x99993,x99996,x99994,x99997,x99998,x99991,x99995,x99992)),f775(f775(f75(x99991,x99992,x99995,x99993),x99998),f535(x99993,x99996,x99994,x99997,x99998,x99991,x99995,x99992)))+~E(x99994,f775(f303(x99995,x99991,x99998),x99997))+E(f775(f775(f11(x99991,x99992),x99993),x99994),f775(f775(f11(x99995,x99992),x99996),x99997)) % 186.05/186.63 [10002]~P66(x100022)+~P29(x100021,x100025,x100028,x100024)+~E(x100027,f775(f303(x100021,x100025,x100028),x100024))+E(f775(f775(f8(x100021,x100022),x100023),x100024),f775(f775(f8(x100025,x100022),x100026),x100027))+P1(f775(f775(f334(x100021),f637(x100026,x100023,x100027,x100024,x100028,x100025,x100021,x100022)),x100024)) % 186.05/186.63 [10003]~P70(x100032)+~P29(x100031,x100035,x100038,x100034)+~E(x100037,f775(f303(x100031,x100035,x100038),x100034))+E(f775(f775(f11(x100031,x100032),x100033),x100034),f775(f775(f11(x100035,x100032),x100036),x100037))+P1(f775(f775(f334(x100031),f535(x100036,x100033,x100037,x100034,x100038,x100035,x100031,x100032)),x100034)) % 186.05/186.63 [10007]~P66(x100072)+~P29(x100075,x100071,x100078,x100077)+~E(x100074,f775(f303(x100075,x100071,x100078),x100077))+~E(f775(x100076,f637(x100073,x100076,x100074,x100077,x100078,x100071,x100075,x100072)),f775(x100073,f775(x100078,f637(x100073,x100076,x100074,x100077,x100078,x100071,x100075,x100072))))+E(f775(f775(f8(x100071,x100072),x100073),x100074),f775(f775(f8(x100075,x100072),x100076),x100077)) % 186.05/186.63 [9408]~E(f775(f181(f851(x94082)),x94085),f775(f181(f851(x94081)),x94083))+~E(f775(f181(f851(x94082)),x94084),f775(f181(f851(x94081)),x94083))+~E(f775(f775(f775(f74(x94081,f854(x94082)),f166(x94081,x94082,f775(f775(f167(x94081,x94082),x94083),x94084))),x94086),f775(f227(x94082),x94087)),f775(f775(f775(f74(x94081,f854(x94082)),f166(x94081,x94082,f775(f775(f167(x94081,x94082),x94083),x94085))),x94086),f775(f227(x94082),x94088)))+E(f166(x94081,x94082,f775(f775(f167(x94081,x94082),x94083),x94084)),f166(x94081,x94082,f775(f775(f167(x94081,x94082),x94083),x94085)))+P1(f775(f775(f334(x94081),x94086),f775(f158(x94081),x94083))) % 186.05/186.63 [9503]~P27(x95036,x95032,x95035,x95037,x95038,x95031)+~P1(f775(f63(x95032),x95034))+~P1(f775(f63(x95032),x95033))+~E(f775(f775(f104(f857(x95032,a844)),x95033),x95034),f180(f857(x95032,a844)))+E(f775(x95031,f775(f775(f103(f857(x95032,a844)),x95033),x95034)),f775(f775(x95035,f775(x95031,x95033)),f775(x95031,x95034))) % 186.05/186.63 [9893]~P27(x98938,x98932,x98935,x98937,x98936,x98931)+~E(f775(x98936,f578(x98934,x98933,x98931,x98936,x98937,x98935,x98932)),x98937)+~P1(f775(f63(x98932),x98933))+~P1(f775(f63(x98932),x98934))+E(f775(x98931,f775(f775(f103(f857(x98932,a844)),x98933),x98934)),f775(f775(x98935,f775(x98931,x98933)),f775(x98931,x98934))) % 186.05/186.63 [9954]~P27(x99548,x99542,x99545,x99547,x99546,x99541)+~P1(f775(f63(x99542),x99543))+~P1(f775(f63(x99542),x99544))+E(f775(x99541,f775(f775(f103(f857(x99542,a844)),x99543),x99544)),f775(f775(x99545,f775(x99541,x99543)),f775(x99541,x99544)))+P1(f775(f775(f334(x99542),f578(x99544,x99543,x99541,x99546,x99547,x99545,x99542)),f775(f775(f104(f857(x99542,a844)),x99543),x99544))) % 186.05/186.63 [9646]~P12(x96464,x96468,x96465)+~P12(x96461,x96469,x96463)+~P17(x96461,x96464,f857(x96462,a844),x96463,x96465,x96467)+P16(x96461,f857(x96462,a844),x96463,f775(f775(f10(f857(x96464,f857(x96462,a844)),f857(x96462,a844),x96461),f775(f46(x96464,f857(x96462,a844)),f775(f277(x96464,x96464,x96465),f775(f775(f302(x96464),x96466),f180(f857(x96464,a844)))))),x96467))+~P1(f775(f775(f334(x96464),x96466),x96468)) % 186.05/186.63 [4931]~P122(x49312)+~P127(x49312)+~P138(x49312)+~P105(x49312)+E(x49311,f2(x49312))+~E(f775(f775(f242(x49312),x49311),x49313),f2(x49312)) % 186.05/186.63 [4932]~P122(x49322)+~P127(x49322)+~P138(x49322)+~P105(x49322)+~E(x49321,f2(a850))+~E(f775(f775(f242(x49322),x49323),x49321),f2(x49322)) % 186.05/186.63 [6372]~P81(x63721)+~E(x63723,f2(x63721))+~E(x63722,f2(x63721))+E(f775(f775(f82(x63721),x63722),x63723),f2(x63721))+~P1(f775(f775(f232(x63721),f2(x63721)),x63723))+~P1(f775(f775(f232(x63721),f2(x63721)),x63722)) % 186.05/186.63 [8758]~E(f775(f240(a850,a850),x87583),f2(a850))+~E(x87581,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x87583)),x87582)),f775(f250(a850,a850),x87583)))+P1(f775(f55(x87581,x87582),x87583))+~P1(f775(f775(f232(a850),f775(f250(a850,a850),x87583)),f2(a850)))+P1(f775(f775(f233(a850),f2(a850)),x87582))+~P1(f775(f775(f233(a850),x87582),f775(f250(a850,a850),x87583))) % 186.05/186.63 [8765]E(x87651,f2(a850))+~E(x87652,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x87653)),x87651)),f775(f250(a850,a850),x87653)))+P1(f775(f55(x87652,x87651),x87653))+~P1(f775(f775(f233(a850),f2(a850)),x87651))+~P1(f775(f775(f232(a850),f2(a850)),f775(f250(a850,a850),x87653)))+~P1(f775(f775(f233(a850),f775(f250(a850,a850),x87653)),x87651)) % 186.05/186.63 [8779]~E(f775(f240(a850,a850),x87793),f2(a850))+~E(x87791,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x87793)),x87792)),f775(f250(a850,a850),x87793)))+P1(f775(f55(x87791,x87792),x87793))+~P1(f775(f775(f233(a850),f2(a850)),x87792))+~P1(f775(f775(f232(a850),f2(a850)),f775(f250(a850,a850),x87793)))+~P1(f775(f775(f233(a850),f775(f250(a850,a850),x87793)),x87792)) % 186.05/186.63 [6774]~P93(x67742)+E(x67741,f180(f857(x67742,a844)))+E(x67743,f180(f857(x67742,a844)))+~P1(f775(f63(x67742),x67741))+~P1(f775(f63(x67742),x67743))+E(f15(x67742,f775(f775(f103(f857(x67742,a844)),x67743),x67741)),f775(f775(f103(x67742),f15(x67742,x67743)),f15(x67742,x67741))) % 186.05/186.63 [6775]~P100(x67752)+E(x67751,f180(f857(x67752,a844)))+E(x67753,f180(f857(x67752,a844)))+~P1(f775(f63(x67752),x67751))+~P1(f775(f63(x67752),x67753))+E(f16(x67752,f775(f775(f103(f857(x67752,a844)),x67753),x67751)),f775(f775(f179(x67752),f16(x67752,x67753)),f16(x67752,x67751))) % 186.05/186.63 [6776]~P100(x67762)+E(x67761,f180(f857(x67762,a844)))+E(x67763,f180(f857(x67762,a844)))+~P1(f775(f63(x67762),x67761))+~P1(f775(f63(x67762),x67763))+E(f17(x67762,f775(f775(f103(f857(x67762,a844)),x67763),x67761)),f775(f775(f236(x67762),f17(x67762,x67763)),f17(x67762,x67761))) % 186.05/186.63 [6777]~P93(x67772)+E(x67771,f180(f857(x67772,a844)))+E(x67773,f180(f857(x67772,a844)))+~P1(f775(f63(x67772),x67771))+~P1(f775(f63(x67772),x67773))+E(f12(x67772,f775(f775(f103(f857(x67772,a844)),x67773),x67771)),f775(f775(f104(x67772),f12(x67772,x67773)),f12(x67772,x67771))) % 186.05/186.63 [7441]~P91(x74412)+E(x74411,f180(f857(x74412,a844)))+E(x74413,f180(f857(x74412,a844)))+~P1(f775(f63(x74412),x74411))+~P1(f775(f63(x74412),x74413))+E(f775(f775(f83(x74412),f775(f65(x74412,f83(x74412)),x74413)),f775(f65(x74412,f83(x74412)),x74411)),f775(f65(x74412,f83(x74412)),f775(f775(f103(f857(x74412,a844)),x74413),x74411))) % 186.05/186.63 [7606]~P100(x76062)+E(x76061,f180(f857(x76062,a844)))+E(x76063,f180(f857(x76062,a844)))+~P1(f775(f63(x76062),x76061))+~P1(f775(f63(x76062),x76063))+E(f775(f775(f179(x76062),f13(x76062,f179(x76062),x76063)),f13(x76062,f179(x76062),x76061)),f13(x76062,f179(x76062),f775(f775(f103(f857(x76062,a844)),x76063),x76061))) % 186.05/186.63 [7607]~P100(x76072)+E(x76071,f180(f857(x76072,a844)))+E(x76073,f180(f857(x76072,a844)))+~P1(f775(f63(x76072),x76071))+~P1(f775(f63(x76072),x76073))+E(f775(f775(f236(x76072),f14(x76072,f236(x76072),x76073)),f14(x76072,f236(x76072),x76071)),f14(x76072,f236(x76072),f775(f775(f103(f857(x76072,a844)),x76073),x76071))) % 186.05/186.63 [8615]~P1(f775(x86151,x86153))+P1(f775(x86151,f354(x86151,x86152)))+P1(f775(x86151,f351(x86151,x86152)))+~P1(f775(f775(f233(a1),f2(a1)),x86152))+~P1(f775(f775(f334(a1),x86153),f295(a1,f80(a1),x86152)))+P1(f775(x86151,f775(f775(f3(a1),f351(x86151,x86152)),f775(f775(f83(a1),f353(x86151,x86152)),x86152)))) % 186.05/186.63 [8877]~P1(f775(x88771,x88773))+~P1(f775(x88771,f351(x88771,x88772)))+P1(f775(x88771,f354(x88771,x88772)))+~P1(f775(f775(f233(a1),f2(a1)),x88772))+~P1(f775(f775(f334(a1),x88773),f295(a1,f80(a1),x88772)))+~P1(f775(x88771,f775(f775(f3(a1),f351(x88771,x88772)),f775(f775(f83(a1),f353(x88771,x88772)),x88772)))) % 186.05/186.63 [10026]~P97(x100262)+E(x100261,f180(f857(x100262,a844)))+E(x100263,f180(f857(x100262,a844)))+~P1(f775(f63(x100262),x100261))+~P1(f775(f63(x100262),x100263))+E(f12(x100262,f775(f256(x100262),f775(f775(f10(f857(x100262,a844),a844,x100262),f89(x100262)),f775(f775(f10(f857(x100262,f857(x100262,a844)),f857(x100262,a844),x100262),f775(f10(f857(x100262,a844),a844,x100262),f89(x100262))),f775(f775(f9(x100262,f857(x100262,f857(x100262,a844)),f857(x100262,f857(x100262,a844))),f775(f775(f10(f857(x100262,f857(f857(x100262,a844),f857(x100262,a844))),f857(f857(x100262,f857(x100262,a844)),f857(x100262,f857(x100262,a844))),x100262),f20(x100262,f857(x100262,a844),f857(x100262,a844))),f775(f775(f10(f857(x100262,f857(x100262,f857(a844,a844))),f857(x100262,f857(f857(x100262,a844),f857(x100262,a844))),x100262),f775(f10(f857(x100262,f857(a844,a844)),f857(f857(x100262,a844),f857(x100262,a844)),x100262),f20(x100262,a844,a844))),f775(f775(f10(f857(x100262,f857(x100262,a844)),f857(x100262,f857(x100262,f857(a844,a844))),x100262),f775(f10(f857(x100262,a844),f857(x100262,f857(a844,a844)),x100262),f775(f10(a844,f857(a844,a844),x100262),a331))),f775(f775(f9(x100262,f857(x100262,f857(x100262,x100262)),f857(x100262,f857(x100262,a844))),f775(f775(f10(f857(f857(x100262,x100262),f857(x100262,a844)),f857(f857(x100262,f857(x100262,x100262)),f857(x100262,f857(x100262,a844))),x100262),f10(f857(x100262,x100262),f857(x100262,a844),x100262)),f775(f775(f10(f857(x100262,a844),f857(f857(x100262,x100262),f857(x100262,a844)),x100262),f10(x100262,a844,x100262)),a330))),f103(x100262)))))),f775(f775(f9(x100262,f857(x100262,a844),f857(x100262,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x100262,a844),f857(x100262,a844)),x100262),f10(a844,a844,x100262)),f775(f775(f10(a844,f857(a844,a844),x100262),a331),f775(f775(f9(x100262,f857(x100262,a844),a844),f334(x100262)),x100263)))),f775(f775(f9(x100262,f857(x100262,a844),a844),f334(x100262)),x100261))))))),f775(f775(f103(x100262),f12(x100262,x100263)),f12(x100262,x100261))) % 186.05/186.63 [10027]~P97(x100272)+E(x100271,f180(f857(x100272,a844)))+E(x100273,f180(f857(x100272,a844)))+~P1(f775(f63(x100272),x100271))+~P1(f775(f63(x100272),x100273))+E(f15(x100272,f775(f256(x100272),f775(f775(f10(f857(x100272,a844),a844,x100272),f89(x100272)),f775(f775(f10(f857(x100272,f857(x100272,a844)),f857(x100272,a844),x100272),f775(f10(f857(x100272,a844),a844,x100272),f89(x100272))),f775(f775(f9(x100272,f857(x100272,f857(x100272,a844)),f857(x100272,f857(x100272,a844))),f775(f775(f10(f857(x100272,f857(f857(x100272,a844),f857(x100272,a844))),f857(f857(x100272,f857(x100272,a844)),f857(x100272,f857(x100272,a844))),x100272),f20(x100272,f857(x100272,a844),f857(x100272,a844))),f775(f775(f10(f857(x100272,f857(x100272,f857(a844,a844))),f857(x100272,f857(f857(x100272,a844),f857(x100272,a844))),x100272),f775(f10(f857(x100272,f857(a844,a844)),f857(f857(x100272,a844),f857(x100272,a844)),x100272),f20(x100272,a844,a844))),f775(f775(f10(f857(x100272,f857(x100272,a844)),f857(x100272,f857(x100272,f857(a844,a844))),x100272),f775(f10(f857(x100272,a844),f857(x100272,f857(a844,a844)),x100272),f775(f10(a844,f857(a844,a844),x100272),a331))),f775(f775(f9(x100272,f857(x100272,f857(x100272,x100272)),f857(x100272,f857(x100272,a844))),f775(f775(f10(f857(f857(x100272,x100272),f857(x100272,a844)),f857(f857(x100272,f857(x100272,x100272)),f857(x100272,f857(x100272,a844))),x100272),f10(f857(x100272,x100272),f857(x100272,a844),x100272)),f775(f775(f10(f857(x100272,a844),f857(f857(x100272,x100272),f857(x100272,a844)),x100272),f10(x100272,a844,x100272)),a330))),f104(x100272)))))),f775(f775(f9(x100272,f857(x100272,a844),f857(x100272,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x100272,a844),f857(x100272,a844)),x100272),f10(a844,a844,x100272)),f775(f775(f10(a844,f857(a844,a844),x100272),a331),f775(f775(f9(x100272,f857(x100272,a844),a844),f334(x100272)),x100273)))),f775(f775(f9(x100272,f857(x100272,a844),a844),f334(x100272)),x100271))))))),f775(f775(f104(x100272),f15(x100272,x100273)),f15(x100272,x100271))) % 186.05/186.63 [10028]~P100(x100282)+E(x100281,f180(f857(x100282,a844)))+E(x100283,f180(f857(x100282,a844)))+~P1(f775(f63(x100282),x100281))+~P1(f775(f63(x100282),x100283))+E(f13(x100282,f179(x100282),f775(f256(x100282),f775(f775(f10(f857(x100282,a844),a844,x100282),f89(x100282)),f775(f775(f10(f857(x100282,f857(x100282,a844)),f857(x100282,a844),x100282),f775(f10(f857(x100282,a844),a844,x100282),f89(x100282))),f775(f775(f9(x100282,f857(x100282,f857(x100282,a844)),f857(x100282,f857(x100282,a844))),f775(f775(f10(f857(x100282,f857(f857(x100282,a844),f857(x100282,a844))),f857(f857(x100282,f857(x100282,a844)),f857(x100282,f857(x100282,a844))),x100282),f20(x100282,f857(x100282,a844),f857(x100282,a844))),f775(f775(f10(f857(x100282,f857(x100282,f857(a844,a844))),f857(x100282,f857(f857(x100282,a844),f857(x100282,a844))),x100282),f775(f10(f857(x100282,f857(a844,a844)),f857(f857(x100282,a844),f857(x100282,a844)),x100282),f20(x100282,a844,a844))),f775(f775(f10(f857(x100282,f857(x100282,a844)),f857(x100282,f857(x100282,f857(a844,a844))),x100282),f775(f10(f857(x100282,a844),f857(x100282,f857(a844,a844)),x100282),f775(f10(a844,f857(a844,a844),x100282),a331))),f775(f775(f9(x100282,f857(x100282,f857(x100282,x100282)),f857(x100282,f857(x100282,a844))),f775(f775(f10(f857(f857(x100282,x100282),f857(x100282,a844)),f857(f857(x100282,f857(x100282,x100282)),f857(x100282,f857(x100282,a844))),x100282),f10(f857(x100282,x100282),f857(x100282,a844),x100282)),f775(f775(f10(f857(x100282,a844),f857(f857(x100282,x100282),f857(x100282,a844)),x100282),f10(x100282,a844,x100282)),a330))),f236(x100282)))))),f775(f775(f9(x100282,f857(x100282,a844),f857(x100282,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x100282,a844),f857(x100282,a844)),x100282),f10(a844,a844,x100282)),f775(f775(f10(a844,f857(a844,a844),x100282),a331),f775(f775(f9(x100282,f857(x100282,a844),a844),f334(x100282)),x100283)))),f775(f775(f9(x100282,f857(x100282,a844),a844),f334(x100282)),x100281))))))),f775(f775(f236(x100282),f13(x100282,f179(x100282),x100283)),f13(x100282,f179(x100282),x100281))) % 186.05/186.63 [10029]~P100(x100292)+E(x100291,f180(f857(x100292,a844)))+E(x100293,f180(f857(x100292,a844)))+~P1(f775(f63(x100292),x100291))+~P1(f775(f63(x100292),x100293))+E(f14(x100292,f236(x100292),f775(f256(x100292),f775(f775(f10(f857(x100292,a844),a844,x100292),f89(x100292)),f775(f775(f10(f857(x100292,f857(x100292,a844)),f857(x100292,a844),x100292),f775(f10(f857(x100292,a844),a844,x100292),f89(x100292))),f775(f775(f9(x100292,f857(x100292,f857(x100292,a844)),f857(x100292,f857(x100292,a844))),f775(f775(f10(f857(x100292,f857(f857(x100292,a844),f857(x100292,a844))),f857(f857(x100292,f857(x100292,a844)),f857(x100292,f857(x100292,a844))),x100292),f20(x100292,f857(x100292,a844),f857(x100292,a844))),f775(f775(f10(f857(x100292,f857(x100292,f857(a844,a844))),f857(x100292,f857(f857(x100292,a844),f857(x100292,a844))),x100292),f775(f10(f857(x100292,f857(a844,a844)),f857(f857(x100292,a844),f857(x100292,a844)),x100292),f20(x100292,a844,a844))),f775(f775(f10(f857(x100292,f857(x100292,a844)),f857(x100292,f857(x100292,f857(a844,a844))),x100292),f775(f10(f857(x100292,a844),f857(x100292,f857(a844,a844)),x100292),f775(f10(a844,f857(a844,a844),x100292),a331))),f775(f775(f9(x100292,f857(x100292,f857(x100292,x100292)),f857(x100292,f857(x100292,a844))),f775(f775(f10(f857(f857(x100292,x100292),f857(x100292,a844)),f857(f857(x100292,f857(x100292,x100292)),f857(x100292,f857(x100292,a844))),x100292),f10(f857(x100292,x100292),f857(x100292,a844),x100292)),f775(f775(f10(f857(x100292,a844),f857(f857(x100292,x100292),f857(x100292,a844)),x100292),f10(x100292,a844,x100292)),a330))),f179(x100292)))))),f775(f775(f9(x100292,f857(x100292,a844),f857(x100292,a844)),f775(f775(f10(f857(a844,a844),f857(f857(x100292,a844),f857(x100292,a844)),x100292),f10(a844,a844,x100292)),f775(f775(f10(a844,f857(a844,a844),x100292),a331),f775(f775(f9(x100292,f857(x100292,a844),a844),f334(x100292)),x100293)))),f775(f775(f9(x100292,f857(x100292,a844),a844),f334(x100292)),x100291))))))),f775(f775(f179(x100292),f14(x100292,f236(x100292),x100293)),f14(x100292,f236(x100292),x100291))) % 186.05/186.63 [7106]~P117(x71063)+E(x71061,x71062)+~E(f775(f775(f242(x71063),x71061),x71064),f775(f775(f242(x71063),x71062),x71064))+~P1(f775(f775(f232(x71063),f2(x71063)),x71062))+~P1(f775(f775(f232(x71063),f2(x71063)),x71061))+~P1(f775(f775(f233(a850),f2(a850)),x71064)) % 186.05/186.63 [7401]~P100(x74012)+E(x74011,f180(f857(x74012,a844)))+~P1(f775(f63(x74012),x74011))+~P1(f775(f775(f334(x74012),x74014),x74011))+P1(f775(f775(f233(x74012),x74013),x74014))+~P1(f775(f775(f233(x74012),x74013),f775(f65(x74012,f236(x74012)),x74011))) % 186.05/186.63 [7402]~P100(x74022)+E(x74021,f180(f857(x74022,a844)))+~P1(f775(f63(x74022),x74021))+~P1(f775(f775(f334(x74022),x74024),x74021))+P1(f775(f775(f232(x74022),x74023),x74024))+~P1(f775(f775(f232(x74022),x74023),f775(f65(x74022,f236(x74022)),x74021))) % 186.05/186.63 [7403]~P98(x74032)+E(x74031,f180(f857(x74032,a844)))+~P1(f775(f63(x74032),x74031))+~P1(f775(f775(f334(x74032),x74034),x74031))+P1(f775(f775(f232(x74032),x74033),x74034))+~P1(f775(f775(f232(x74032),x74033),f775(f65(x74032,f104(x74032)),x74031))) % 186.05/186.63 [7297]E(x72971,f2(a1))+E(f775(f775(f43(a1),x72972),x72971),x72973)+~P1(f775(f775(f232(a1),x72974),f2(a1)))+~E(x72972,f775(f775(f82(a1),f775(f775(f83(a1),x72971),x72973)),x72974))+P1(f775(f775(f233(a1),f2(a1)),x72971))+~P1(f775(f775(f233(a1),x72971),x72974)) % 186.05/186.63 [7313]E(f52(a1,x73132,x73131),x73133)+E(x73131,f2(a1))+~P1(f775(f775(f232(a1),x73133),f2(a1)))+~E(x73132,f775(f775(f82(a1),f775(f775(f83(a1),x73131),x73134)),x73133))+P1(f775(f775(f233(a1),f2(a1)),x73131))+~P1(f775(f775(f233(a1),x73131),x73133)) % 186.05/186.63 [7440]E(x74401,f2(a1))+E(f775(f775(f43(a1),x74402),x74401),x74403)+~E(x74402,f775(f775(f82(a1),f775(f775(f83(a1),x74401),x74403)),x74404))+~P1(f775(f775(f233(a1),f2(a1)),x74401))+~P1(f775(f775(f232(a1),f2(a1)),x74404))+~P1(f775(f775(f233(a1),x74404),x74401)) % 186.05/186.63 [7465]E(f52(a1,x74652,x74651),x74653)+E(x74651,f2(a1))+~E(x74652,f775(f775(f82(a1),f775(f775(f83(a1),x74651),x74654)),x74653))+~P1(f775(f775(f233(a1),f2(a1)),x74651))+~P1(f775(f775(f232(a1),f2(a1)),x74653))+~P1(f775(f775(f233(a1),x74653),x74651)) % 186.05/186.63 [7610]~P100(x76102)+E(x76101,f180(f857(x76102,a844)))+~P1(f775(f63(x76102),x76101))+~P1(f775(f775(f233(x76102),x76104),x76103))+~P1(f775(f775(f334(x76102),x76104),x76101))+P1(f775(f775(f233(x76102),f775(f65(x76102,f236(x76102)),x76101)),x76103)) % 186.05/186.63 [7611]~P100(x76112)+E(x76111,f180(f857(x76112,a844)))+~P1(f775(f63(x76112),x76111))+~P1(f775(f775(f232(x76112),x76114),x76113))+~P1(f775(f775(f334(x76112),x76114),x76111))+P1(f775(f775(f232(x76112),f775(f65(x76112,f236(x76112)),x76111)),x76113)) % 186.05/186.63 [8174]~P1(f775(f775(f232(a1),x81744),f2(a1)))+~E(x81741,f775(f775(f82(a1),f775(f775(f83(a1),x81742),x81743)),x81744))+~P1(f775(f775(f232(a1),f2(a1)),x81744))+~P1(f775(f775(f233(a1),x81744),x81742))+~P1(f775(f775(f233(a1),x81742),x81744))+P1(f775(f56(x81741,x81742),f775(f775(f241(a1,a1),x81743),x81744))) % 186.05/186.63 [8340]~P99(x83401)+P1(f775(f775(f233(f857(x83401,a844)),f295(x83401,x83402,x83403)),f295(x83401,x83404,x83405)))+~P1(f775(f775(f233(x83401),x83403),x83405))+~P1(f775(f775(f232(x83401),x83404),x83402))+~P1(f775(f775(f232(x83401),x83404),x83405))+~P1(f775(f775(f232(x83401),x83403),x83405)) % 186.05/186.63 [8341]~P99(x83411)+P1(f775(f775(f233(f857(x83411,a844)),f295(x83411,x83412,x83413)),f295(x83411,x83414,x83415)))+~P1(f775(f775(f233(x83411),x83414),x83412))+~P1(f775(f775(f232(x83411),x83413),x83415))+~P1(f775(f775(f232(x83411),x83414),x83415))+~P1(f775(f775(f232(x83411),x83414),x83412)) % 186.05/186.63 [9123]P57(x91232,x91233,x91234,x91231)+E(x91231,f180(f857(x91232,a844)))+~P1(f775(f63(x91232),x91234))+~P1(f775(f63(x91232),x91231))+~P1(f775(f775(x91233,f537(x91231,x91234,x91233,x91232)),x91235))+~P1(f775(f775(f334(x91232),x91235),x91231)) % 186.05/186.63 [9249]~E(x92493,x92495)+~P66(x92491)+~P70(x92491)+~P38(x92493)+E(f775(f775(f8(a1,x92491),x92492),x92493),f775(f775(f8(a1,x92491),x92494),x92495))+P1(f775(f775(f232(a1),f2(a1)),f380(x92492,x92494,x92493,x92495,x92491))) % 186.05/186.63 [9250]~E(x92503,x92505)+~P66(x92501)+~P70(x92501)+~P38(x92503)+E(f775(f775(f11(a1,x92501),x92502),x92503),f775(f775(f11(a1,x92501),x92504),x92505))+P1(f775(f775(f232(a1),f2(a1)),f533(x92502,x92504,x92503,x92505,x92501))) % 186.05/186.63 [9415]~E(x94155,x94153)+~P66(x94151)+~P70(x94151)+~P38(x94155)+~E(f775(x94152,f380(x94154,x94152,x94155,x94153,x94151)),f775(x94154,f380(x94154,x94152,x94155,x94153,x94151)))+E(f775(f775(f8(a1,x94151),x94152),x94153),f775(f775(f8(a1,x94151),x94154),x94155)) % 186.05/186.63 [9416]~E(x94165,x94163)+~P66(x94161)+~P70(x94161)+~P38(x94165)+~E(f775(x94162,f533(x94164,x94162,x94165,x94163,x94161)),f775(x94164,f533(x94164,x94162,x94165,x94163,x94161)))+E(f775(f775(f11(a1,x94161),x94162),x94163),f775(f775(f11(a1,x94161),x94164),x94165)) % 186.05/186.63 [9500]~P77(x95003)+E(f775(x95001,x95002),f2(x95003))+~E(f775(f775(f8(x95004,x95003),x95001),x95005),f2(x95003))+~P1(f775(f63(x95004),x95005))+P1(f775(f775(f334(x95004),f463(x95002,x95001,x95005,x95004,x95003)),x95005))+~P1(f775(f775(f334(x95004),x95002),x95005)) % 186.05/186.63 [9622]~P77(x96223)+E(f775(x96221,x96222),f2(x96223))+~E(f775(f775(f8(x96224,x96223),x96221),x96225),f2(x96223))+~P1(f775(f63(x96224),x96225))+~P1(f775(f775(f334(x96224),x96222),x96225))+~P1(f775(f775(f232(x96223),f2(x96223)),f775(x96221,f463(x96222,x96221,x96225,x96224,x96223)))) % 186.05/186.63 [8253]~P123(x82531)+~P1(f775(f775(f232(x82531),f2(x82531)),x82533))+~P1(f775(f775(f233(x82531),x82533),x82535))+~P1(f775(f775(f233(x82531),x82532),x82534))+~P1(f775(f775(f233(x82531),f2(x82531)),x82534))+P1(f775(f775(f233(x82531),f775(f775(f83(x82531),x82532),x82533)),f775(f775(f83(x82531),x82534),x82535))) % 186.05/186.63 [8254]~P123(x82541)+~P1(f775(f775(f232(x82541),f2(x82541)),x82543))+~P1(f775(f775(f232(x82541),f2(x82541)),x82542))+~P1(f775(f775(f233(x82541),x82543),x82545))+~P1(f775(f775(f233(x82541),x82542),x82544))+P1(f775(f775(f233(x82541),f775(f775(f83(x82541),x82542),x82543)),f775(f775(f83(x82541),x82544),x82545))) % 186.05/186.63 [8255]~P123(x82551)+~P1(f775(f775(f232(x82551),x82552),x82554))+~P1(f775(f775(f232(x82551),f2(x82551)),x82553))+~P1(f775(f775(f233(x82551),x82553),x82555))+~P1(f775(f775(f233(x82551),f2(x82551)),x82552))+P1(f775(f775(f233(x82551),f775(f775(f83(x82551),x82552),x82553)),f775(f775(f83(x82551),x82554),x82555))) % 186.05/186.63 [8256]~P123(x82561)+~P1(f775(f775(f232(x82561),x82563),x82565))+~P1(f775(f775(f232(x82561),f2(x82561)),x82562))+~P1(f775(f775(f233(x82561),x82562),x82564))+~P1(f775(f775(f233(x82561),f2(x82561)),x82563))+P1(f775(f775(f233(x82561),f775(f775(f83(x82561),x82562),x82563)),f775(f775(f83(x82561),x82564),x82565))) % 186.05/186.63 [8257]~P63(x82571)+~P1(f775(f775(f232(x82571),x82572),x82574))+~P1(f775(f775(f233(x82571),x82575),x82573))+~P1(f775(f775(f233(x82571),f2(x82571)),x82575))+~P1(f775(f775(f233(x82571),f2(x82571)),x82572))+P1(f775(f775(f233(x82571),f775(f775(f283(x82571),x82572),x82573)),f775(f775(f283(x82571),x82574),x82575))) % 186.05/186.63 [8258]~P63(x82581)+~P1(f775(f775(f232(x82581),x82585),x82583))+~P1(f775(f775(f232(x82581),f2(x82581)),x82582))+~P1(f775(f775(f233(x82581),x82582),x82584))+~P1(f775(f775(f233(x82581),f2(x82581)),x82585))+P1(f775(f775(f233(x82581),f775(f775(f283(x82581),x82582),x82583)),f775(f775(f283(x82581),x82584),x82585))) % 186.05/186.63 [8259]~P131(x82591)+~P1(f775(f775(f232(x82591),x82593),x82595))+~P1(f775(f775(f232(x82591),x82592),x82594))+~P1(f775(f775(f232(x82591),f2(x82591)),x82593))+~P1(f775(f775(f232(x82591),f2(x82591)),x82594))+P1(f775(f775(f232(x82591),f775(f775(f83(x82591),x82592),x82593)),f775(f775(f83(x82591),x82594),x82595))) % 186.05/186.63 [8260]~P131(x82601)+~P1(f775(f775(f232(x82601),x82603),x82605))+~P1(f775(f775(f232(x82601),x82602),x82604))+~P1(f775(f775(f232(x82601),f2(x82601)),x82603))+~P1(f775(f775(f232(x82601),f2(x82601)),x82602))+P1(f775(f775(f232(x82601),f775(f775(f83(x82601),x82602),x82603)),f775(f775(f83(x82601),x82604),x82605))) % 186.05/186.63 [8261]~P63(x82611)+~P1(f775(f775(f233(x82611),f2(x82611)),x82615))+~P1(f775(f775(f232(x82611),x82615),x82613))+~P1(f775(f775(f232(x82611),x82612),x82614))+~P1(f775(f775(f232(x82611),f2(x82611)),x82612))+P1(f775(f775(f232(x82611),f775(f775(f283(x82611),x82612),x82613)),f775(f775(f283(x82611),x82614),x82615))) % 186.05/186.63 [9537]~P66(x95375)+~P80(x95375)+E(x95371,f180(f857(x95372,a844)))+~P1(f775(f63(x95372),x95371))+P1(f775(f775(f334(x95372),f489(x95373,x95374,x95371,x95372,x95375)),x95371))+P1(f775(f775(f233(x95375),f775(f775(f8(x95372,x95375),x95374),x95371)),f775(f775(f8(x95372,x95375),x95373),x95371))) % 186.05/186.63 [9642]~P66(x96421)+~P78(x96421)+~P1(f775(f63(x96422),x96425))+~P1(f775(f775(f232(x96421),f2(x96421)),f775(x96423,f413(x96423,x96424,x96425,x96422,x96421))))+P1(f775(f775(f232(x96421),f775(f775(f8(x96422,x96421),x96423),x96424)),f775(f775(f8(x96422,x96421),x96423),x96425)))+~P1(f775(f775(f232(f857(x96422,a844)),x96424),x96425)) % 186.05/186.63 [9808]~P66(x98083)+~P80(x98083)+E(x98081,f180(f857(x98082,a844)))+~P1(f775(f63(x98082),x98081))+~P1(f775(f775(f233(x98083),f775(x98084,f489(x98085,x98084,x98081,x98082,x98083))),f775(x98085,f489(x98085,x98084,x98081,x98082,x98083))))+P1(f775(f775(f233(x98083),f775(f775(f8(x98082,x98083),x98084),x98081)),f775(f775(f8(x98082,x98083),x98085),x98081))) % 186.05/186.63 [6966]~P21(x69662,x69665,x69664)+E(x69661,f180(f857(x69662,a844)))+E(x69663,f180(f857(x69662,a844)))+~P1(f775(f63(x69662),x69661))+~P1(f775(f63(x69662),x69663))+E(f775(x69664,f775(f775(f103(f857(x69662,a844)),x69663),x69661)),f775(f775(x69665,f775(x69664,x69663)),f775(x69664,x69661))) % 186.05/186.63 [7575]~P141(x75751,x75754,x75753)+P1(f775(x75751,x75752))+~P1(f775(f775(f233(a1),x75754),f2(a1)))+~P1(f775(f775(f232(a1),x75755),f2(a1)))+~E(x75753,f775(f775(f82(a1),f775(f775(f83(a1),x75754),x75752)),x75755))+~P1(f775(f775(f233(a1),x75754),x75755)) % 186.05/186.63 [7576]~P140(x75761,x75764,x75763)+P1(f775(x75761,x75762))+~P1(f775(f775(f233(a1),x75764),f2(a1)))+~P1(f775(f775(f232(a1),x75762),f2(a1)))+~E(x75763,f775(f775(f82(a1),f775(f775(f83(a1),x75764),x75765)),x75762))+~P1(f775(f775(f233(a1),x75764),x75762)) % 186.05/186.63 [7619]~P141(x76191,x76194,x76193)+P1(f775(x76191,x76192))+~E(x76193,f775(f775(f82(a1),f775(f775(f83(a1),x76194),x76192)),x76195))+~P1(f775(f775(f233(a1),f2(a1)),x76194))+~P1(f775(f775(f232(a1),f2(a1)),x76195))+~P1(f775(f775(f233(a1),x76195),x76194)) % 186.05/186.63 [7620]~P140(x76201,x76204,x76203)+P1(f775(x76201,x76202))+~E(x76203,f775(f775(f82(a1),f775(f775(f83(a1),x76204),x76205)),x76202))+~P1(f775(f775(f233(a1),f2(a1)),x76204))+~P1(f775(f775(f232(a1),f2(a1)),x76202))+~P1(f775(f775(f233(a1),x76202),x76204)) % 186.05/186.63 [8545]P1(f775(f775(x85451,x85452),x85453))+~P1(f775(f775(x85451,f775(f775(f43(a1),x85454),x85455)),f52(a1,x85454,x85455)))+~P1(f775(f775(f233(a1),x85455),f2(a1)))+~P1(f775(f775(f232(a1),x85453),f2(a1)))+~E(x85454,f775(f775(f82(a1),f775(f775(f83(a1),x85455),x85452)),x85453))+~P1(f775(f775(f233(a1),x85455),x85453)) % 186.05/186.63 [8552]P1(f775(f775(x85521,x85522),x85523))+~P1(f775(f775(x85521,f775(f775(f43(a1),x85524),x85525)),f52(a1,x85524,x85525)))+~E(x85524,f775(f775(f82(a1),f775(f775(f83(a1),x85525),x85522)),x85523))+~P1(f775(f775(f233(a1),f2(a1)),x85525))+~P1(f775(f775(f232(a1),f2(a1)),x85523))+~P1(f775(f775(f233(a1),x85523),x85525)) % 186.05/186.63 [8771]E(x87711,x87712)+~P54(x87713,x87715,x87714)+~P1(f775(f775(f334(x87713),x87712),x87715))+~P1(f775(f775(f334(x87713),x87711),x87715))+P1(f775(f775(f334(f856(x87713,x87713)),f775(f775(f241(x87713,x87713),x87711),x87712)),x87714))+P1(f775(f775(f334(f856(x87713,x87713)),f775(f775(f241(x87713,x87713),x87712),x87711)),x87714)) % 186.05/186.63 [9566]~P66(x95665)+~P78(x95665)+~P1(f775(f63(x95661),x95664))+P1(f775(f775(f232(x95665),f775(f775(f8(x95661,x95665),x95662),x95663)),f775(f775(f8(x95661,x95665),x95662),x95664)))+~P1(f775(f775(f232(f857(x95661,a844)),x95663),x95664))+P1(f775(f775(f334(x95661),f413(x95662,x95663,x95664,x95661,x95665)),f775(f775(f3(f857(x95661,a844)),x95664),x95663))) % 186.05/186.63 [9649]E(x96491,f180(f857(x96492,a844)))+~P1(f775(f63(x96492),x96493))+~P1(f775(f63(x96492),x96491))+P1(f775(f775(f334(f856(f857(x96492,a844),f857(x96492,a844))),f775(f775(f241(f857(x96492,a844),f857(x96492,a844)),x96493),x96491)),f324(x96492,x96494)))+~P1(f775(f775(f334(x96492),x96495),x96491))+~P1(f775(f775(f334(f856(x96492,x96492)),f775(f775(f241(x96492,x96492),f539(x96494,x96491,x96493,x96492)),x96495)),x96494)) % 186.05/186.63 [9650]E(x96501,f180(f857(x96502,a844)))+~P1(f775(f63(x96502),x96503))+~P1(f775(f63(x96502),x96501))+P1(f775(f775(f334(f856(f857(x96502,a844),f857(x96502,a844))),f775(f775(f241(f857(x96502,a844),f857(x96502,a844)),x96503),x96501)),f324(x96502,x96504)))+~P1(f775(f775(f334(x96502),x96505),x96501))+~P1(f775(f775(f334(f856(x96502,x96502)),f775(f775(f241(x96502,x96502),f624(x96504,x96501,x96503,x96502)),x96505)),x96504)) % 186.05/186.63 [9811]~P77(x98111)+~E(f775(f775(f8(x98115,x98111),x98112),x98116),x98114)+~P1(f775(f63(x98115),x98116))+P1(f775(f775(f334(x98115),f464(x98113,x98114,x98112,x98116,x98115,x98111)),x98116))+P1(f775(f775(f232(x98111),f775(x98112,x98113)),x98114))+~P1(f775(f775(f334(x98115),x98113),x98116)) % 186.05/186.63 [9865]~P77(x98651)+~E(f775(f775(f8(x98655,x98651),x98652),x98656),x98654)+~P1(f775(f63(x98655),x98656))+~P1(f775(f775(f334(x98655),x98653),x98656))+~P1(f775(f775(f232(x98651),f2(x98651)),f775(x98652,f464(x98653,x98654,x98652,x98656,x98655,x98651))))+P1(f775(f775(f232(x98651),f775(x98652,x98653)),x98654)) % 186.05/186.63 [9982]~E(x99825,x99828)+~E(x99824,x99827)+~P66(x99822)+~P102(x99821)+E(f775(f775(f8(x99821,x99822),x99823),f775(f294(x99821,x99824),x99825)),f775(f775(f8(x99821,x99822),x99826),f775(f294(x99821,x99827),x99828)))+P1(f775(f775(f232(x99821),x99824),f372(x99823,x99826,x99825,x99828,x99824,x99827,x99821,x99822))) % 186.05/186.63 [9998]~E(x99987,x99984)+~E(x99988,x99985)+~P66(x99982)+~P102(x99981)+~E(f775(x99983,f372(x99986,x99983,x99988,x99985,x99987,x99984,x99981,x99982)),f775(x99986,f372(x99986,x99983,x99988,x99985,x99987,x99984,x99981,x99982)))+E(f775(f775(f8(x99981,x99982),x99983),f775(f294(x99981,x99984),x99985)),f775(f775(f8(x99981,x99982),x99986),f775(f294(x99981,x99987),x99988))) % 186.05/186.63 [10001]~E(x100014,x100017)+~E(x100015,x100018)+~P66(x100012)+~P102(x100011)+E(f775(f775(f8(x100011,x100012),x100013),f775(f294(x100011,x100014),x100015)),f775(f775(f8(x100011,x100012),x100016),f775(f294(x100011,x100017),x100018)))+P1(f775(f775(f233(x100011),f372(x100013,x100016,x100015,x100018,x100014,x100017,x100011,x100012)),x100015)) % 186.05/186.63 [9654]~P12(x96545,x96549,x96546)+~P12(x96541,x965410,x96543)+~P17(x96541,x96545,f857(x96542,a844),x96543,x96546,x96548)+~P1(f775(f775(f334(x96545),x96547),x96549))+~P1(f775(f775(f334(x96541),x96544),x965410))+E(f775(f775(f46(x96541,f857(x96542,a844)),f775(f277(x96541,x96541,x96543),f775(f775(f302(x96541),x96544),f180(f857(x96541,a844))))),f775(f775(f10(f857(x96545,f857(x96542,a844)),f857(x96542,a844),x96541),f775(f46(x96545,f857(x96542,a844)),f775(f277(x96545,x96545,x96546),f775(f775(f302(x96545),x96547),f180(f857(x96545,a844)))))),x96548)),f775(f775(x96548,x96544),x96547)) % 186.05/186.63 [5461]~P100(x54613)+~P18(x54613,x54612)+~P18(x54613,x54611)+E(x54611,x54612)+~E(f775(f158(x54613),x54611),f775(f158(x54613),x54612))+~P1(f775(f127(x54613),x54612))+~P1(f775(f127(x54613),x54611)) % 186.05/186.63 [4815]~P122(x48152)+~P127(x48152)+~P138(x48152)+~P105(x48152)+~E(x48153,f2(x48152))+E(x48151,f2(a850))+E(f775(f775(f242(x48152),x48153),x48151),f2(x48152)) % 186.05/186.63 [9009]E(x90091,f2(a850))+~E(x90092,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x90093)),x90091)),f775(f250(a850,a850),x90093)))+P1(f775(f55(x90092,x90091),x90093))+~P1(f775(f775(f232(a850),f775(f250(a850,a850),x90093)),f2(a850)))+~P1(f775(f775(f232(a850),f2(a850)),f775(f250(a850,a850),x90093)))+~P1(f775(f775(f233(a850),x90091),f775(f250(a850,a850),x90093)))+~P1(f775(f775(f233(a850),f775(f250(a850,a850),x90093)),x90091)) % 186.05/186.63 [9017]~E(f775(f240(a850,a850),x90173),f2(a850))+~E(x90171,f775(f775(f82(a850),f775(f775(f83(a850),f775(f240(a850,a850),x90173)),x90172)),f775(f250(a850,a850),x90173)))+P1(f775(f55(x90171,x90172),x90173))+~P1(f775(f775(f232(a850),f775(f250(a850,a850),x90173)),f2(a850)))+~P1(f775(f775(f232(a850),f2(a850)),f775(f250(a850,a850),x90173)))+~P1(f775(f775(f233(a850),x90172),f775(f250(a850,a850),x90173)))+~P1(f775(f775(f233(a850),f775(f250(a850,a850),x90173)),x90172)) % 186.05/186.63 [7934]~P64(x79342)+E(x79341,f180(f857(x79342,a844)))+E(x79343,f180(f857(x79342,a844)))+~P1(f775(f63(x79342),x79341))+~P1(f775(f63(x79342),x79343))+~E(f775(f775(f104(f857(x79342,a844)),x79343),x79341),f180(f857(x79342,a844)))+E(f775(f775(f83(x79342),f775(f65(x79342,f83(x79342)),x79343)),f775(f65(x79342,f83(x79342)),x79341)),f775(f65(x79342,f83(x79342)),f775(f775(f103(f857(x79342,a844)),x79343),x79341))) % 186.05/186.63 [7713]E(x77131,f2(a1))+E(f775(f775(f43(a1),x77132),x77131),x77133)+~P1(f775(f775(f232(a1),x77134),f2(a1)))+~E(x77132,f775(f775(f82(a1),f775(f775(f83(a1),x77131),x77133)),x77134))+~P1(f775(f775(f232(a1),f2(a1)),x77134))+~P1(f775(f775(f233(a1),x77134),x77131))+~P1(f775(f775(f233(a1),x77131),x77134)) % 186.05/186.63 [7719]E(f52(a1,x77192,x77191),x77193)+E(x77191,f2(a1))+~P1(f775(f775(f232(a1),x77193),f2(a1)))+~E(x77192,f775(f775(f82(a1),f775(f775(f83(a1),x77191),x77194)),x77193))+~P1(f775(f775(f232(a1),f2(a1)),x77193))+~P1(f775(f775(f233(a1),x77193),x77191))+~P1(f775(f775(f233(a1),x77191),x77193)) % 186.05/186.63 [6740]~P7(x67402)+E(x67401,f2(x67402))+E(x67403,f2(x67402))+~E(f775(f775(f43(x67402),x67404),x67403),f775(f775(f43(x67402),x67405),x67401))+E(f775(f775(f83(x67402),x67404),x67401),f775(f775(f83(x67402),x67403),x67405))+~P1(f775(f775(f279(x67402),x67401),x67405))+~P1(f775(f775(f279(x67402),x67403),x67404)) % 186.05/186.63 [6741]~P7(x67412)+E(x67411,f2(x67412))+E(x67413,f2(x67412))+~E(f775(f775(f83(x67412),x67414),x67413),f775(f775(f83(x67412),x67411),x67415))+E(f775(f775(f43(x67412),x67414),x67411),f775(f775(f43(x67412),x67415),x67413))+~P1(f775(f775(f279(x67412),x67411),x67414))+~P1(f775(f775(f279(x67412),x67413),x67415)) % 186.05/186.63 [7628]~P22(x76282,x76285,x76284)+E(x76281,f180(f857(x76282,a844)))+E(x76283,f180(f857(x76282,a844)))+~P1(f775(f63(x76282),x76281))+~P1(f775(f63(x76282),x76283))+~E(f775(f775(f104(f857(x76282,a844)),x76283),x76281),f180(f857(x76282,a844)))+E(f775(x76284,f775(f775(f103(f857(x76282,a844)),x76283),x76281)),f775(f775(x76285,f775(x76284,x76283)),f775(x76284,x76281))) % 186.05/186.63 [9221]~P29(x92213,x92211,x92215,x92214)+~P29(x92211,x92213,x92216,x92212)+E(f775(f42(x92211),x92212),f775(f42(x92213),x92214))+~P1(f775(f63(x92213),x92214))+~P1(f775(f63(x92211),x92212))+~P1(f775(f775(f232(f857(x92213,a844)),f775(f303(x92211,x92213,x92216),x92212)),x92214))+~P1(f775(f775(f232(f857(x92211,a844)),f775(f303(x92213,x92211,x92215),x92214)),x92212)) % 186.05/186.63 [9169]~P1(f775(f775(f233(a1),f775(f775(f82(a1),f775(f775(f83(a1),x91695),x91691)),x91696)),f2(a1)))+~E(f775(f775(f82(a1),f775(f775(f83(a1),x91693),x91692)),x91694),f775(f775(f82(a1),f775(f775(f83(a1),x91695),x91691)),x91696))+~P1(f775(f775(f233(a1),f2(a1)),x91695))+~P1(f775(f775(f232(a1),f2(a1)),x91696))+~P1(f775(f775(f233(a1),x91694),x91693))+~P1(f775(f775(f232(a1),x91695),x91693))+P1(f775(f775(f232(a1),x91691),x91692)) % 186.05/186.63 [8960]~E(f775(f775(f82(a1),f775(f775(f83(a1),x89603),x89601)),x89604),f775(f775(f82(a1),f775(f775(f83(a1),x89605),x89602)),x89606))+~P1(f775(f775(f233(a1),f2(a1)),x89605))+~P1(f775(f775(f232(a1),f2(a1)),x89604))+~P1(f775(f775(f233(a1),x89606),x89605))+~P1(f775(f775(f232(a1),x89605),x89603))+P1(f775(f775(f232(a1),x89601),x89602))+~P1(f775(f775(f232(a1),f2(a1)),f775(f775(f82(a1),f775(f775(f83(a1),x89605),x89602)),x89606))) % 186.05/186.63 [9125]~P124(x91251)+~E(f775(f775(f82(x91251),x91252),x91254),f80(x91251))+~P1(f775(f775(f232(x91251),f2(x91251)),x91254))+~P1(f775(f775(f232(x91251),f2(x91251)),x91252))+~P1(f775(f775(f233(x91251),x91255),x91256))+~P1(f775(f775(f233(x91251),x91253),x91256))+P1(f775(f775(f233(x91251),f775(f775(f82(x91251),f775(f775(f83(x91251),x91252),x91253)),f775(f775(f83(x91251),x91254),x91255))),x91256)) % 186.05/186.63 [9126]~P126(x91261)+~E(f775(f775(f82(x91261),x91262),x91264),f80(x91261))+~P1(f775(f775(f232(x91261),x91265),x91266))+~P1(f775(f775(f232(x91261),x91263),x91266))+~P1(f775(f775(f232(x91261),f2(x91261)),x91264))+~P1(f775(f775(f232(x91261),f2(x91261)),x91262))+P1(f775(f775(f232(x91261),f775(f775(f82(x91261),f775(f775(f83(x91261),x91262),x91263)),f775(f775(f83(x91261),x91264),x91265))),x91266)) % 186.05/186.63 [9907]~P12(x99077,x99076,x99075)+E(x99071,x99072)+~P16(x99077,f857(x99074,a844),x99075,x99073)+E(f775(x99073,f499(x99071,x99072,x99073,x99074,x99075,x99076,x99077)),f775(x99073,f500(x99071,x99072,x99073,x99074,x99075,x99076,x99077)))+~E(f775(f775(f46(x99077,f857(x99074,a844)),x99071),x99073),f775(f775(f46(x99077,f857(x99074,a844)),x99072),x99073))+~P1(f775(f775(f334(f857(x99077,a844)),x99072),f775(f775(f61(x99077),x99076),x99075)))+~P1(f775(f775(f334(f857(x99077,a844)),x99071),f775(f775(f61(x99077),x99076),x99075))) % 186.05/186.63 [9947]~P12(x99473,x99477,x99476)+E(x99471,x99472)+~P16(x99473,f857(x99475,a844),x99476,x99474)+~E(f775(f775(f46(x99473,f857(x99475,a844)),x99471),x99474),f775(f775(f46(x99473,f857(x99475,a844)),x99472),x99474))+P1(f775(f775(f334(x99473),f500(x99471,x99472,x99474,x99475,x99476,x99477,x99473)),x99477))+~P1(f775(f775(f334(f857(x99473,a844)),x99472),f775(f775(f61(x99473),x99477),x99476)))+~P1(f775(f775(f334(f857(x99473,a844)),x99471),f775(f775(f61(x99473),x99477),x99476))) % 186.05/186.63 [9948]~P12(x99483,x99487,x99486)+E(x99481,x99482)+~P16(x99483,f857(x99485,a844),x99486,x99484)+~E(f775(f775(f46(x99483,f857(x99485,a844)),x99481),x99484),f775(f775(f46(x99483,f857(x99485,a844)),x99482),x99484))+P1(f775(f775(f334(x99483),f499(x99481,x99482,x99484,x99485,x99486,x99487,x99483)),x99487))+~P1(f775(f775(f334(f857(x99483,a844)),x99482),f775(f775(f61(x99483),x99487),x99486)))+~P1(f775(f775(f334(f857(x99483,a844)),x99481),f775(f775(f61(x99483),x99487),x99486))) % 186.05/186.63 [10014]E(x100141,x100142)+~P12(x100143,x100146,x100147)+~P16(x100143,f857(x100144,a844),x100147,x100145)+~E(f775(f775(f46(x100143,f857(x100144,a844)),x100141),x100145),f775(f775(f46(x100143,f857(x100144,a844)),x100142),x100145))+~P1(f775(f775(f334(f856(x100143,x100143)),f775(f775(f241(x100143,x100143),f500(x100141,x100142,x100145,x100144,x100147,x100146,x100143)),f499(x100141,x100142,x100145,x100144,x100147,x100146,x100143))),x100147))+~P1(f775(f775(f334(f857(x100143,a844)),x100142),f775(f775(f61(x100143),x100146),x100147)))+~P1(f775(f775(f334(f857(x100143,a844)),x100141),f775(f775(f61(x100143),x100146),x100147))) % 186.05/186.63 [8959]~P12(x89591,x89597,x89594)+~E(x89595,x89596)+~P1(f775(f775(f334(x89591),x89593),x89596))+~P1(f775(f775(f334(x89591),x89592),x89595))+~P1(f775(f775(f334(f857(x89591,a844)),x89596),f775(f775(f61(x89591),x89597),x89594)))+~P1(f775(f775(f334(f857(x89591,a844)),x89595),f775(f775(f61(x89591),x89597),x89594)))+P1(f775(f775(f334(f856(x89591,x89591)),f775(f775(f241(x89591,x89591),x89592),x89593)),x89594)) % 186.05/186.63 [9090]E(x90901,x90902)+~P12(x90903,x90904,x90905)+~P1(f775(f775(f334(x90903),x90906),x90902))+~P1(f775(f775(f334(x90903),x90907),x90901))+~P1(f775(f775(f334(f857(x90903,a844)),x90902),f775(f775(f61(x90903),x90904),x90905)))+~P1(f775(f775(f334(f857(x90903,a844)),x90901),f775(f775(f61(x90903),x90904),x90905)))+~P1(f775(f775(f334(f856(x90903,x90903)),f775(f775(f241(x90903,x90903),x90907),x90906)),x90905)) % 186.05/186.63 [10031]~P12(x100319,x100318,x100317)+~P12(x100311,x1003111,x1003110)+~P17(x100311,x100319,f857(x100316,a844),x1003110,x100317,x100315)+P1(f775(f775(f334(x100311),f501(x100312,x100313,x100314,x100315,x100316,x100317,x100318,x100319,x1003110,x1003111,x100311)),x1003111))+~P1(f775(f775(f334(f857(x100319,a844)),x100313),f775(f775(f61(x100319),x100318),x100317)))+~P1(f775(f775(f334(f857(x100311,a844)),x100314),f775(f775(f61(x100311),x1003111),x1003110)))+P1(f775(f775(f334(f857(x100316,a844)),f775(f775(f46(x100311,f857(x100316,a844)),x100314),f775(f775(f10(f857(x100319,f857(x100316,a844)),f857(x100316,a844),x100311),f775(f46(x100319,f857(x100316,a844)),x100313)),x100315))),x100312)) % 186.05/186.63 [10032]~P12(x1003211,x1003210,x100329)+~P12(x100321,x100328,x100327)+~P17(x1003211,x100321,f857(x100326,a844),x100329,x100327,x100325)+P1(f775(f775(f334(x100321),f502(x100322,x100323,x100324,x100325,x100326,x100327,x100328,x100321,x100329,x1003210,x1003211)),x100328))+~P1(f775(f775(f334(f857(x1003211,a844)),x100324),f775(f775(f61(x1003211),x1003210),x100329)))+~P1(f775(f775(f334(f857(x100321,a844)),x100323),f775(f775(f61(x100321),x100328),x100327)))+P1(f775(f775(f334(f857(x100326,a844)),f775(f775(f46(x1003211,f857(x100326,a844)),x100324),f775(f775(f10(f857(x100321,f857(x100326,a844)),f857(x100326,a844),x1003211),f775(f46(x100321,f857(x100326,a844)),x100323)),x100325))),x100322)) % 186.05/186.63 [10035]~P12(x100352,x100358,x100359)+~P12(x100354,x1003510,x1003511)+~P17(x100352,x100354,f857(x100351,a844),x100359,x1003511,x100356)+~P1(f775(f775(f334(f857(x100352,a844)),x100353),f775(f775(f61(x100352),x100358),x100359)))+~P1(f775(f775(f334(f857(x100354,a844)),x100355),f775(f775(f61(x100354),x1003510),x1003511)))+~P1(f775(f775(f334(f857(x100351,a844)),f775(f775(x100356,f501(x100357,x100355,x100353,x100356,x100351,x1003511,x1003510,x100354,x100359,x100358,x100352)),f502(x100357,x100355,x100353,x100356,x100351,x1003511,x1003510,x100354,x100359,x100358,x100352))),x100357))+P1(f775(f775(f334(f857(x100351,a844)),f775(f775(f46(x100352,f857(x100351,a844)),x100353),f775(f775(f10(f857(x100354,f857(x100351,a844)),f857(x100351,a844),x100352),f775(f46(x100354,f857(x100351,a844)),x100355)),x100356))),x100357)) % 186.05/186.63 [9002]E(x90021,x90022)+~P100(x90024)+~P29(x90023,x90024,x90025,f775(f775(f103(f857(x90023,a844)),f775(f158(x90023),x90021)),f775(f158(x90023),x90022)))+~E(f775(f158(x90023),x90021),f775(f158(x90023),x90022))+~P18(x90024,f775(f775(f143(x90023,x90024),x90025),x90022))+~P18(x90024,f775(f775(f143(x90023,x90024),x90025),x90021))+~P1(f775(f127(x90024),f775(f775(f143(x90023,x90024),x90025),x90022)))+~P1(f775(f127(x90024),f775(f775(f143(x90023,x90024),x90025),x90021))) % 186.05/186.63 %EqnAxiom % 186.05/186.63 [1]E(x11,x11) % 186.05/186.63 [2]E(x22,x21)+~E(x21,x22) % 186.05/186.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 186.05/186.63 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 186.05/186.63 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 186.05/186.63 [6]~E(x61,x62)+E(f102(x61),f102(x62)) % 186.05/186.63 [7]~E(x71,x72)+E(f34(x71),f34(x72)) % 186.05/186.63 [8]~E(x81,x82)+E(f775(x81,x83),f775(x82,x83)) % 186.05/186.63 [9]~E(x91,x92)+E(f775(x93,x91),f775(x93,x92)) % 186.05/186.63 [10]~E(x101,x102)+E(f86(x101),f86(x102)) % 186.05/186.63 [11]~E(x111,x112)+E(f586(x111,x113,x114,x115,x116,x117),f586(x112,x113,x114,x115,x116,x117)) % 186.05/186.63 [12]~E(x121,x122)+E(f586(x123,x121,x124,x125,x126,x127),f586(x123,x122,x124,x125,x126,x127)) % 186.05/186.63 [13]~E(x131,x132)+E(f586(x133,x134,x131,x135,x136,x137),f586(x133,x134,x132,x135,x136,x137)) % 186.05/186.63 [14]~E(x141,x142)+E(f586(x143,x144,x145,x141,x146,x147),f586(x143,x144,x145,x142,x146,x147)) % 186.05/186.63 [15]~E(x151,x152)+E(f586(x153,x154,x155,x156,x151,x157),f586(x153,x154,x155,x156,x152,x157)) % 186.05/186.63 [16]~E(x161,x162)+E(f586(x163,x164,x165,x166,x167,x161),f586(x163,x164,x165,x166,x167,x162)) % 186.05/186.63 [17]~E(x171,x172)+E(f170(x171,x173,x174,x175),f170(x172,x173,x174,x175)) % 186.05/186.63 [18]~E(x181,x182)+E(f170(x183,x181,x184,x185),f170(x183,x182,x184,x185)) % 186.05/186.63 [19]~E(x191,x192)+E(f170(x193,x194,x191,x195),f170(x193,x194,x192,x195)) % 186.05/186.63 [20]~E(x201,x202)+E(f170(x203,x204,x205,x201),f170(x203,x204,x205,x202)) % 186.05/186.63 [21]~E(x211,x212)+E(f9(x211,x213,x214),f9(x212,x213,x214)) % 186.05/186.63 [22]~E(x221,x222)+E(f9(x223,x221,x224),f9(x223,x222,x224)) % 186.05/186.63 [23]~E(x231,x232)+E(f9(x233,x234,x231),f9(x233,x234,x232)) % 186.05/186.63 [24]~E(x241,x242)+E(f179(x241),f179(x242)) % 186.05/186.63 [25]~E(x251,x252)+E(f103(x251),f103(x252)) % 186.05/186.63 [26]~E(x261,x262)+E(f180(x261),f180(x262)) % 186.05/186.63 [27]~E(x271,x272)+E(f502(x271,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f502(x272,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712)) % 186.05/186.63 [28]~E(x281,x282)+E(f502(x283,x281,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812),f502(x283,x282,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812)) % 186.05/186.63 [29]~E(x291,x292)+E(f502(x293,x294,x291,x295,x296,x297,x298,x299,x2910,x2911,x2912),f502(x293,x294,x292,x295,x296,x297,x298,x299,x2910,x2911,x2912)) % 186.05/186.63 [30]~E(x301,x302)+E(f502(x303,x304,x305,x301,x306,x307,x308,x309,x3010,x3011,x3012),f502(x303,x304,x305,x302,x306,x307,x308,x309,x3010,x3011,x3012)) % 186.05/186.63 [31]~E(x311,x312)+E(f502(x313,x314,x315,x316,x311,x317,x318,x319,x3110,x3111,x3112),f502(x313,x314,x315,x316,x312,x317,x318,x319,x3110,x3111,x3112)) % 186.05/186.63 [32]~E(x321,x322)+E(f502(x323,x324,x325,x326,x327,x321,x328,x329,x3210,x3211,x3212),f502(x323,x324,x325,x326,x327,x322,x328,x329,x3210,x3211,x3212)) % 186.05/186.63 [33]~E(x331,x332)+E(f502(x333,x334,x335,x336,x337,x338,x331,x339,x3310,x3311,x3312),f502(x333,x334,x335,x336,x337,x338,x332,x339,x3310,x3311,x3312)) % 186.05/186.63 [34]~E(x341,x342)+E(f502(x343,x344,x345,x346,x347,x348,x349,x341,x3410,x3411,x3412),f502(x343,x344,x345,x346,x347,x348,x349,x342,x3410,x3411,x3412)) % 186.05/186.63 [35]~E(x351,x352)+E(f502(x353,x354,x355,x356,x357,x358,x359,x3510,x351,x3511,x3512),f502(x353,x354,x355,x356,x357,x358,x359,x3510,x352,x3511,x3512)) % 186.05/186.63 [36]~E(x361,x362)+E(f502(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x361,x3612),f502(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x362,x3612)) % 186.05/186.63 [37]~E(x371,x372)+E(f502(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x371),f502(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x372)) % 186.05/186.63 [38]~E(x381,x382)+E(f236(x381),f236(x382)) % 186.05/186.63 [39]~E(x391,x392)+E(f104(x391),f104(x392)) % 186.05/186.63 [40]~E(x401,x402)+E(f105(x401),f105(x402)) % 186.05/186.63 [41]~E(x411,x412)+E(f39(x411),f39(x412)) % 186.05/186.63 [42]~E(x421,x422)+E(f334(x421),f334(x422)) % 186.05/186.63 [43]~E(x431,x432)+E(f80(x431),f80(x432)) % 186.05/186.63 [44]~E(x441,x442)+E(f501(x441,x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412),f501(x442,x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412)) % 186.05/186.63 [45]~E(x451,x452)+E(f501(x453,x451,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512),f501(x453,x452,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512)) % 186.05/186.63 [46]~E(x461,x462)+E(f501(x463,x464,x461,x465,x466,x467,x468,x469,x4610,x4611,x4612),f501(x463,x464,x462,x465,x466,x467,x468,x469,x4610,x4611,x4612)) % 186.05/186.63 [47]~E(x471,x472)+E(f501(x473,x474,x475,x471,x476,x477,x478,x479,x4710,x4711,x4712),f501(x473,x474,x475,x472,x476,x477,x478,x479,x4710,x4711,x4712)) % 186.05/186.63 [48]~E(x481,x482)+E(f501(x483,x484,x485,x486,x481,x487,x488,x489,x4810,x4811,x4812),f501(x483,x484,x485,x486,x482,x487,x488,x489,x4810,x4811,x4812)) % 186.05/186.63 [49]~E(x491,x492)+E(f501(x493,x494,x495,x496,x497,x491,x498,x499,x4910,x4911,x4912),f501(x493,x494,x495,x496,x497,x492,x498,x499,x4910,x4911,x4912)) % 186.05/186.63 [50]~E(x501,x502)+E(f501(x503,x504,x505,x506,x507,x508,x501,x509,x5010,x5011,x5012),f501(x503,x504,x505,x506,x507,x508,x502,x509,x5010,x5011,x5012)) % 186.05/186.63 [51]~E(x511,x512)+E(f501(x513,x514,x515,x516,x517,x518,x519,x511,x5110,x5111,x5112),f501(x513,x514,x515,x516,x517,x518,x519,x512,x5110,x5111,x5112)) % 186.05/186.63 [52]~E(x521,x522)+E(f501(x523,x524,x525,x526,x527,x528,x529,x5210,x521,x5211,x5212),f501(x523,x524,x525,x526,x527,x528,x529,x5210,x522,x5211,x5212)) % 186.05/186.63 [53]~E(x531,x532)+E(f501(x533,x534,x535,x536,x537,x538,x539,x5310,x5311,x531,x5312),f501(x533,x534,x535,x536,x537,x538,x539,x5310,x5311,x532,x5312)) % 186.05/186.63 [54]~E(x541,x542)+E(f501(x543,x544,x545,x546,x547,x548,x549,x5410,x5411,x5412,x541),f501(x543,x544,x545,x546,x547,x548,x549,x5410,x5411,x5412,x542)) % 186.05/186.63 [55]~E(x551,x552)+E(f113(x551),f113(x552)) % 186.05/186.63 [56]~E(x561,x562)+E(f44(x561,x563),f44(x562,x563)) % 186.05/186.63 [57]~E(x571,x572)+E(f44(x573,x571),f44(x573,x572)) % 186.05/186.63 [58]~E(x581,x582)+E(f857(x581,x583),f857(x582,x583)) % 186.05/186.63 [59]~E(x591,x592)+E(f857(x593,x591),f857(x593,x592)) % 186.05/186.63 [60]~E(x601,x602)+E(f6(x601),f6(x602)) % 186.05/186.63 [61]~E(x611,x612)+E(f82(x611),f82(x612)) % 186.05/186.63 [62]~E(x621,x622)+E(f81(x621),f81(x622)) % 186.05/186.63 [63]~E(x631,x632)+E(f63(x631),f63(x632)) % 186.05/186.63 [64]~E(x641,x642)+E(f181(x641),f181(x642)) % 186.05/186.63 [65]~E(x651,x652)+E(f10(x651,x653,x654),f10(x652,x653,x654)) % 186.05/186.63 [66]~E(x661,x662)+E(f10(x663,x661,x664),f10(x663,x662,x664)) % 186.05/186.63 [67]~E(x671,x672)+E(f10(x673,x674,x671),f10(x673,x674,x672)) % 186.05/186.63 [68]~E(x681,x682)+E(f106(x681),f106(x682)) % 186.05/186.63 [69]~E(x691,x692)+E(f8(x691,x693),f8(x692,x693)) % 186.05/186.63 [70]~E(x701,x702)+E(f8(x703,x701),f8(x703,x702)) % 186.05/186.63 [71]~E(x711,x712)+E(f20(x711,x713,x714),f20(x712,x713,x714)) % 186.05/186.63 [72]~E(x721,x722)+E(f20(x723,x721,x724),f20(x723,x722,x724)) % 186.05/186.63 [73]~E(x731,x732)+E(f20(x733,x734,x731),f20(x733,x734,x732)) % 186.05/186.63 [74]~E(x741,x742)+E(f256(x741),f256(x742)) % 186.05/186.63 [75]~E(x751,x752)+E(f42(x751),f42(x752)) % 186.05/186.63 [76]~E(x761,x762)+E(f61(x761),f61(x762)) % 186.05/186.63 [77]~E(x771,x772)+E(f233(x771),f233(x772)) % 186.05/186.63 [78]~E(x781,x782)+E(f83(x781),f83(x782)) % 186.05/186.63 [79]~E(x791,x792)+E(f305(x791,x793,x794),f305(x792,x793,x794)) % 186.05/186.63 [80]~E(x801,x802)+E(f305(x803,x801,x804),f305(x803,x802,x804)) % 186.05/186.63 [81]~E(x811,x812)+E(f305(x813,x814,x811),f305(x813,x814,x812)) % 186.05/186.63 [82]~E(x821,x822)+E(f405(x821,x823,x824),f405(x822,x823,x824)) % 186.05/186.63 [83]~E(x831,x832)+E(f405(x833,x831,x834),f405(x833,x832,x834)) % 186.05/186.63 [84]~E(x841,x842)+E(f405(x843,x844,x841),f405(x843,x844,x842)) % 186.05/186.63 [85]~E(x851,x852)+E(f851(x851),f851(x852)) % 186.05/186.63 [86]~E(x861,x862)+E(f31(x861,x863,x864),f31(x862,x863,x864)) % 186.05/186.63 [87]~E(x871,x872)+E(f31(x873,x871,x874),f31(x873,x872,x874)) % 186.05/186.63 [88]~E(x881,x882)+E(f31(x883,x884,x881),f31(x883,x884,x882)) % 186.05/186.63 [89]~E(x891,x892)+E(f127(x891),f127(x892)) % 186.05/186.63 [90]~E(x901,x902)+E(f294(x901,x903),f294(x902,x903)) % 186.05/186.63 [91]~E(x911,x912)+E(f294(x913,x911),f294(x913,x912)) % 186.05/186.63 [92]~E(x921,x922)+E(f232(x921),f232(x922)) % 186.05/186.63 [93]~E(x931,x932)+E(f734(x931,x933,x934,x935,x936),f734(x932,x933,x934,x935,x936)) % 186.05/186.63 [94]~E(x941,x942)+E(f734(x943,x941,x944,x945,x946),f734(x943,x942,x944,x945,x946)) % 186.05/186.63 [95]~E(x951,x952)+E(f734(x953,x954,x951,x955,x956),f734(x953,x954,x952,x955,x956)) % 186.05/186.63 [96]~E(x961,x962)+E(f734(x963,x964,x965,x961,x966),f734(x963,x964,x965,x962,x966)) % 186.05/186.63 [97]~E(x971,x972)+E(f734(x973,x974,x975,x976,x971),f734(x973,x974,x975,x976,x972)) % 186.05/186.63 [98]~E(x981,x982)+E(f130(x981,x983),f130(x982,x983)) % 186.05/186.63 [99]~E(x991,x992)+E(f130(x993,x991),f130(x993,x992)) % 186.05/186.63 [100]~E(x1001,x1002)+E(f302(x1001),f302(x1002)) % 186.05/186.63 [101]~E(x1011,x1012)+E(f140(x1011),f140(x1012)) % 186.05/186.63 [102]~E(x1021,x1022)+E(f33(x1021,x1023,x1024),f33(x1022,x1023,x1024)) % 186.05/186.63 [103]~E(x1031,x1032)+E(f33(x1033,x1031,x1034),f33(x1033,x1032,x1034)) % 186.05/186.63 [104]~E(x1041,x1042)+E(f33(x1043,x1044,x1041),f33(x1043,x1044,x1042)) % 186.05/186.63 [105]~E(x1051,x1052)+E(f248(x1051,x1053),f248(x1052,x1053)) % 186.05/186.63 [106]~E(x1061,x1062)+E(f248(x1063,x1061),f248(x1063,x1062)) % 186.05/186.63 [107]~E(x1071,x1072)+E(f187(x1071),f187(x1072)) % 186.05/186.63 [108]~E(x1081,x1082)+E(f283(x1081),f283(x1082)) % 186.05/186.63 [109]~E(x1091,x1092)+E(f159(x1091),f159(x1092)) % 186.05/186.63 [110]~E(x1101,x1102)+E(f131(x1101),f131(x1102)) % 186.05/186.63 [111]~E(x1111,x1112)+E(f46(x1111,x1113),f46(x1112,x1113)) % 186.05/186.63 [112]~E(x1121,x1122)+E(f46(x1123,x1121),f46(x1123,x1122)) % 186.05/186.63 [113]~E(x1131,x1132)+E(f300(x1131,x1133),f300(x1132,x1133)) % 186.05/186.63 [114]~E(x1141,x1142)+E(f300(x1143,x1141),f300(x1143,x1142)) % 186.05/186.63 [115]~E(x1151,x1152)+E(f125(x1151),f125(x1152)) % 186.05/186.63 [116]~E(x1161,x1162)+E(f142(x1161),f142(x1162)) % 186.05/186.63 [117]~E(x1171,x1172)+E(f241(x1171,x1173),f241(x1172,x1173)) % 186.05/186.63 [118]~E(x1181,x1182)+E(f241(x1183,x1181),f241(x1183,x1182)) % 186.05/186.63 [119]~E(x1191,x1192)+E(f257(x1191),f257(x1192)) % 186.05/186.63 [120]~E(x1201,x1202)+E(f92(x1201,x1203),f92(x1202,x1203)) % 186.05/186.63 [121]~E(x1211,x1212)+E(f92(x1213,x1211),f92(x1213,x1212)) % 186.05/186.63 [122]~E(x1221,x1222)+E(f93(x1221),f93(x1222)) % 186.05/186.63 [123]~E(x1231,x1232)+E(f852(x1231),f852(x1232)) % 186.05/186.63 [124]~E(x1241,x1242)+E(f856(x1241,x1243),f856(x1242,x1243)) % 186.05/186.63 [125]~E(x1251,x1252)+E(f856(x1253,x1251),f856(x1253,x1252)) % 186.05/186.63 [126]~E(x1261,x1262)+E(f303(x1261,x1263,x1264),f303(x1262,x1263,x1264)) % 186.05/186.63 [127]~E(x1271,x1272)+E(f303(x1273,x1271,x1274),f303(x1273,x1272,x1274)) % 186.05/186.63 [128]~E(x1281,x1282)+E(f303(x1283,x1284,x1281),f303(x1283,x1284,x1282)) % 186.05/186.63 [129]~E(x1291,x1292)+E(f137(x1291,x1293),f137(x1292,x1293)) % 186.05/186.63 [130]~E(x1301,x1302)+E(f137(x1303,x1301),f137(x1303,x1302)) % 186.05/186.63 [131]~E(x1311,x1312)+E(f854(x1311),f854(x1312)) % 186.05/186.63 [132]~E(x1321,x1322)+E(f157(x1321),f157(x1322)) % 186.05/186.63 [133]~E(x1331,x1332)+E(f297(x1331,x1333,x1334),f297(x1332,x1333,x1334)) % 186.05/186.63 [134]~E(x1341,x1342)+E(f297(x1343,x1341,x1344),f297(x1343,x1342,x1344)) % 186.05/186.63 [135]~E(x1351,x1352)+E(f297(x1353,x1354,x1351),f297(x1353,x1354,x1352)) % 186.05/186.63 [136]~E(x1361,x1362)+E(f295(x1361,x1363,x1364),f295(x1362,x1363,x1364)) % 186.05/186.63 [137]~E(x1371,x1372)+E(f295(x1373,x1371,x1374),f295(x1373,x1372,x1374)) % 186.05/186.63 [138]~E(x1381,x1382)+E(f295(x1383,x1384,x1381),f295(x1383,x1384,x1382)) % 186.05/186.63 [139]~E(x1391,x1392)+E(f108(x1391),f108(x1392)) % 186.05/186.63 [140]~E(x1401,x1402)+E(f110(x1401),f110(x1402)) % 186.05/186.63 [141]~E(x1411,x1412)+E(f333(x1411),f333(x1412)) % 186.05/186.63 [142]~E(x1421,x1422)+E(f780(x1421,x1423,x1424),f780(x1422,x1423,x1424)) % 186.05/186.63 [143]~E(x1431,x1432)+E(f780(x1433,x1431,x1434),f780(x1433,x1432,x1434)) % 186.05/186.63 [144]~E(x1441,x1442)+E(f780(x1443,x1444,x1441),f780(x1443,x1444,x1442)) % 186.05/186.63 [145]~E(x1451,x1452)+E(f132(x1451,x1453,x1454,x1455),f132(x1452,x1453,x1454,x1455)) % 186.05/186.63 [146]~E(x1461,x1462)+E(f132(x1463,x1461,x1464,x1465),f132(x1463,x1462,x1464,x1465)) % 186.05/186.63 [147]~E(x1471,x1472)+E(f132(x1473,x1474,x1471,x1475),f132(x1473,x1474,x1472,x1475)) % 186.05/186.63 [148]~E(x1481,x1482)+E(f132(x1483,x1484,x1485,x1481),f132(x1483,x1484,x1485,x1482)) % 186.05/186.63 [149]~E(x1491,x1492)+E(f238(x1491,x1493),f238(x1492,x1493)) % 186.05/186.63 [150]~E(x1501,x1502)+E(f238(x1503,x1501),f238(x1503,x1502)) % 186.05/186.63 [151]~E(x1511,x1512)+E(f56(x1511,x1513),f56(x1512,x1513)) % 186.05/186.63 [152]~E(x1521,x1522)+E(f56(x1523,x1521),f56(x1523,x1522)) % 186.05/186.63 [153]~E(x1531,x1532)+E(f183(x1531),f183(x1532)) % 186.05/186.63 [154]~E(x1541,x1542)+E(f158(x1541),f158(x1542)) % 186.05/186.63 [155]~E(x1551,x1552)+E(f89(x1551),f89(x1552)) % 186.05/186.63 [156]~E(x1561,x1562)+E(f43(x1561),f43(x1562)) % 186.05/186.63 [157]~E(x1571,x1572)+E(f7(x1571),f7(x1572)) % 186.05/186.63 [158]~E(x1581,x1582)+E(f52(x1581,x1583,x1584),f52(x1582,x1583,x1584)) % 186.05/186.63 [159]~E(x1591,x1592)+E(f52(x1593,x1591,x1594),f52(x1593,x1592,x1594)) % 186.05/186.63 [160]~E(x1601,x1602)+E(f52(x1603,x1604,x1601),f52(x1603,x1604,x1602)) % 186.05/186.63 [161]~E(x1611,x1612)+E(f35(x1611,x1613),f35(x1612,x1613)) % 186.05/186.63 [162]~E(x1621,x1622)+E(f35(x1623,x1621),f35(x1623,x1622)) % 186.05/186.63 [163]~E(x1631,x1632)+E(f174(x1631,x1633,x1634),f174(x1632,x1633,x1634)) % 186.05/186.63 [164]~E(x1641,x1642)+E(f174(x1643,x1641,x1644),f174(x1643,x1642,x1644)) % 186.05/186.63 [165]~E(x1651,x1652)+E(f174(x1653,x1654,x1651),f174(x1653,x1654,x1652)) % 186.05/186.63 [166]~E(x1661,x1662)+E(f505(x1661,x1663,x1664,x1665),f505(x1662,x1663,x1664,x1665)) % 186.05/186.63 [167]~E(x1671,x1672)+E(f505(x1673,x1671,x1674,x1675),f505(x1673,x1672,x1674,x1675)) % 186.05/186.63 [168]~E(x1681,x1682)+E(f505(x1683,x1684,x1681,x1685),f505(x1683,x1684,x1682,x1685)) % 186.05/186.63 [169]~E(x1691,x1692)+E(f505(x1693,x1694,x1695,x1691),f505(x1693,x1694,x1695,x1692)) % 186.05/186.63 [170]~E(x1701,x1702)+E(f396(x1701,x1703,x1704,x1705,x1706),f396(x1702,x1703,x1704,x1705,x1706)) % 186.05/186.63 [171]~E(x1711,x1712)+E(f396(x1713,x1711,x1714,x1715,x1716),f396(x1713,x1712,x1714,x1715,x1716)) % 186.05/186.63 [172]~E(x1721,x1722)+E(f396(x1723,x1724,x1721,x1725,x1726),f396(x1723,x1724,x1722,x1725,x1726)) % 186.05/186.63 [173]~E(x1731,x1732)+E(f396(x1733,x1734,x1735,x1731,x1736),f396(x1733,x1734,x1735,x1732,x1736)) % 186.05/186.63 [174]~E(x1741,x1742)+E(f396(x1743,x1744,x1745,x1746,x1741),f396(x1743,x1744,x1745,x1746,x1742)) % 186.05/186.63 [175]~E(x1751,x1752)+E(f133(x1751,x1753),f133(x1752,x1753)) % 186.05/186.63 [176]~E(x1761,x1762)+E(f133(x1763,x1761),f133(x1763,x1762)) % 186.05/186.63 [177]~E(x1771,x1772)+E(f536(x1771,x1773,x1774,x1775,x1776),f536(x1772,x1773,x1774,x1775,x1776)) % 186.05/186.63 [178]~E(x1781,x1782)+E(f536(x1783,x1781,x1784,x1785,x1786),f536(x1783,x1782,x1784,x1785,x1786)) % 186.05/186.63 [179]~E(x1791,x1792)+E(f536(x1793,x1794,x1791,x1795,x1796),f536(x1793,x1794,x1792,x1795,x1796)) % 186.05/186.63 [180]~E(x1801,x1802)+E(f536(x1803,x1804,x1805,x1801,x1806),f536(x1803,x1804,x1805,x1802,x1806)) % 186.05/186.63 [181]~E(x1811,x1812)+E(f536(x1813,x1814,x1815,x1816,x1811),f536(x1813,x1814,x1815,x1816,x1812)) % 186.05/186.63 [182]~E(x1821,x1822)+E(f752(x1821,x1823,x1824,x1825),f752(x1822,x1823,x1824,x1825)) % 186.05/186.63 [183]~E(x1831,x1832)+E(f752(x1833,x1831,x1834,x1835),f752(x1833,x1832,x1834,x1835)) % 186.05/186.63 [184]~E(x1841,x1842)+E(f752(x1843,x1844,x1841,x1845),f752(x1843,x1844,x1842,x1845)) % 186.05/186.63 [185]~E(x1851,x1852)+E(f752(x1853,x1854,x1855,x1851),f752(x1853,x1854,x1855,x1852)) % 186.05/186.63 [186]~E(x1861,x1862)+E(f277(x1861,x1863,x1864),f277(x1862,x1863,x1864)) % 186.05/186.63 [187]~E(x1871,x1872)+E(f277(x1873,x1871,x1874),f277(x1873,x1872,x1874)) % 186.05/186.63 [188]~E(x1881,x1882)+E(f277(x1883,x1884,x1881),f277(x1883,x1884,x1882)) % 186.05/186.63 [189]~E(x1891,x1892)+E(f84(x1891,x1893),f84(x1892,x1893)) % 186.05/186.63 [190]~E(x1901,x1902)+E(f84(x1903,x1901),f84(x1903,x1902)) % 186.05/186.63 [191]~E(x1911,x1912)+E(f298(x1911,x1913,x1914),f298(x1912,x1913,x1914)) % 186.05/186.63 [192]~E(x1921,x1922)+E(f298(x1923,x1921,x1924),f298(x1923,x1922,x1924)) % 186.05/186.63 [193]~E(x1931,x1932)+E(f298(x1933,x1934,x1931),f298(x1933,x1934,x1932)) % 186.05/186.63 [194]~E(x1941,x1942)+E(f279(x1941),f279(x1942)) % 186.05/186.63 [195]~E(x1951,x1952)+E(f196(x1951,x1953),f196(x1952,x1953)) % 186.05/186.63 [196]~E(x1961,x1962)+E(f196(x1963,x1961),f196(x1963,x1962)) % 186.05/186.63 [197]~E(x1971,x1972)+E(f18(x1971,x1973),f18(x1972,x1973)) % 186.05/186.63 [198]~E(x1981,x1982)+E(f18(x1983,x1981),f18(x1983,x1982)) % 186.05/186.63 [199]~E(x1991,x1992)+E(f175(x1991,x1993,x1994,x1995),f175(x1992,x1993,x1994,x1995)) % 186.05/186.63 [200]~E(x2001,x2002)+E(f175(x2003,x2001,x2004,x2005),f175(x2003,x2002,x2004,x2005)) % 186.05/186.63 [201]~E(x2011,x2012)+E(f175(x2013,x2014,x2011,x2015),f175(x2013,x2014,x2012,x2015)) % 186.05/186.63 [202]~E(x2021,x2022)+E(f175(x2023,x2024,x2025,x2021),f175(x2023,x2024,x2025,x2022)) % 186.05/186.63 [203]~E(x2031,x2032)+E(f304(x2031,x2033),f304(x2032,x2033)) % 186.05/186.63 [204]~E(x2041,x2042)+E(f304(x2043,x2041),f304(x2043,x2042)) % 186.05/186.63 [205]~E(x2051,x2052)+E(f242(x2051),f242(x2052)) % 186.05/186.63 [206]~E(x2061,x2062)+E(f250(x2061,x2063),f250(x2062,x2063)) % 186.05/186.63 [207]~E(x2071,x2072)+E(f250(x2073,x2071),f250(x2073,x2072)) % 186.05/186.63 [208]~E(x2081,x2082)+E(f172(x2081,x2083,x2084,x2085),f172(x2082,x2083,x2084,x2085)) % 186.05/186.63 [209]~E(x2091,x2092)+E(f172(x2093,x2091,x2094,x2095),f172(x2093,x2092,x2094,x2095)) % 186.05/186.63 [210]~E(x2101,x2102)+E(f172(x2103,x2104,x2101,x2105),f172(x2103,x2104,x2102,x2105)) % 186.05/186.63 [211]~E(x2111,x2112)+E(f172(x2113,x2114,x2115,x2111),f172(x2113,x2114,x2115,x2112)) % 186.05/186.63 [212]~E(x2121,x2122)+E(f126(x2121,x2123),f126(x2122,x2123)) % 186.05/186.63 [213]~E(x2131,x2132)+E(f126(x2133,x2131),f126(x2133,x2132)) % 186.05/186.63 [214]~E(x2141,x2142)+E(f171(x2141,x2143,x2144),f171(x2142,x2143,x2144)) % 186.05/186.63 [215]~E(x2151,x2152)+E(f171(x2153,x2151,x2154),f171(x2153,x2152,x2154)) % 186.05/186.63 [216]~E(x2161,x2162)+E(f171(x2163,x2164,x2161),f171(x2163,x2164,x2162)) % 186.05/186.63 [217]~E(x2171,x2172)+E(f14(x2171,x2173,x2174),f14(x2172,x2173,x2174)) % 186.05/186.63 [218]~E(x2181,x2182)+E(f14(x2183,x2181,x2184),f14(x2183,x2182,x2184)) % 186.05/186.63 [219]~E(x2191,x2192)+E(f14(x2193,x2194,x2191),f14(x2193,x2194,x2192)) % 186.05/186.63 [220]~E(x2201,x2202)+E(f301(x2201),f301(x2202)) % 186.05/186.63 [221]~E(x2211,x2212)+E(f12(x2211,x2213),f12(x2212,x2213)) % 186.05/186.63 [222]~E(x2221,x2222)+E(f12(x2223,x2221),f12(x2223,x2222)) % 186.05/186.63 [223]~E(x2231,x2232)+E(f115(x2231),f115(x2232)) % 186.05/186.63 [224]~E(x2241,x2242)+E(f77(x2241),f77(x2242)) % 186.05/186.63 [225]~E(x2251,x2252)+E(f795(x2251,x2253,x2254),f795(x2252,x2253,x2254)) % 186.05/186.63 [226]~E(x2261,x2262)+E(f795(x2263,x2261,x2264),f795(x2263,x2262,x2264)) % 186.05/186.63 [227]~E(x2271,x2272)+E(f795(x2273,x2274,x2271),f795(x2273,x2274,x2272)) % 186.05/186.63 [228]~E(x2281,x2282)+E(f240(x2281,x2283),f240(x2282,x2283)) % 186.05/186.63 [229]~E(x2291,x2292)+E(f240(x2293,x2291),f240(x2293,x2292)) % 186.05/186.63 [230]~E(x2301,x2302)+E(f155(x2301),f155(x2302)) % 186.05/186.63 [231]~E(x2311,x2312)+E(f11(x2311,x2313),f11(x2312,x2313)) % 186.05/186.63 [232]~E(x2321,x2322)+E(f11(x2323,x2321),f11(x2323,x2322)) % 186.05/186.63 [233]~E(x2331,x2332)+E(f148(x2331,x2333),f148(x2332,x2333)) % 186.05/186.63 [234]~E(x2341,x2342)+E(f148(x2343,x2341),f148(x2343,x2342)) % 186.05/186.63 [235]~E(x2351,x2352)+E(f151(x2351,x2353,x2354),f151(x2352,x2353,x2354)) % 186.05/186.63 [236]~E(x2361,x2362)+E(f151(x2363,x2361,x2364),f151(x2363,x2362,x2364)) % 186.05/186.63 [237]~E(x2371,x2372)+E(f151(x2373,x2374,x2371),f151(x2373,x2374,x2372)) % 186.05/186.63 [238]~E(x2381,x2382)+E(f143(x2381,x2383),f143(x2382,x2383)) % 186.05/186.63 [239]~E(x2391,x2392)+E(f143(x2393,x2391),f143(x2393,x2392)) % 186.05/186.63 [240]~E(x2401,x2402)+E(f47(x2401,x2403),f47(x2402,x2403)) % 186.05/186.63 [241]~E(x2411,x2412)+E(f47(x2413,x2411),f47(x2413,x2412)) % 186.05/186.63 [242]~E(x2421,x2422)+E(f163(x2421,x2423),f163(x2422,x2423)) % 186.05/186.63 [243]~E(x2431,x2432)+E(f163(x2433,x2431),f163(x2433,x2432)) % 186.05/186.63 [244]~E(x2441,x2442)+E(f75(x2441,x2443,x2444,x2445),f75(x2442,x2443,x2444,x2445)) % 186.05/186.63 [245]~E(x2451,x2452)+E(f75(x2453,x2451,x2454,x2455),f75(x2453,x2452,x2454,x2455)) % 186.05/186.63 [246]~E(x2461,x2462)+E(f75(x2463,x2464,x2461,x2465),f75(x2463,x2464,x2462,x2465)) % 186.05/186.63 [247]~E(x2471,x2472)+E(f75(x2473,x2474,x2475,x2471),f75(x2473,x2474,x2475,x2472)) % 186.05/186.63 [248]~E(x2481,x2482)+E(f116(x2481,x2483),f116(x2482,x2483)) % 186.05/186.63 [249]~E(x2491,x2492)+E(f116(x2493,x2491),f116(x2493,x2492)) % 186.05/186.63 [250]~E(x2501,x2502)+E(f164(x2501,x2503),f164(x2502,x2503)) % 186.05/186.63 [251]~E(x2511,x2512)+E(f164(x2513,x2511),f164(x2513,x2512)) % 186.05/186.63 [252]~E(x2521,x2522)+E(f184(x2521),f184(x2522)) % 186.05/186.63 [253]~E(x2531,x2532)+E(f278(x2531,x2533),f278(x2532,x2533)) % 186.05/186.63 [254]~E(x2541,x2542)+E(f278(x2543,x2541),f278(x2543,x2542)) % 186.05/186.63 [255]~E(x2551,x2552)+E(f117(x2551),f117(x2552)) % 186.05/186.63 [256]~E(x2561,x2562)+E(f408(x2561,x2563,x2564,x2565),f408(x2562,x2563,x2564,x2565)) % 186.05/186.63 [257]~E(x2571,x2572)+E(f408(x2573,x2571,x2574,x2575),f408(x2573,x2572,x2574,x2575)) % 186.05/186.63 [258]~E(x2581,x2582)+E(f408(x2583,x2584,x2581,x2585),f408(x2583,x2584,x2582,x2585)) % 186.05/186.63 [259]~E(x2591,x2592)+E(f408(x2593,x2594,x2595,x2591),f408(x2593,x2594,x2595,x2592)) % 186.05/186.63 [260]~E(x2601,x2602)+E(f166(x2601,x2603,x2604),f166(x2602,x2603,x2604)) % 186.05/186.63 [261]~E(x2611,x2612)+E(f166(x2613,x2611,x2614),f166(x2613,x2612,x2614)) % 186.05/186.63 [262]~E(x2621,x2622)+E(f166(x2623,x2624,x2621),f166(x2623,x2624,x2622)) % 186.05/186.63 [263]~E(x2631,x2632)+E(f227(x2631),f227(x2632)) % 186.05/186.63 [264]~E(x2641,x2642)+E(f802(x2641,x2643,x2644),f802(x2642,x2643,x2644)) % 186.05/186.63 [265]~E(x2651,x2652)+E(f802(x2653,x2651,x2654),f802(x2653,x2652,x2654)) % 186.05/186.63 [266]~E(x2661,x2662)+E(f802(x2663,x2664,x2661),f802(x2663,x2664,x2662)) % 186.05/186.63 [267]~E(x2671,x2672)+E(f349(x2671,x2673,x2674,x2675),f349(x2672,x2673,x2674,x2675)) % 186.05/186.63 [268]~E(x2681,x2682)+E(f349(x2683,x2681,x2684,x2685),f349(x2683,x2682,x2684,x2685)) % 186.05/186.63 [269]~E(x2691,x2692)+E(f349(x2693,x2694,x2691,x2695),f349(x2693,x2694,x2692,x2695)) % 186.05/186.63 [270]~E(x2701,x2702)+E(f349(x2703,x2704,x2705,x2701),f349(x2703,x2704,x2705,x2702)) % 186.05/186.63 [271]~E(x2711,x2712)+E(f141(x2711),f141(x2712)) % 186.05/186.63 [272]~E(x2721,x2722)+E(f135(x2721,x2723),f135(x2722,x2723)) % 186.05/186.63 [273]~E(x2731,x2732)+E(f135(x2733,x2731),f135(x2733,x2732)) % 186.05/186.63 [274]~E(x2741,x2742)+E(f781(x2741,x2743,x2744),f781(x2742,x2743,x2744)) % 186.05/186.63 [275]~E(x2751,x2752)+E(f781(x2753,x2751,x2754),f781(x2753,x2752,x2754)) % 186.05/186.63 [276]~E(x2761,x2762)+E(f781(x2763,x2764,x2761),f781(x2763,x2764,x2762)) % 186.05/186.63 [277]~E(x2771,x2772)+E(f153(x2771),f153(x2772)) % 186.05/186.63 [278]~E(x2781,x2782)+E(f147(x2781,x2783),f147(x2782,x2783)) % 186.05/186.63 [279]~E(x2791,x2792)+E(f147(x2793,x2791),f147(x2793,x2792)) % 186.05/186.63 [280]~E(x2801,x2802)+E(f784(x2801,x2803,x2804),f784(x2802,x2803,x2804)) % 186.05/186.63 [281]~E(x2811,x2812)+E(f784(x2813,x2811,x2814),f784(x2813,x2812,x2814)) % 186.05/186.63 [282]~E(x2821,x2822)+E(f784(x2823,x2824,x2821),f784(x2823,x2824,x2822)) % 186.05/186.63 [283]~E(x2831,x2832)+E(f650(x2831,x2833,x2834,x2835),f650(x2832,x2833,x2834,x2835)) % 186.05/186.63 [284]~E(x2841,x2842)+E(f650(x2843,x2841,x2844,x2845),f650(x2843,x2842,x2844,x2845)) % 186.05/186.63 [285]~E(x2851,x2852)+E(f650(x2853,x2854,x2851,x2855),f650(x2853,x2854,x2852,x2855)) % 186.05/186.63 [286]~E(x2861,x2862)+E(f650(x2863,x2864,x2865,x2861),f650(x2863,x2864,x2865,x2862)) % 186.05/186.63 [287]~E(x2871,x2872)+E(f176(x2871),f176(x2872)) % 186.05/186.63 [288]~E(x2881,x2882)+E(f221(x2881,x2883),f221(x2882,x2883)) % 186.05/186.63 [289]~E(x2891,x2892)+E(f221(x2893,x2891),f221(x2893,x2892)) % 186.05/186.63 [290]~E(x2901,x2902)+E(f66(x2901,x2903,x2904),f66(x2902,x2903,x2904)) % 186.05/186.63 [291]~E(x2911,x2912)+E(f66(x2913,x2911,x2914),f66(x2913,x2912,x2914)) % 186.05/186.63 [292]~E(x2921,x2922)+E(f66(x2923,x2924,x2921),f66(x2923,x2924,x2922)) % 186.05/186.63 [293]~E(x2931,x2932)+E(f440(x2931,x2933,x2934,x2935,x2936),f440(x2932,x2933,x2934,x2935,x2936)) % 186.05/186.63 [294]~E(x2941,x2942)+E(f440(x2943,x2941,x2944,x2945,x2946),f440(x2943,x2942,x2944,x2945,x2946)) % 186.05/186.63 [295]~E(x2951,x2952)+E(f440(x2953,x2954,x2951,x2955,x2956),f440(x2953,x2954,x2952,x2955,x2956)) % 186.05/186.63 [296]~E(x2961,x2962)+E(f440(x2963,x2964,x2965,x2961,x2966),f440(x2963,x2964,x2965,x2962,x2966)) % 186.05/186.63 [297]~E(x2971,x2972)+E(f440(x2973,x2974,x2975,x2976,x2971),f440(x2973,x2974,x2975,x2976,x2972)) % 186.05/186.63 [298]~E(x2981,x2982)+E(f533(x2981,x2983,x2984,x2985,x2986),f533(x2982,x2983,x2984,x2985,x2986)) % 186.05/186.63 [299]~E(x2991,x2992)+E(f533(x2993,x2991,x2994,x2995,x2996),f533(x2993,x2992,x2994,x2995,x2996)) % 186.05/186.63 [300]~E(x3001,x3002)+E(f533(x3003,x3004,x3001,x3005,x3006),f533(x3003,x3004,x3002,x3005,x3006)) % 186.05/186.63 [301]~E(x3011,x3012)+E(f533(x3013,x3014,x3015,x3011,x3016),f533(x3013,x3014,x3015,x3012,x3016)) % 186.05/186.63 [302]~E(x3021,x3022)+E(f533(x3023,x3024,x3025,x3026,x3021),f533(x3023,x3024,x3025,x3026,x3022)) % 186.05/186.63 [303]~E(x3031,x3032)+E(f239(x3031),f239(x3032)) % 186.05/186.63 [304]~E(x3041,x3042)+E(f477(x3041,x3043,x3044),f477(x3042,x3043,x3044)) % 186.05/186.63 [305]~E(x3051,x3052)+E(f477(x3053,x3051,x3054),f477(x3053,x3052,x3054)) % 186.05/186.63 [306]~E(x3061,x3062)+E(f477(x3063,x3064,x3061),f477(x3063,x3064,x3062)) % 186.05/186.63 [307]~E(x3071,x3072)+E(f252(x3071,x3073,x3074,x3075,x3076,x3077),f252(x3072,x3073,x3074,x3075,x3076,x3077)) % 186.05/186.63 [308]~E(x3081,x3082)+E(f252(x3083,x3081,x3084,x3085,x3086,x3087),f252(x3083,x3082,x3084,x3085,x3086,x3087)) % 186.05/186.63 [309]~E(x3091,x3092)+E(f252(x3093,x3094,x3091,x3095,x3096,x3097),f252(x3093,x3094,x3092,x3095,x3096,x3097)) % 186.05/186.63 [310]~E(x3101,x3102)+E(f252(x3103,x3104,x3105,x3101,x3106,x3107),f252(x3103,x3104,x3105,x3102,x3106,x3107)) % 186.05/186.63 [311]~E(x3111,x3112)+E(f252(x3113,x3114,x3115,x3116,x3111,x3117),f252(x3113,x3114,x3115,x3116,x3112,x3117)) % 186.05/186.63 [312]~E(x3121,x3122)+E(f252(x3123,x3124,x3125,x3126,x3127,x3121),f252(x3123,x3124,x3125,x3126,x3127,x3122)) % 186.05/186.63 [313]~E(x3131,x3132)+E(f149(x3131,x3133),f149(x3132,x3133)) % 186.05/186.63 [314]~E(x3141,x3142)+E(f149(x3143,x3141),f149(x3143,x3142)) % 186.05/186.63 [315]~E(x3151,x3152)+E(f28(x3151,x3153),f28(x3152,x3153)) % 186.05/186.63 [316]~E(x3161,x3162)+E(f28(x3163,x3161),f28(x3163,x3162)) % 186.05/186.63 [317]~E(x3171,x3172)+E(f289(x3171,x3173,x3174,x3175,x3176),f289(x3172,x3173,x3174,x3175,x3176)) % 186.05/186.63 [318]~E(x3181,x3182)+E(f289(x3183,x3181,x3184,x3185,x3186),f289(x3183,x3182,x3184,x3185,x3186)) % 186.05/186.63 [319]~E(x3191,x3192)+E(f289(x3193,x3194,x3191,x3195,x3196),f289(x3193,x3194,x3192,x3195,x3196)) % 186.05/186.63 [320]~E(x3201,x3202)+E(f289(x3203,x3204,x3205,x3201,x3206),f289(x3203,x3204,x3205,x3202,x3206)) % 186.05/186.63 [321]~E(x3211,x3212)+E(f289(x3213,x3214,x3215,x3216,x3211),f289(x3213,x3214,x3215,x3216,x3212)) % 186.05/186.63 [322]~E(x3221,x3222)+E(f198(x3221,x3223),f198(x3222,x3223)) % 186.05/186.63 [323]~E(x3231,x3232)+E(f198(x3233,x3231),f198(x3233,x3232)) % 186.05/186.63 [324]~E(x3241,x3242)+E(f16(x3241,x3243),f16(x3242,x3243)) % 186.05/186.63 [325]~E(x3251,x3252)+E(f16(x3253,x3251),f16(x3253,x3252)) % 186.05/186.63 [326]~E(x3261,x3262)+E(f324(x3261,x3263),f324(x3262,x3263)) % 186.05/186.63 [327]~E(x3271,x3272)+E(f324(x3273,x3271),f324(x3273,x3272)) % 186.05/186.63 [328]~E(x3281,x3282)+E(f160(x3281,x3283,x3284),f160(x3282,x3283,x3284)) % 186.05/186.63 [329]~E(x3291,x3292)+E(f160(x3293,x3291,x3294),f160(x3293,x3292,x3294)) % 186.05/186.63 [330]~E(x3301,x3302)+E(f160(x3303,x3304,x3301),f160(x3303,x3304,x3302)) % 186.05/186.63 [331]~E(x3311,x3312)+E(f326(x3311,x3313),f326(x3312,x3313)) % 186.05/186.63 [332]~E(x3321,x3322)+E(f326(x3323,x3321),f326(x3323,x3322)) % 186.05/186.63 [333]~E(x3331,x3332)+E(f683(x3331,x3333),f683(x3332,x3333)) % 186.05/186.63 [334]~E(x3341,x3342)+E(f683(x3343,x3341),f683(x3343,x3342)) % 186.05/186.63 [335]~E(x3351,x3352)+E(f65(x3351,x3353),f65(x3352,x3353)) % 186.05/186.63 [336]~E(x3361,x3362)+E(f65(x3363,x3361),f65(x3363,x3362)) % 186.05/186.63 [337]~E(x3371,x3372)+E(f785(x3371,x3373,x3374),f785(x3372,x3373,x3374)) % 186.05/186.63 [338]~E(x3381,x3382)+E(f785(x3383,x3381,x3384),f785(x3383,x3382,x3384)) % 186.05/186.63 [339]~E(x3391,x3392)+E(f785(x3393,x3394,x3391),f785(x3393,x3394,x3392)) % 186.05/186.63 [340]~E(x3401,x3402)+E(f182(x3401,x3403,x3404,x3405),f182(x3402,x3403,x3404,x3405)) % 186.05/186.63 [341]~E(x3411,x3412)+E(f182(x3413,x3411,x3414,x3415),f182(x3413,x3412,x3414,x3415)) % 186.05/186.63 [342]~E(x3421,x3422)+E(f182(x3423,x3424,x3421,x3425),f182(x3423,x3424,x3422,x3425)) % 186.05/186.63 [343]~E(x3431,x3432)+E(f182(x3433,x3434,x3435,x3431),f182(x3433,x3434,x3435,x3432)) % 186.05/186.63 [344]~E(x3441,x3442)+E(f17(x3441,x3443),f17(x3442,x3443)) % 186.05/186.63 [345]~E(x3451,x3452)+E(f17(x3453,x3451),f17(x3453,x3452)) % 186.05/186.63 [346]~E(x3461,x3462)+E(f849(x3461),f849(x3462)) % 186.05/186.63 [347]~E(x3471,x3472)+E(f245(x3471,x3473),f245(x3472,x3473)) % 186.05/186.63 [348]~E(x3481,x3482)+E(f245(x3483,x3481),f245(x3483,x3482)) % 186.05/186.63 [349]~E(x3491,x3492)+E(f57(x3491,x3493),f57(x3492,x3493)) % 186.05/186.63 [350]~E(x3501,x3502)+E(f57(x3503,x3501),f57(x3503,x3502)) % 186.05/186.63 [351]~E(x3511,x3512)+E(f167(x3511,x3513),f167(x3512,x3513)) % 186.05/186.63 [352]~E(x3521,x3522)+E(f167(x3523,x3521),f167(x3523,x3522)) % 186.05/186.63 [353]~E(x3531,x3532)+E(f841(x3531,x3533,x3534),f841(x3532,x3533,x3534)) % 186.05/186.63 [354]~E(x3541,x3542)+E(f841(x3543,x3541,x3544),f841(x3543,x3542,x3544)) % 186.05/186.63 [355]~E(x3551,x3552)+E(f841(x3553,x3554,x3551),f841(x3553,x3554,x3552)) % 186.05/186.63 [356]~E(x3561,x3562)+E(f307(x3561,x3563,x3564),f307(x3562,x3563,x3564)) % 186.05/186.63 [357]~E(x3571,x3572)+E(f307(x3573,x3571,x3574),f307(x3573,x3572,x3574)) % 186.05/186.63 [358]~E(x3581,x3582)+E(f307(x3583,x3584,x3581),f307(x3583,x3584,x3582)) % 186.05/186.63 [359]~E(x3591,x3592)+E(f568(x3591,x3593,x3594),f568(x3592,x3593,x3594)) % 186.05/186.63 [360]~E(x3601,x3602)+E(f568(x3603,x3601,x3604),f568(x3603,x3602,x3604)) % 186.05/186.63 [361]~E(x3611,x3612)+E(f568(x3613,x3614,x3611),f568(x3613,x3614,x3612)) % 186.05/186.63 [362]~E(x3621,x3622)+E(f54(x3621,x3623),f54(x3622,x3623)) % 186.05/186.63 [363]~E(x3631,x3632)+E(f54(x3633,x3631),f54(x3633,x3632)) % 186.05/186.63 [364]~E(x3641,x3642)+E(f787(x3641,x3643,x3644),f787(x3642,x3643,x3644)) % 186.05/186.63 [365]~E(x3651,x3652)+E(f787(x3653,x3651,x3654),f787(x3653,x3652,x3654)) % 186.05/186.63 [366]~E(x3661,x3662)+E(f787(x3663,x3664,x3661),f787(x3663,x3664,x3662)) % 186.05/186.63 [367]~E(x3671,x3672)+E(f173(x3671,x3673),f173(x3672,x3673)) % 186.05/186.63 [368]~E(x3681,x3682)+E(f173(x3683,x3681),f173(x3683,x3682)) % 186.05/186.63 [369]~E(x3691,x3692)+E(f261(x3691,x3693),f261(x3692,x3693)) % 186.05/186.63 [370]~E(x3701,x3702)+E(f261(x3703,x3701),f261(x3703,x3702)) % 186.05/186.63 [371]~E(x3711,x3712)+E(f87(x3711,x3713),f87(x3712,x3713)) % 186.05/186.63 [372]~E(x3721,x3722)+E(f87(x3723,x3721),f87(x3723,x3722)) % 186.05/186.63 [373]~E(x3731,x3732)+E(f493(x3731,x3733,x3734),f493(x3732,x3733,x3734)) % 186.05/186.63 [374]~E(x3741,x3742)+E(f493(x3743,x3741,x3744),f493(x3743,x3742,x3744)) % 186.05/186.63 [375]~E(x3751,x3752)+E(f493(x3753,x3754,x3751),f493(x3753,x3754,x3752)) % 186.05/186.63 [376]~E(x3761,x3762)+E(f663(x3761,x3763,x3764,x3765),f663(x3762,x3763,x3764,x3765)) % 186.05/186.63 [377]~E(x3771,x3772)+E(f663(x3773,x3771,x3774,x3775),f663(x3773,x3772,x3774,x3775)) % 186.05/186.63 [378]~E(x3781,x3782)+E(f663(x3783,x3784,x3781,x3785),f663(x3783,x3784,x3782,x3785)) % 186.05/186.63 [379]~E(x3791,x3792)+E(f663(x3793,x3794,x3795,x3791),f663(x3793,x3794,x3795,x3792)) % 186.05/186.63 [380]~E(x3801,x3802)+E(f713(x3801,x3803,x3804,x3805,x3806,x3807,x3808),f713(x3802,x3803,x3804,x3805,x3806,x3807,x3808)) % 186.05/186.63 [381]~E(x3811,x3812)+E(f713(x3813,x3811,x3814,x3815,x3816,x3817,x3818),f713(x3813,x3812,x3814,x3815,x3816,x3817,x3818)) % 186.05/186.63 [382]~E(x3821,x3822)+E(f713(x3823,x3824,x3821,x3825,x3826,x3827,x3828),f713(x3823,x3824,x3822,x3825,x3826,x3827,x3828)) % 186.05/186.63 [383]~E(x3831,x3832)+E(f713(x3833,x3834,x3835,x3831,x3836,x3837,x3838),f713(x3833,x3834,x3835,x3832,x3836,x3837,x3838)) % 186.05/186.63 [384]~E(x3841,x3842)+E(f713(x3843,x3844,x3845,x3846,x3841,x3847,x3848),f713(x3843,x3844,x3845,x3846,x3842,x3847,x3848)) % 186.05/186.63 [385]~E(x3851,x3852)+E(f713(x3853,x3854,x3855,x3856,x3857,x3851,x3858),f713(x3853,x3854,x3855,x3856,x3857,x3852,x3858)) % 186.05/186.63 [386]~E(x3861,x3862)+E(f713(x3863,x3864,x3865,x3866,x3867,x3868,x3861),f713(x3863,x3864,x3865,x3866,x3867,x3868,x3862)) % 186.05/186.63 [387]~E(x3871,x3872)+E(f858(x3871,x3873),f858(x3872,x3873)) % 186.05/186.63 [388]~E(x3881,x3882)+E(f858(x3883,x3881),f858(x3883,x3882)) % 186.05/186.63 [389]~E(x3891,x3892)+E(f169(x3891,x3893,x3894),f169(x3892,x3893,x3894)) % 186.05/186.63 [390]~E(x3901,x3902)+E(f169(x3903,x3901,x3904),f169(x3903,x3902,x3904)) % 186.05/186.63 [391]~E(x3911,x3912)+E(f169(x3913,x3914,x3911),f169(x3913,x3914,x3912)) % 186.05/186.63 [392]~E(x3921,x3922)+E(f249(x3921,x3923,x3924,x3925),f249(x3922,x3923,x3924,x3925)) % 186.05/186.63 [393]~E(x3931,x3932)+E(f249(x3933,x3931,x3934,x3935),f249(x3933,x3932,x3934,x3935)) % 186.05/186.63 [394]~E(x3941,x3942)+E(f249(x3943,x3944,x3941,x3945),f249(x3943,x3944,x3942,x3945)) % 186.05/186.63 [395]~E(x3951,x3952)+E(f249(x3953,x3954,x3955,x3951),f249(x3953,x3954,x3955,x3952)) % 186.05/186.63 [396]~E(x3961,x3962)+E(f758(x3961,x3963,x3964,x3965),f758(x3962,x3963,x3964,x3965)) % 186.05/186.63 [397]~E(x3971,x3972)+E(f758(x3973,x3971,x3974,x3975),f758(x3973,x3972,x3974,x3975)) % 186.05/186.63 [398]~E(x3981,x3982)+E(f758(x3983,x3984,x3981,x3985),f758(x3983,x3984,x3982,x3985)) % 186.05/186.63 [399]~E(x3991,x3992)+E(f758(x3993,x3994,x3995,x3991),f758(x3993,x3994,x3995,x3992)) % 186.05/186.63 [400]~E(x4001,x4002)+E(f736(x4001,x4003,x4004,x4005,x4006),f736(x4002,x4003,x4004,x4005,x4006)) % 186.05/186.63 [401]~E(x4011,x4012)+E(f736(x4013,x4011,x4014,x4015,x4016),f736(x4013,x4012,x4014,x4015,x4016)) % 186.05/186.63 [402]~E(x4021,x4022)+E(f736(x4023,x4024,x4021,x4025,x4026),f736(x4023,x4024,x4022,x4025,x4026)) % 186.05/186.63 [403]~E(x4031,x4032)+E(f736(x4033,x4034,x4035,x4031,x4036),f736(x4033,x4034,x4035,x4032,x4036)) % 186.05/186.63 [404]~E(x4041,x4042)+E(f736(x4043,x4044,x4045,x4046,x4041),f736(x4043,x4044,x4045,x4046,x4042)) % 186.05/186.63 [405]~E(x4051,x4052)+E(f282(x4051,x4053,x4054,x4055),f282(x4052,x4053,x4054,x4055)) % 186.05/186.63 [406]~E(x4061,x4062)+E(f282(x4063,x4061,x4064,x4065),f282(x4063,x4062,x4064,x4065)) % 186.05/186.63 [407]~E(x4071,x4072)+E(f282(x4073,x4074,x4071,x4075),f282(x4073,x4074,x4072,x4075)) % 186.05/186.63 [408]~E(x4081,x4082)+E(f282(x4083,x4084,x4085,x4081),f282(x4083,x4084,x4085,x4082)) % 186.05/186.63 [409]~E(x4091,x4092)+E(f251(x4091,x4093,x4094),f251(x4092,x4093,x4094)) % 186.05/186.63 [410]~E(x4101,x4102)+E(f251(x4103,x4101,x4104),f251(x4103,x4102,x4104)) % 186.05/186.63 [411]~E(x4111,x4112)+E(f251(x4113,x4114,x4111),f251(x4113,x4114,x4112)) % 186.05/186.63 [412]~E(x4121,x4122)+E(f88(x4121,x4123),f88(x4122,x4123)) % 186.05/186.63 [413]~E(x4131,x4132)+E(f88(x4133,x4131),f88(x4133,x4132)) % 186.05/186.63 [414]~E(x4141,x4142)+E(f786(x4141,x4143,x4144),f786(x4142,x4143,x4144)) % 186.05/186.63 [415]~E(x4151,x4152)+E(f786(x4153,x4151,x4154),f786(x4153,x4152,x4154)) % 186.05/186.63 [416]~E(x4161,x4162)+E(f786(x4163,x4164,x4161),f786(x4163,x4164,x4162)) % 186.05/186.63 [417]~E(x4171,x4172)+E(f55(x4171,x4173),f55(x4172,x4173)) % 186.05/186.63 [418]~E(x4181,x4182)+E(f55(x4183,x4181),f55(x4183,x4182)) % 186.05/186.63 [419]~E(x4191,x4192)+E(f352(x4191,x4193),f352(x4192,x4193)) % 186.05/186.63 [420]~E(x4201,x4202)+E(f352(x4203,x4201),f352(x4203,x4202)) % 186.05/186.63 [421]~E(x4211,x4212)+E(f281(x4211,x4213,x4214),f281(x4212,x4213,x4214)) % 186.05/186.63 [422]~E(x4221,x4222)+E(f281(x4223,x4221,x4224),f281(x4223,x4222,x4224)) % 186.05/186.63 [423]~E(x4231,x4232)+E(f281(x4233,x4234,x4231),f281(x4233,x4234,x4232)) % 186.05/186.63 [424]~E(x4241,x4242)+E(f94(x4241,x4243,x4244),f94(x4242,x4243,x4244)) % 186.05/186.63 [425]~E(x4251,x4252)+E(f94(x4253,x4251,x4254),f94(x4253,x4252,x4254)) % 186.05/186.63 [426]~E(x4261,x4262)+E(f94(x4263,x4264,x4261),f94(x4263,x4264,x4262)) % 186.05/186.63 [427]~E(x4271,x4272)+E(f729(x4271),f729(x4272)) % 186.05/186.63 [428]~E(x4281,x4282)+E(f652(x4281,x4283,x4284,x4285),f652(x4282,x4283,x4284,x4285)) % 186.05/186.63 [429]~E(x4291,x4292)+E(f652(x4293,x4291,x4294,x4295),f652(x4293,x4292,x4294,x4295)) % 186.05/186.63 [430]~E(x4301,x4302)+E(f652(x4303,x4304,x4301,x4305),f652(x4303,x4304,x4302,x4305)) % 186.05/186.63 [431]~E(x4311,x4312)+E(f652(x4313,x4314,x4315,x4311),f652(x4313,x4314,x4315,x4312)) % 186.05/186.63 [432]~E(x4321,x4322)+E(f625(x4321,x4323,x4324,x4325,x4326),f625(x4322,x4323,x4324,x4325,x4326)) % 186.05/186.63 [433]~E(x4331,x4332)+E(f625(x4333,x4331,x4334,x4335,x4336),f625(x4333,x4332,x4334,x4335,x4336)) % 186.05/186.63 [434]~E(x4341,x4342)+E(f625(x4343,x4344,x4341,x4345,x4346),f625(x4343,x4344,x4342,x4345,x4346)) % 186.05/186.63 [435]~E(x4351,x4352)+E(f625(x4353,x4354,x4355,x4351,x4356),f625(x4353,x4354,x4355,x4352,x4356)) % 186.05/186.63 [436]~E(x4361,x4362)+E(f625(x4363,x4364,x4365,x4366,x4361),f625(x4363,x4364,x4365,x4366,x4362)) % 186.05/186.63 [437]~E(x4371,x4372)+E(f522(x4371,x4373,x4374,x4375),f522(x4372,x4373,x4374,x4375)) % 186.05/186.63 [438]~E(x4381,x4382)+E(f522(x4383,x4381,x4384,x4385),f522(x4383,x4382,x4384,x4385)) % 186.05/186.63 [439]~E(x4391,x4392)+E(f522(x4393,x4394,x4391,x4395),f522(x4393,x4394,x4392,x4395)) % 186.05/186.63 [440]~E(x4401,x4402)+E(f522(x4403,x4404,x4405,x4401),f522(x4403,x4404,x4405,x4402)) % 186.05/186.63 [441]~E(x4411,x4412)+E(f215(x4411,x4413,x4414,x4415),f215(x4412,x4413,x4414,x4415)) % 186.05/186.63 [442]~E(x4421,x4422)+E(f215(x4423,x4421,x4424,x4425),f215(x4423,x4422,x4424,x4425)) % 186.05/186.63 [443]~E(x4431,x4432)+E(f215(x4433,x4434,x4431,x4435),f215(x4433,x4434,x4432,x4435)) % 186.05/186.63 [444]~E(x4441,x4442)+E(f215(x4443,x4444,x4445,x4441),f215(x4443,x4444,x4445,x4442)) % 186.05/186.63 [445]~E(x4451,x4452)+E(f638(x4451,x4453,x4454,x4455,x4456),f638(x4452,x4453,x4454,x4455,x4456)) % 186.05/186.63 [446]~E(x4461,x4462)+E(f638(x4463,x4461,x4464,x4465,x4466),f638(x4463,x4462,x4464,x4465,x4466)) % 186.05/186.63 [447]~E(x4471,x4472)+E(f638(x4473,x4474,x4471,x4475,x4476),f638(x4473,x4474,x4472,x4475,x4476)) % 186.05/186.63 [448]~E(x4481,x4482)+E(f638(x4483,x4484,x4485,x4481,x4486),f638(x4483,x4484,x4485,x4482,x4486)) % 186.05/186.63 [449]~E(x4491,x4492)+E(f638(x4493,x4494,x4495,x4496,x4491),f638(x4493,x4494,x4495,x4496,x4492)) % 186.05/186.63 [450]~E(x4501,x4502)+E(f314(x4501,x4503,x4504,x4505),f314(x4502,x4503,x4504,x4505)) % 186.05/186.63 [451]~E(x4511,x4512)+E(f314(x4513,x4511,x4514,x4515),f314(x4513,x4512,x4514,x4515)) % 186.05/186.63 [452]~E(x4521,x4522)+E(f314(x4523,x4524,x4521,x4525),f314(x4523,x4524,x4522,x4525)) % 186.05/186.63 [453]~E(x4531,x4532)+E(f314(x4533,x4534,x4535,x4531),f314(x4533,x4534,x4535,x4532)) % 186.05/186.63 [454]~E(x4541,x4542)+E(f680(x4541,x4543,x4544),f680(x4542,x4543,x4544)) % 186.05/186.63 [455]~E(x4551,x4552)+E(f680(x4553,x4551,x4554),f680(x4553,x4552,x4554)) % 186.05/186.63 [456]~E(x4561,x4562)+E(f680(x4563,x4564,x4561),f680(x4563,x4564,x4562)) % 186.05/186.63 [457]~E(x4571,x4572)+E(f128(x4571),f128(x4572)) % 186.05/186.63 [458]~E(x4581,x4582)+E(f798(x4581,x4583,x4584,x4585),f798(x4582,x4583,x4584,x4585)) % 186.05/186.63 [459]~E(x4591,x4592)+E(f798(x4593,x4591,x4594,x4595),f798(x4593,x4592,x4594,x4595)) % 186.05/186.63 [460]~E(x4601,x4602)+E(f798(x4603,x4604,x4601,x4605),f798(x4603,x4604,x4602,x4605)) % 186.05/186.63 [461]~E(x4611,x4612)+E(f798(x4613,x4614,x4615,x4611),f798(x4613,x4614,x4615,x4612)) % 186.05/186.63 [462]~E(x4621,x4622)+E(f50(x4621),f50(x4622)) % 186.05/186.63 [463]~E(x4631,x4632)+E(f207(x4631),f207(x4632)) % 186.05/186.63 [464]~E(x4641,x4642)+E(f74(x4641,x4643),f74(x4642,x4643)) % 186.05/186.63 [465]~E(x4651,x4652)+E(f74(x4653,x4651),f74(x4653,x4652)) % 186.05/186.63 [466]~E(x4661,x4662)+E(f472(x4661,x4663,x4664),f472(x4662,x4663,x4664)) % 186.05/186.63 [467]~E(x4671,x4672)+E(f472(x4673,x4671,x4674),f472(x4673,x4672,x4674)) % 186.05/186.63 [468]~E(x4681,x4682)+E(f472(x4683,x4684,x4681),f472(x4683,x4684,x4682)) % 186.05/186.63 [469]~E(x4691,x4692)+E(f651(x4691,x4693,x4694),f651(x4692,x4693,x4694)) % 186.05/186.63 [470]~E(x4701,x4702)+E(f651(x4703,x4701,x4704),f651(x4703,x4702,x4704)) % 186.05/186.63 [471]~E(x4711,x4712)+E(f651(x4713,x4714,x4711),f651(x4713,x4714,x4712)) % 186.05/186.63 [472]~E(x4721,x4722)+E(f325(x4721,x4723,x4724,x4725),f325(x4722,x4723,x4724,x4725)) % 186.05/186.63 [473]~E(x4731,x4732)+E(f325(x4733,x4731,x4734,x4735),f325(x4733,x4732,x4734,x4735)) % 186.05/186.63 [474]~E(x4741,x4742)+E(f325(x4743,x4744,x4741,x4745),f325(x4743,x4744,x4742,x4745)) % 186.05/186.63 [475]~E(x4751,x4752)+E(f325(x4753,x4754,x4755,x4751),f325(x4753,x4754,x4755,x4752)) % 186.05/186.63 [476]~E(x4761,x4762)+E(f299(x4761),f299(x4762)) % 186.05/186.63 [477]~E(x4771,x4772)+E(f68(x4771,x4773,x4774,x4775,x4776),f68(x4772,x4773,x4774,x4775,x4776)) % 186.05/186.63 [478]~E(x4781,x4782)+E(f68(x4783,x4781,x4784,x4785,x4786),f68(x4783,x4782,x4784,x4785,x4786)) % 186.05/186.63 [479]~E(x4791,x4792)+E(f68(x4793,x4794,x4791,x4795,x4796),f68(x4793,x4794,x4792,x4795,x4796)) % 186.05/186.63 [480]~E(x4801,x4802)+E(f68(x4803,x4804,x4805,x4801,x4806),f68(x4803,x4804,x4805,x4802,x4806)) % 186.05/186.63 [481]~E(x4811,x4812)+E(f68(x4813,x4814,x4815,x4816,x4811),f68(x4813,x4814,x4815,x4816,x4812)) % 186.05/186.63 [482]~E(x4821,x4822)+E(f284(x4821,x4823),f284(x4822,x4823)) % 186.05/186.63 [483]~E(x4831,x4832)+E(f284(x4833,x4831),f284(x4833,x4832)) % 186.05/186.63 [484]~E(x4841,x4842)+E(f145(x4841,x4843,x4844,x4845),f145(x4842,x4843,x4844,x4845)) % 186.05/186.63 [485]~E(x4851,x4852)+E(f145(x4853,x4851,x4854,x4855),f145(x4853,x4852,x4854,x4855)) % 186.05/186.63 [486]~E(x4861,x4862)+E(f145(x4863,x4864,x4861,x4865),f145(x4863,x4864,x4862,x4865)) % 186.05/186.63 [487]~E(x4871,x4872)+E(f145(x4873,x4874,x4875,x4871),f145(x4873,x4874,x4875,x4872)) % 186.05/186.63 [488]~E(x4881,x4882)+E(f395(x4881,x4883,x4884),f395(x4882,x4883,x4884)) % 186.05/186.63 [489]~E(x4891,x4892)+E(f395(x4893,x4891,x4894),f395(x4893,x4892,x4894)) % 186.05/186.63 [490]~E(x4901,x4902)+E(f395(x4903,x4904,x4901),f395(x4903,x4904,x4902)) % 186.05/186.63 [491]~E(x4911,x4912)+E(f112(x4911),f112(x4912)) % 186.05/186.63 [492]~E(x4921,x4922)+E(f139(x4921,x4923,x4924,x4925,x4926),f139(x4922,x4923,x4924,x4925,x4926)) % 186.05/186.63 [493]~E(x4931,x4932)+E(f139(x4933,x4931,x4934,x4935,x4936),f139(x4933,x4932,x4934,x4935,x4936)) % 186.05/186.63 [494]~E(x4941,x4942)+E(f139(x4943,x4944,x4941,x4945,x4946),f139(x4943,x4944,x4942,x4945,x4946)) % 186.05/186.63 [495]~E(x4951,x4952)+E(f139(x4953,x4954,x4955,x4951,x4956),f139(x4953,x4954,x4955,x4952,x4956)) % 186.05/186.63 [496]~E(x4961,x4962)+E(f139(x4963,x4964,x4965,x4966,x4961),f139(x4963,x4964,x4965,x4966,x4962)) % 186.05/186.63 [497]~E(x4971,x4972)+E(f258(x4971),f258(x4972)) % 186.05/186.63 [498]~E(x4981,x4982)+E(f98(x4981),f98(x4982)) % 186.05/186.63 [499]~E(x4991,x4992)+E(f783(x4991,x4993,x4994,x4995),f783(x4992,x4993,x4994,x4995)) % 186.05/186.63 [500]~E(x5001,x5002)+E(f783(x5003,x5001,x5004,x5005),f783(x5003,x5002,x5004,x5005)) % 186.05/186.63 [501]~E(x5011,x5012)+E(f783(x5013,x5014,x5011,x5015),f783(x5013,x5014,x5012,x5015)) % 186.05/186.63 [502]~E(x5021,x5022)+E(f783(x5023,x5024,x5025,x5021),f783(x5023,x5024,x5025,x5022)) % 186.05/186.63 [503]~E(x5031,x5032)+E(f13(x5031,x5033,x5034),f13(x5032,x5033,x5034)) % 186.05/186.63 [504]~E(x5041,x5042)+E(f13(x5043,x5041,x5044),f13(x5043,x5042,x5044)) % 186.05/186.63 [505]~E(x5051,x5052)+E(f13(x5053,x5054,x5051),f13(x5053,x5054,x5052)) % 186.05/186.63 [506]~E(x5061,x5062)+E(f321(x5061,x5063),f321(x5062,x5063)) % 186.05/186.63 [507]~E(x5071,x5072)+E(f321(x5073,x5071),f321(x5073,x5072)) % 186.05/186.63 [508]~E(x5081,x5082)+E(f165(x5081),f165(x5082)) % 186.05/186.63 [509]~E(x5091,x5092)+E(f674(x5091,x5093,x5094,x5095,x5096),f674(x5092,x5093,x5094,x5095,x5096)) % 186.05/186.63 [510]~E(x5101,x5102)+E(f674(x5103,x5101,x5104,x5105,x5106),f674(x5103,x5102,x5104,x5105,x5106)) % 186.05/186.63 [511]~E(x5111,x5112)+E(f674(x5113,x5114,x5111,x5115,x5116),f674(x5113,x5114,x5112,x5115,x5116)) % 186.05/186.63 [512]~E(x5121,x5122)+E(f674(x5123,x5124,x5125,x5121,x5126),f674(x5123,x5124,x5125,x5122,x5126)) % 186.05/186.63 [513]~E(x5131,x5132)+E(f674(x5133,x5134,x5135,x5136,x5131),f674(x5133,x5134,x5135,x5136,x5132)) % 186.05/186.63 [514]~E(x5141,x5142)+E(f146(x5141,x5143),f146(x5142,x5143)) % 186.05/186.63 [515]~E(x5151,x5152)+E(f146(x5153,x5151),f146(x5153,x5152)) % 186.05/186.63 [516]~E(x5161,x5162)+E(f253(x5161,x5163,x5164,x5165),f253(x5162,x5163,x5164,x5165)) % 186.05/186.63 [517]~E(x5171,x5172)+E(f253(x5173,x5171,x5174,x5175),f253(x5173,x5172,x5174,x5175)) % 186.05/186.63 [518]~E(x5181,x5182)+E(f253(x5183,x5184,x5181,x5185),f253(x5183,x5184,x5182,x5185)) % 186.05/186.63 [519]~E(x5191,x5192)+E(f253(x5193,x5194,x5195,x5191),f253(x5193,x5194,x5195,x5192)) % 186.05/186.63 [520]~E(x5201,x5202)+E(f488(x5201,x5203,x5204,x5205,x5206),f488(x5202,x5203,x5204,x5205,x5206)) % 186.05/186.63 [521]~E(x5211,x5212)+E(f488(x5213,x5211,x5214,x5215,x5216),f488(x5213,x5212,x5214,x5215,x5216)) % 186.05/186.63 [522]~E(x5221,x5222)+E(f488(x5223,x5224,x5221,x5225,x5226),f488(x5223,x5224,x5222,x5225,x5226)) % 186.05/186.63 [523]~E(x5231,x5232)+E(f488(x5233,x5234,x5235,x5231,x5236),f488(x5233,x5234,x5235,x5232,x5236)) % 186.05/186.63 [524]~E(x5241,x5242)+E(f488(x5243,x5244,x5245,x5246,x5241),f488(x5243,x5244,x5245,x5246,x5242)) % 186.05/186.63 [525]~E(x5251,x5252)+E(f804(x5251,x5253,x5254),f804(x5252,x5253,x5254)) % 186.05/186.63 [526]~E(x5261,x5262)+E(f804(x5263,x5261,x5264),f804(x5263,x5262,x5264)) % 186.05/186.63 [527]~E(x5271,x5272)+E(f804(x5273,x5274,x5271),f804(x5273,x5274,x5272)) % 186.05/186.63 [528]~E(x5281,x5282)+E(f344(x5281,x5283),f344(x5282,x5283)) % 186.05/186.63 [529]~E(x5291,x5292)+E(f344(x5293,x5291),f344(x5293,x5292)) % 186.05/186.63 [530]~E(x5301,x5302)+E(f463(x5301,x5303,x5304,x5305,x5306),f463(x5302,x5303,x5304,x5305,x5306)) % 186.05/186.63 [531]~E(x5311,x5312)+E(f463(x5313,x5311,x5314,x5315,x5316),f463(x5313,x5312,x5314,x5315,x5316)) % 186.05/186.63 [532]~E(x5321,x5322)+E(f463(x5323,x5324,x5321,x5325,x5326),f463(x5323,x5324,x5322,x5325,x5326)) % 186.05/186.63 [533]~E(x5331,x5332)+E(f463(x5333,x5334,x5335,x5331,x5336),f463(x5333,x5334,x5335,x5332,x5336)) % 186.05/186.63 [534]~E(x5341,x5342)+E(f463(x5343,x5344,x5345,x5346,x5341),f463(x5343,x5344,x5345,x5346,x5342)) % 186.05/186.63 [535]~E(x5351,x5352)+E(f835(x5351,x5353,x5354),f835(x5352,x5353,x5354)) % 186.05/186.63 [536]~E(x5361,x5362)+E(f835(x5363,x5361,x5364),f835(x5363,x5362,x5364)) % 186.05/186.63 [537]~E(x5371,x5372)+E(f835(x5373,x5374,x5371),f835(x5373,x5374,x5372)) % 186.05/186.63 [538]~E(x5381,x5382)+E(f709(x5381,x5383,x5384,x5385,x5386,x5387),f709(x5382,x5383,x5384,x5385,x5386,x5387)) % 186.05/186.63 [539]~E(x5391,x5392)+E(f709(x5393,x5391,x5394,x5395,x5396,x5397),f709(x5393,x5392,x5394,x5395,x5396,x5397)) % 186.05/186.63 [540]~E(x5401,x5402)+E(f709(x5403,x5404,x5401,x5405,x5406,x5407),f709(x5403,x5404,x5402,x5405,x5406,x5407)) % 186.05/186.63 [541]~E(x5411,x5412)+E(f709(x5413,x5414,x5415,x5411,x5416,x5417),f709(x5413,x5414,x5415,x5412,x5416,x5417)) % 186.05/186.63 [542]~E(x5421,x5422)+E(f709(x5423,x5424,x5425,x5426,x5421,x5427),f709(x5423,x5424,x5425,x5426,x5422,x5427)) % 186.05/186.63 [543]~E(x5431,x5432)+E(f709(x5433,x5434,x5435,x5436,x5437,x5431),f709(x5433,x5434,x5435,x5436,x5437,x5432)) % 186.05/186.63 [544]~E(x5441,x5442)+E(f710(x5441,x5443,x5444,x5445,x5446,x5447),f710(x5442,x5443,x5444,x5445,x5446,x5447)) % 186.05/186.63 [545]~E(x5451,x5452)+E(f710(x5453,x5451,x5454,x5455,x5456,x5457),f710(x5453,x5452,x5454,x5455,x5456,x5457)) % 186.05/186.63 [546]~E(x5461,x5462)+E(f710(x5463,x5464,x5461,x5465,x5466,x5467),f710(x5463,x5464,x5462,x5465,x5466,x5467)) % 186.05/186.63 [547]~E(x5471,x5472)+E(f710(x5473,x5474,x5475,x5471,x5476,x5477),f710(x5473,x5474,x5475,x5472,x5476,x5477)) % 186.05/186.63 [548]~E(x5481,x5482)+E(f710(x5483,x5484,x5485,x5486,x5481,x5487),f710(x5483,x5484,x5485,x5486,x5482,x5487)) % 186.05/186.63 [549]~E(x5491,x5492)+E(f710(x5493,x5494,x5495,x5496,x5497,x5491),f710(x5493,x5494,x5495,x5496,x5497,x5492)) % 186.05/186.63 [550]~E(x5501,x5502)+E(f727(x5501,x5503),f727(x5502,x5503)) % 186.05/186.63 [551]~E(x5511,x5512)+E(f727(x5513,x5511),f727(x5513,x5512)) % 186.05/186.63 [552]~E(x5521,x5522)+E(f735(x5521,x5523,x5524,x5525,x5526),f735(x5522,x5523,x5524,x5525,x5526)) % 186.05/186.63 [553]~E(x5531,x5532)+E(f735(x5533,x5531,x5534,x5535,x5536),f735(x5533,x5532,x5534,x5535,x5536)) % 186.05/186.63 [554]~E(x5541,x5542)+E(f735(x5543,x5544,x5541,x5545,x5546),f735(x5543,x5544,x5542,x5545,x5546)) % 186.05/186.63 [555]~E(x5551,x5552)+E(f735(x5553,x5554,x5555,x5551,x5556),f735(x5553,x5554,x5555,x5552,x5556)) % 186.05/186.63 [556]~E(x5561,x5562)+E(f735(x5563,x5564,x5565,x5566,x5561),f735(x5563,x5564,x5565,x5566,x5562)) % 186.05/186.63 [557]~E(x5571,x5572)+E(f292(x5571,x5573,x5574,x5575,x5576),f292(x5572,x5573,x5574,x5575,x5576)) % 186.05/186.63 [558]~E(x5581,x5582)+E(f292(x5583,x5581,x5584,x5585,x5586),f292(x5583,x5582,x5584,x5585,x5586)) % 186.05/186.63 [559]~E(x5591,x5592)+E(f292(x5593,x5594,x5591,x5595,x5596),f292(x5593,x5594,x5592,x5595,x5596)) % 186.05/186.63 [560]~E(x5601,x5602)+E(f292(x5603,x5604,x5605,x5601,x5606),f292(x5603,x5604,x5605,x5602,x5606)) % 186.05/186.63 [561]~E(x5611,x5612)+E(f292(x5613,x5614,x5615,x5616,x5611),f292(x5613,x5614,x5615,x5616,x5612)) % 186.05/186.63 [562]~E(x5621,x5622)+E(f779(x5621),f779(x5622)) % 186.05/186.63 [563]~E(x5631,x5632)+E(f346(x5631,x5633,x5634,x5635),f346(x5632,x5633,x5634,x5635)) % 186.05/186.63 [564]~E(x5641,x5642)+E(f346(x5643,x5641,x5644,x5645),f346(x5643,x5642,x5644,x5645)) % 186.05/186.63 [565]~E(x5651,x5652)+E(f346(x5653,x5654,x5651,x5655),f346(x5653,x5654,x5652,x5655)) % 186.05/186.63 [566]~E(x5661,x5662)+E(f346(x5663,x5664,x5665,x5661),f346(x5663,x5664,x5665,x5662)) % 186.05/186.63 [567]~E(x5671,x5672)+E(f134(x5671,x5673),f134(x5672,x5673)) % 186.05/186.63 [568]~E(x5681,x5682)+E(f134(x5683,x5681),f134(x5683,x5682)) % 186.05/186.63 [569]~E(x5691,x5692)+E(f673(x5691,x5693,x5694),f673(x5692,x5693,x5694)) % 186.05/186.63 [570]~E(x5701,x5702)+E(f673(x5703,x5701,x5704),f673(x5703,x5702,x5704)) % 186.05/186.63 [571]~E(x5711,x5712)+E(f673(x5713,x5714,x5711),f673(x5713,x5714,x5712)) % 186.05/186.63 [572]~E(x5721,x5722)+E(f451(x5721,x5723,x5724,x5725),f451(x5722,x5723,x5724,x5725)) % 186.05/186.63 [573]~E(x5731,x5732)+E(f451(x5733,x5731,x5734,x5735),f451(x5733,x5732,x5734,x5735)) % 186.05/186.63 [574]~E(x5741,x5742)+E(f451(x5743,x5744,x5741,x5745),f451(x5743,x5744,x5742,x5745)) % 186.05/186.63 [575]~E(x5751,x5752)+E(f451(x5753,x5754,x5755,x5751),f451(x5753,x5754,x5755,x5752)) % 186.05/186.63 [576]~E(x5761,x5762)+E(f226(x5761,x5763),f226(x5762,x5763)) % 186.05/186.63 [577]~E(x5771,x5772)+E(f226(x5773,x5771),f226(x5773,x5772)) % 186.05/186.63 [578]~E(x5781,x5782)+E(f782(x5781,x5783,x5784),f782(x5782,x5783,x5784)) % 186.05/186.63 [579]~E(x5791,x5792)+E(f782(x5793,x5791,x5794),f782(x5793,x5792,x5794)) % 186.05/186.63 [580]~E(x5801,x5802)+E(f782(x5803,x5804,x5801),f782(x5803,x5804,x5802)) % 186.05/186.63 [581]~E(x5811,x5812)+E(f45(x5811,x5813),f45(x5812,x5813)) % 186.05/186.63 [582]~E(x5821,x5822)+E(f45(x5823,x5821),f45(x5823,x5822)) % 186.05/186.63 [583]~E(x5831,x5832)+E(f293(x5831),f293(x5832)) % 186.05/186.63 [584]~E(x5841,x5842)+E(f255(x5841,x5843,x5844,x5845,x5846),f255(x5842,x5843,x5844,x5845,x5846)) % 186.05/186.63 [585]~E(x5851,x5852)+E(f255(x5853,x5851,x5854,x5855,x5856),f255(x5853,x5852,x5854,x5855,x5856)) % 186.05/186.63 [586]~E(x5861,x5862)+E(f255(x5863,x5864,x5861,x5865,x5866),f255(x5863,x5864,x5862,x5865,x5866)) % 186.05/186.63 [587]~E(x5871,x5872)+E(f255(x5873,x5874,x5875,x5871,x5876),f255(x5873,x5874,x5875,x5872,x5876)) % 186.05/186.63 [588]~E(x5881,x5882)+E(f255(x5883,x5884,x5885,x5886,x5881),f255(x5883,x5884,x5885,x5886,x5882)) % 186.05/186.63 [589]~E(x5891,x5892)+E(f793(x5891,x5893,x5894),f793(x5892,x5893,x5894)) % 186.05/186.63 [590]~E(x5901,x5902)+E(f793(x5903,x5901,x5904),f793(x5903,x5902,x5904)) % 186.05/186.63 [591]~E(x5911,x5912)+E(f793(x5913,x5914,x5911),f793(x5913,x5914,x5912)) % 186.05/186.63 [592]~E(x5921,x5922)+E(f706(x5921,x5923,x5924,x5925,x5926,x5927),f706(x5922,x5923,x5924,x5925,x5926,x5927)) % 186.05/186.63 [593]~E(x5931,x5932)+E(f706(x5933,x5931,x5934,x5935,x5936,x5937),f706(x5933,x5932,x5934,x5935,x5936,x5937)) % 186.05/186.63 [594]~E(x5941,x5942)+E(f706(x5943,x5944,x5941,x5945,x5946,x5947),f706(x5943,x5944,x5942,x5945,x5946,x5947)) % 186.05/186.63 [595]~E(x5951,x5952)+E(f706(x5953,x5954,x5955,x5951,x5956,x5957),f706(x5953,x5954,x5955,x5952,x5956,x5957)) % 186.05/186.63 [596]~E(x5961,x5962)+E(f706(x5963,x5964,x5965,x5966,x5961,x5967),f706(x5963,x5964,x5965,x5966,x5962,x5967)) % 186.05/186.63 [597]~E(x5971,x5972)+E(f706(x5973,x5974,x5975,x5976,x5977,x5971),f706(x5973,x5974,x5975,x5976,x5977,x5972)) % 186.05/186.63 [598]~E(x5981,x5982)+E(f740(x5981,x5983,x5984,x5985),f740(x5982,x5983,x5984,x5985)) % 186.05/186.63 [599]~E(x5991,x5992)+E(f740(x5993,x5991,x5994,x5995),f740(x5993,x5992,x5994,x5995)) % 186.05/186.63 [600]~E(x6001,x6002)+E(f740(x6003,x6004,x6001,x6005),f740(x6003,x6004,x6002,x6005)) % 186.05/186.63 [601]~E(x6011,x6012)+E(f740(x6013,x6014,x6015,x6011),f740(x6013,x6014,x6015,x6012)) % 186.05/186.63 [602]~E(x6021,x6022)+E(f313(x6021,x6023),f313(x6022,x6023)) % 186.05/186.63 [603]~E(x6031,x6032)+E(f313(x6033,x6031),f313(x6033,x6032)) % 186.05/186.63 [604]~E(x6041,x6042)+E(f162(x6041,x6043,x6044),f162(x6042,x6043,x6044)) % 186.05/186.63 [605]~E(x6051,x6052)+E(f162(x6053,x6051,x6054),f162(x6053,x6052,x6054)) % 186.05/186.63 [606]~E(x6061,x6062)+E(f162(x6063,x6064,x6061),f162(x6063,x6064,x6062)) % 186.05/186.63 [607]~E(x6071,x6072)+E(f67(x6071,x6073,x6074),f67(x6072,x6073,x6074)) % 186.05/186.63 [608]~E(x6081,x6082)+E(f67(x6083,x6081,x6084),f67(x6083,x6082,x6084)) % 186.05/186.63 [609]~E(x6091,x6092)+E(f67(x6093,x6094,x6091),f67(x6093,x6094,x6092)) % 186.05/186.63 [610]~E(x6101,x6102)+E(f378(x6101,x6103,x6104,x6105),f378(x6102,x6103,x6104,x6105)) % 186.05/186.63 [611]~E(x6111,x6112)+E(f378(x6113,x6111,x6114,x6115),f378(x6113,x6112,x6114,x6115)) % 186.05/186.63 [612]~E(x6121,x6122)+E(f378(x6123,x6124,x6121,x6125),f378(x6123,x6124,x6122,x6125)) % 186.05/186.63 [613]~E(x6131,x6132)+E(f378(x6133,x6134,x6135,x6131),f378(x6133,x6134,x6135,x6132)) % 186.05/186.63 [614]~E(x6141,x6142)+E(f506(x6141,x6143,x6144),f506(x6142,x6143,x6144)) % 186.05/186.63 [615]~E(x6151,x6152)+E(f506(x6153,x6151,x6154),f506(x6153,x6152,x6154)) % 186.05/186.63 [616]~E(x6161,x6162)+E(f506(x6163,x6164,x6161),f506(x6163,x6164,x6162)) % 186.05/186.63 [617]~E(x6171,x6172)+E(f60(x6171,x6173),f60(x6172,x6173)) % 186.05/186.63 [618]~E(x6181,x6182)+E(f60(x6183,x6181),f60(x6183,x6182)) % 186.05/186.63 [619]~E(x6191,x6192)+E(f211(x6191,x6193),f211(x6192,x6193)) % 186.05/186.63 [620]~E(x6201,x6202)+E(f211(x6203,x6201),f211(x6203,x6202)) % 186.05/186.63 [621]~E(x6211,x6212)+E(f259(x6211,x6213),f259(x6212,x6213)) % 186.05/186.63 [622]~E(x6221,x6222)+E(f259(x6223,x6221),f259(x6223,x6222)) % 186.05/186.63 [623]~E(x6231,x6232)+E(f666(x6231,x6233,x6234,x6235,x6236),f666(x6232,x6233,x6234,x6235,x6236)) % 186.05/186.63 [624]~E(x6241,x6242)+E(f666(x6243,x6241,x6244,x6245,x6246),f666(x6243,x6242,x6244,x6245,x6246)) % 186.05/186.63 [625]~E(x6251,x6252)+E(f666(x6253,x6254,x6251,x6255,x6256),f666(x6253,x6254,x6252,x6255,x6256)) % 186.05/186.63 [626]~E(x6261,x6262)+E(f666(x6263,x6264,x6265,x6261,x6266),f666(x6263,x6264,x6265,x6262,x6266)) % 186.05/186.63 [627]~E(x6271,x6272)+E(f666(x6273,x6274,x6275,x6276,x6271),f666(x6273,x6274,x6275,x6276,x6272)) % 186.05/186.63 [628]~E(x6281,x6282)+E(f418(x6281,x6283,x6284),f418(x6282,x6283,x6284)) % 186.05/186.63 [629]~E(x6291,x6292)+E(f418(x6293,x6291,x6294),f418(x6293,x6292,x6294)) % 186.05/186.63 [630]~E(x6301,x6302)+E(f418(x6303,x6304,x6301),f418(x6303,x6304,x6302)) % 186.05/186.63 [631]~E(x6311,x6312)+E(f121(x6311,x6313,x6314,x6315),f121(x6312,x6313,x6314,x6315)) % 186.05/186.63 [632]~E(x6321,x6322)+E(f121(x6323,x6321,x6324,x6325),f121(x6323,x6322,x6324,x6325)) % 186.05/186.63 [633]~E(x6331,x6332)+E(f121(x6333,x6334,x6331,x6335),f121(x6333,x6334,x6332,x6335)) % 186.05/186.63 [634]~E(x6341,x6342)+E(f121(x6343,x6344,x6345,x6341),f121(x6343,x6344,x6345,x6342)) % 186.05/186.63 [635]~E(x6351,x6352)+E(f243(x6351,x6353,x6354),f243(x6352,x6353,x6354)) % 186.05/186.63 [636]~E(x6361,x6362)+E(f243(x6363,x6361,x6364),f243(x6363,x6362,x6364)) % 186.05/186.63 [637]~E(x6371,x6372)+E(f243(x6373,x6374,x6371),f243(x6373,x6374,x6372)) % 186.05/186.63 [638]~E(x6381,x6382)+E(f722(x6381,x6383),f722(x6382,x6383)) % 186.05/186.63 [639]~E(x6391,x6392)+E(f722(x6393,x6391),f722(x6393,x6392)) % 186.05/186.63 [640]~E(x6401,x6402)+E(f855(x6401,x6403),f855(x6402,x6403)) % 186.05/186.63 [641]~E(x6411,x6412)+E(f855(x6413,x6411),f855(x6413,x6412)) % 186.05/186.63 [642]~E(x6421,x6422)+E(f642(x6421,x6423),f642(x6422,x6423)) % 186.05/186.63 [643]~E(x6431,x6432)+E(f642(x6433,x6431),f642(x6433,x6432)) % 186.05/186.63 [644]~E(x6441,x6442)+E(f725(x6441,x6443,x6444),f725(x6442,x6443,x6444)) % 186.05/186.63 [645]~E(x6451,x6452)+E(f725(x6453,x6451,x6454),f725(x6453,x6452,x6454)) % 186.05/186.63 [646]~E(x6461,x6462)+E(f725(x6463,x6464,x6461),f725(x6463,x6464,x6462)) % 186.05/186.63 [647]~E(x6471,x6472)+E(f828(x6471,x6473,x6474),f828(x6472,x6473,x6474)) % 186.05/186.63 [648]~E(x6481,x6482)+E(f828(x6483,x6481,x6484),f828(x6483,x6482,x6484)) % 186.05/186.63 [649]~E(x6491,x6492)+E(f828(x6493,x6494,x6491),f828(x6493,x6494,x6492)) % 186.05/186.63 [650]~E(x6501,x6502)+E(f69(x6501,x6503,x6504),f69(x6502,x6503,x6504)) % 186.05/186.63 [651]~E(x6511,x6512)+E(f69(x6513,x6511,x6514),f69(x6513,x6512,x6514)) % 186.05/186.63 [652]~E(x6521,x6522)+E(f69(x6523,x6524,x6521),f69(x6523,x6524,x6522)) % 186.05/186.63 [653]~E(x6531,x6532)+E(f743(x6531,x6533,x6534,x6535),f743(x6532,x6533,x6534,x6535)) % 186.05/186.63 [654]~E(x6541,x6542)+E(f743(x6543,x6541,x6544,x6545),f743(x6543,x6542,x6544,x6545)) % 186.05/186.63 [655]~E(x6551,x6552)+E(f743(x6553,x6554,x6551,x6555),f743(x6553,x6554,x6552,x6555)) % 186.05/186.63 [656]~E(x6561,x6562)+E(f743(x6563,x6564,x6565,x6561),f743(x6563,x6564,x6565,x6562)) % 186.05/186.63 [657]~E(x6571,x6572)+E(f364(x6571,x6573,x6574,x6575,x6576),f364(x6572,x6573,x6574,x6575,x6576)) % 186.05/186.63 [658]~E(x6581,x6582)+E(f364(x6583,x6581,x6584,x6585,x6586),f364(x6583,x6582,x6584,x6585,x6586)) % 186.05/186.63 [659]~E(x6591,x6592)+E(f364(x6593,x6594,x6591,x6595,x6596),f364(x6593,x6594,x6592,x6595,x6596)) % 186.05/186.63 [660]~E(x6601,x6602)+E(f364(x6603,x6604,x6605,x6601,x6606),f364(x6603,x6604,x6605,x6602,x6606)) % 186.05/186.63 [661]~E(x6611,x6612)+E(f364(x6613,x6614,x6615,x6616,x6611),f364(x6613,x6614,x6615,x6616,x6612)) % 186.05/186.63 [662]~E(x6621,x6622)+E(f15(x6621,x6623),f15(x6622,x6623)) % 186.05/186.63 [663]~E(x6631,x6632)+E(f15(x6633,x6631),f15(x6633,x6632)) % 186.05/186.63 [664]~E(x6641,x6642)+E(f540(x6641,x6643,x6644,x6645,x6646),f540(x6642,x6643,x6644,x6645,x6646)) % 186.05/186.63 [665]~E(x6651,x6652)+E(f540(x6653,x6651,x6654,x6655,x6656),f540(x6653,x6652,x6654,x6655,x6656)) % 186.05/186.63 [666]~E(x6661,x6662)+E(f540(x6663,x6664,x6661,x6665,x6666),f540(x6663,x6664,x6662,x6665,x6666)) % 186.05/186.63 [667]~E(x6671,x6672)+E(f540(x6673,x6674,x6675,x6671,x6676),f540(x6673,x6674,x6675,x6672,x6676)) % 186.05/186.63 [668]~E(x6681,x6682)+E(f540(x6683,x6684,x6685,x6686,x6681),f540(x6683,x6684,x6685,x6686,x6682)) % 186.05/186.63 [669]~E(x6691,x6692)+E(f515(x6691,x6693,x6694,x6695),f515(x6692,x6693,x6694,x6695)) % 186.05/186.63 [670]~E(x6701,x6702)+E(f515(x6703,x6701,x6704,x6705),f515(x6703,x6702,x6704,x6705)) % 186.05/186.63 [671]~E(x6711,x6712)+E(f515(x6713,x6714,x6711,x6715),f515(x6713,x6714,x6712,x6715)) % 186.05/186.63 [672]~E(x6721,x6722)+E(f515(x6723,x6724,x6725,x6721),f515(x6723,x6724,x6725,x6722)) % 186.05/186.63 [673]~E(x6731,x6732)+E(f320(x6731,x6733,x6734,x6735,x6736,x6737),f320(x6732,x6733,x6734,x6735,x6736,x6737)) % 186.05/186.63 [674]~E(x6741,x6742)+E(f320(x6743,x6741,x6744,x6745,x6746,x6747),f320(x6743,x6742,x6744,x6745,x6746,x6747)) % 186.05/186.63 [675]~E(x6751,x6752)+E(f320(x6753,x6754,x6751,x6755,x6756,x6757),f320(x6753,x6754,x6752,x6755,x6756,x6757)) % 186.05/186.63 [676]~E(x6761,x6762)+E(f320(x6763,x6764,x6765,x6761,x6766,x6767),f320(x6763,x6764,x6765,x6762,x6766,x6767)) % 186.05/186.63 [677]~E(x6771,x6772)+E(f320(x6773,x6774,x6775,x6776,x6771,x6777),f320(x6773,x6774,x6775,x6776,x6772,x6777)) % 186.05/186.63 [678]~E(x6781,x6782)+E(f320(x6783,x6784,x6785,x6786,x6787,x6781),f320(x6783,x6784,x6785,x6786,x6787,x6782)) % 186.05/186.63 [679]~E(x6791,x6792)+E(f438(x6791,x6793,x6794,x6795),f438(x6792,x6793,x6794,x6795)) % 186.05/186.63 [680]~E(x6801,x6802)+E(f438(x6803,x6801,x6804,x6805),f438(x6803,x6802,x6804,x6805)) % 186.05/186.63 [681]~E(x6811,x6812)+E(f438(x6813,x6814,x6811,x6815),f438(x6813,x6814,x6812,x6815)) % 186.05/186.63 [682]~E(x6821,x6822)+E(f438(x6823,x6824,x6825,x6821),f438(x6823,x6824,x6825,x6822)) % 186.05/186.63 [683]~E(x6831,x6832)+E(f809(x6831,x6833,x6834),f809(x6832,x6833,x6834)) % 186.05/186.63 [684]~E(x6841,x6842)+E(f809(x6843,x6841,x6844),f809(x6843,x6842,x6844)) % 186.05/186.63 [685]~E(x6851,x6852)+E(f809(x6853,x6854,x6851),f809(x6853,x6854,x6852)) % 186.05/186.63 [686]~E(x6861,x6862)+E(f561(x6861,x6863,x6864,x6865),f561(x6862,x6863,x6864,x6865)) % 186.05/186.63 [687]~E(x6871,x6872)+E(f561(x6873,x6871,x6874,x6875),f561(x6873,x6872,x6874,x6875)) % 186.05/186.63 [688]~E(x6881,x6882)+E(f561(x6883,x6884,x6881,x6885),f561(x6883,x6884,x6882,x6885)) % 186.05/186.63 [689]~E(x6891,x6892)+E(f561(x6893,x6894,x6895,x6891),f561(x6893,x6894,x6895,x6892)) % 186.05/186.63 [690]~E(x6901,x6902)+E(f374(x6901,x6903,x6904),f374(x6902,x6903,x6904)) % 186.05/186.63 [691]~E(x6911,x6912)+E(f374(x6913,x6911,x6914),f374(x6913,x6912,x6914)) % 186.05/186.63 [692]~E(x6921,x6922)+E(f374(x6923,x6924,x6921),f374(x6923,x6924,x6922)) % 186.05/186.63 [693]~E(x6931,x6932)+E(f412(x6931,x6933,x6934,x6935),f412(x6932,x6933,x6934,x6935)) % 186.05/186.63 [694]~E(x6941,x6942)+E(f412(x6943,x6941,x6944,x6945),f412(x6943,x6942,x6944,x6945)) % 186.05/186.63 [695]~E(x6951,x6952)+E(f412(x6953,x6954,x6951,x6955),f412(x6953,x6954,x6952,x6955)) % 186.05/186.63 [696]~E(x6961,x6962)+E(f412(x6963,x6964,x6965,x6961),f412(x6963,x6964,x6965,x6962)) % 186.05/186.63 [697]~E(x6971,x6972)+E(f317(x6971,x6973,x6974,x6975),f317(x6972,x6973,x6974,x6975)) % 186.05/186.63 [698]~E(x6981,x6982)+E(f317(x6983,x6981,x6984,x6985),f317(x6983,x6982,x6984,x6985)) % 186.05/186.63 [699]~E(x6991,x6992)+E(f317(x6993,x6994,x6991,x6995),f317(x6993,x6994,x6992,x6995)) % 186.05/186.63 [700]~E(x7001,x7002)+E(f317(x7003,x7004,x7005,x7001),f317(x7003,x7004,x7005,x7002)) % 186.05/186.63 [701]~E(x7011,x7012)+E(f587(x7011,x7013,x7014,x7015,x7016,x7017),f587(x7012,x7013,x7014,x7015,x7016,x7017)) % 186.05/186.63 [702]~E(x7021,x7022)+E(f587(x7023,x7021,x7024,x7025,x7026,x7027),f587(x7023,x7022,x7024,x7025,x7026,x7027)) % 186.05/186.63 [703]~E(x7031,x7032)+E(f587(x7033,x7034,x7031,x7035,x7036,x7037),f587(x7033,x7034,x7032,x7035,x7036,x7037)) % 186.05/186.63 [704]~E(x7041,x7042)+E(f587(x7043,x7044,x7045,x7041,x7046,x7047),f587(x7043,x7044,x7045,x7042,x7046,x7047)) % 186.05/186.63 [705]~E(x7051,x7052)+E(f587(x7053,x7054,x7055,x7056,x7051,x7057),f587(x7053,x7054,x7055,x7056,x7052,x7057)) % 186.05/186.63 [706]~E(x7061,x7062)+E(f587(x7063,x7064,x7065,x7066,x7067,x7061),f587(x7063,x7064,x7065,x7066,x7067,x7062)) % 186.05/186.63 [707]~E(x7071,x7072)+E(f382(x7071,x7073,x7074,x7075),f382(x7072,x7073,x7074,x7075)) % 186.05/186.63 [708]~E(x7081,x7082)+E(f382(x7083,x7081,x7084,x7085),f382(x7083,x7082,x7084,x7085)) % 186.05/186.63 [709]~E(x7091,x7092)+E(f382(x7093,x7094,x7091,x7095),f382(x7093,x7094,x7092,x7095)) % 186.05/186.63 [710]~E(x7101,x7102)+E(f382(x7103,x7104,x7105,x7101),f382(x7103,x7104,x7105,x7102)) % 186.05/186.63 [711]~E(x7111,x7112)+E(f322(x7111,x7113),f322(x7112,x7113)) % 186.05/186.63 [712]~E(x7121,x7122)+E(f322(x7123,x7121),f322(x7123,x7122)) % 186.05/186.63 [713]~E(x7131,x7132)+E(f229(x7131,x7133,x7134,x7135),f229(x7132,x7133,x7134,x7135)) % 186.05/186.63 [714]~E(x7141,x7142)+E(f229(x7143,x7141,x7144,x7145),f229(x7143,x7142,x7144,x7145)) % 186.05/186.63 [715]~E(x7151,x7152)+E(f229(x7153,x7154,x7151,x7155),f229(x7153,x7154,x7152,x7155)) % 186.05/186.63 [716]~E(x7161,x7162)+E(f229(x7163,x7164,x7165,x7161),f229(x7163,x7164,x7165,x7162)) % 186.05/186.63 [717]~E(x7171,x7172)+E(f808(x7171,x7173,x7174),f808(x7172,x7173,x7174)) % 186.05/186.63 [718]~E(x7181,x7182)+E(f808(x7183,x7181,x7184),f808(x7183,x7182,x7184)) % 186.05/186.63 [719]~E(x7191,x7192)+E(f808(x7193,x7194,x7191),f808(x7193,x7194,x7192)) % 186.05/186.63 [720]~E(x7201,x7202)+E(f38(x7201,x7203,x7204,x7205,x7206,x7207,x7208,x7209,x72010,x72011),f38(x7202,x7203,x7204,x7205,x7206,x7207,x7208,x7209,x72010,x72011)) % 186.05/186.63 [721]~E(x7211,x7212)+E(f38(x7213,x7211,x7214,x7215,x7216,x7217,x7218,x7219,x72110,x72111),f38(x7213,x7212,x7214,x7215,x7216,x7217,x7218,x7219,x72110,x72111)) % 186.05/186.63 [722]~E(x7221,x7222)+E(f38(x7223,x7224,x7221,x7225,x7226,x7227,x7228,x7229,x72210,x72211),f38(x7223,x7224,x7222,x7225,x7226,x7227,x7228,x7229,x72210,x72211)) % 186.05/186.63 [723]~E(x7231,x7232)+E(f38(x7233,x7234,x7235,x7231,x7236,x7237,x7238,x7239,x72310,x72311),f38(x7233,x7234,x7235,x7232,x7236,x7237,x7238,x7239,x72310,x72311)) % 186.05/186.63 [724]~E(x7241,x7242)+E(f38(x7243,x7244,x7245,x7246,x7241,x7247,x7248,x7249,x72410,x72411),f38(x7243,x7244,x7245,x7246,x7242,x7247,x7248,x7249,x72410,x72411)) % 186.05/186.63 [725]~E(x7251,x7252)+E(f38(x7253,x7254,x7255,x7256,x7257,x7251,x7258,x7259,x72510,x72511),f38(x7253,x7254,x7255,x7256,x7257,x7252,x7258,x7259,x72510,x72511)) % 186.05/186.63 [726]~E(x7261,x7262)+E(f38(x7263,x7264,x7265,x7266,x7267,x7268,x7261,x7269,x72610,x72611),f38(x7263,x7264,x7265,x7266,x7267,x7268,x7262,x7269,x72610,x72611)) % 186.05/186.63 [727]~E(x7271,x7272)+E(f38(x7273,x7274,x7275,x7276,x7277,x7278,x7279,x7271,x72710,x72711),f38(x7273,x7274,x7275,x7276,x7277,x7278,x7279,x7272,x72710,x72711)) % 186.05/186.63 [728]~E(x7281,x7282)+E(f38(x7283,x7284,x7285,x7286,x7287,x7288,x7289,x72810,x7281,x72811),f38(x7283,x7284,x7285,x7286,x7287,x7288,x7289,x72810,x7282,x72811)) % 186.05/186.63 [729]~E(x7291,x7292)+E(f38(x7293,x7294,x7295,x7296,x7297,x7298,x7299,x72910,x72911,x7291),f38(x7293,x7294,x7295,x7296,x7297,x7298,x7299,x72910,x72911,x7292)) % 186.05/186.63 [730]~E(x7301,x7302)+E(f517(x7301,x7303,x7304,x7305),f517(x7302,x7303,x7304,x7305)) % 186.05/186.63 [731]~E(x7311,x7312)+E(f517(x7313,x7311,x7314,x7315),f517(x7313,x7312,x7314,x7315)) % 186.05/186.63 [732]~E(x7321,x7322)+E(f517(x7323,x7324,x7321,x7325),f517(x7323,x7324,x7322,x7325)) % 186.05/186.63 [733]~E(x7331,x7332)+E(f517(x7333,x7334,x7335,x7331),f517(x7333,x7334,x7335,x7332)) % 186.05/186.63 [734]~E(x7341,x7342)+E(f685(x7341,x7343,x7344),f685(x7342,x7343,x7344)) % 186.05/186.63 [735]~E(x7351,x7352)+E(f685(x7353,x7351,x7354),f685(x7353,x7352,x7354)) % 186.05/186.63 [736]~E(x7361,x7362)+E(f685(x7363,x7364,x7361),f685(x7363,x7364,x7362)) % 186.05/186.63 [737]~E(x7371,x7372)+E(f144(x7371,x7373,x7374),f144(x7372,x7373,x7374)) % 186.05/186.63 [738]~E(x7381,x7382)+E(f144(x7383,x7381,x7384),f144(x7383,x7382,x7384)) % 186.05/186.63 [739]~E(x7391,x7392)+E(f144(x7393,x7394,x7391),f144(x7393,x7394,x7392)) % 186.05/186.63 [740]~E(x7401,x7402)+E(f821(x7401,x7403,x7404),f821(x7402,x7403,x7404)) % 186.05/186.63 [741]~E(x7411,x7412)+E(f821(x7413,x7411,x7414),f821(x7413,x7412,x7414)) % 186.05/186.63 [742]~E(x7421,x7422)+E(f821(x7423,x7424,x7421),f821(x7423,x7424,x7422)) % 186.05/186.63 [743]~E(x7431,x7432)+E(f823(x7431,x7433,x7434,x7435,x7436),f823(x7432,x7433,x7434,x7435,x7436)) % 186.05/186.63 [744]~E(x7441,x7442)+E(f823(x7443,x7441,x7444,x7445,x7446),f823(x7443,x7442,x7444,x7445,x7446)) % 186.05/186.63 [745]~E(x7451,x7452)+E(f823(x7453,x7454,x7451,x7455,x7456),f823(x7453,x7454,x7452,x7455,x7456)) % 186.05/186.63 [746]~E(x7461,x7462)+E(f823(x7463,x7464,x7465,x7461,x7466),f823(x7463,x7464,x7465,x7462,x7466)) % 186.05/186.63 [747]~E(x7471,x7472)+E(f823(x7473,x7474,x7475,x7476,x7471),f823(x7473,x7474,x7475,x7476,x7472)) % 186.05/186.63 [748]~E(x7481,x7482)+E(f732(x7481,x7483,x7484,x7485,x7486),f732(x7482,x7483,x7484,x7485,x7486)) % 186.05/186.63 [749]~E(x7491,x7492)+E(f732(x7493,x7491,x7494,x7495,x7496),f732(x7493,x7492,x7494,x7495,x7496)) % 186.05/186.63 [750]~E(x7501,x7502)+E(f732(x7503,x7504,x7501,x7505,x7506),f732(x7503,x7504,x7502,x7505,x7506)) % 186.05/186.63 [751]~E(x7511,x7512)+E(f732(x7513,x7514,x7515,x7511,x7516),f732(x7513,x7514,x7515,x7512,x7516)) % 186.05/186.63 [752]~E(x7521,x7522)+E(f732(x7523,x7524,x7525,x7526,x7521),f732(x7523,x7524,x7525,x7526,x7522)) % 186.05/186.63 [753]~E(x7531,x7532)+E(f276(x7531),f276(x7532)) % 186.05/186.63 [754]~E(x7541,x7542)+E(f525(x7541,x7543,x7544,x7545),f525(x7542,x7543,x7544,x7545)) % 186.05/186.63 [755]~E(x7551,x7552)+E(f525(x7553,x7551,x7554,x7555),f525(x7553,x7552,x7554,x7555)) % 186.05/186.63 [756]~E(x7561,x7562)+E(f525(x7563,x7564,x7561,x7565),f525(x7563,x7564,x7562,x7565)) % 186.05/186.63 [757]~E(x7571,x7572)+E(f525(x7573,x7574,x7575,x7571),f525(x7573,x7574,x7575,x7572)) % 186.05/186.63 [758]~E(x7581,x7582)+E(f32(x7581,x7583,x7584),f32(x7582,x7583,x7584)) % 186.05/186.63 [759]~E(x7591,x7592)+E(f32(x7593,x7591,x7594),f32(x7593,x7592,x7594)) % 186.05/186.63 [760]~E(x7601,x7602)+E(f32(x7603,x7604,x7601),f32(x7603,x7604,x7602)) % 186.05/186.63 [761]~E(x7611,x7612)+E(f363(x7611,x7613,x7614,x7615,x7616),f363(x7612,x7613,x7614,x7615,x7616)) % 186.05/186.63 [762]~E(x7621,x7622)+E(f363(x7623,x7621,x7624,x7625,x7626),f363(x7623,x7622,x7624,x7625,x7626)) % 186.05/186.63 [763]~E(x7631,x7632)+E(f363(x7633,x7634,x7631,x7635,x7636),f363(x7633,x7634,x7632,x7635,x7636)) % 186.05/186.63 [764]~E(x7641,x7642)+E(f363(x7643,x7644,x7645,x7641,x7646),f363(x7643,x7644,x7645,x7642,x7646)) % 186.05/186.63 [765]~E(x7651,x7652)+E(f363(x7653,x7654,x7655,x7656,x7651),f363(x7653,x7654,x7655,x7656,x7652)) % 186.05/186.63 [766]~E(x7661,x7662)+E(f636(x7661,x7663,x7664),f636(x7662,x7663,x7664)) % 186.05/186.63 [767]~E(x7671,x7672)+E(f636(x7673,x7671,x7674),f636(x7673,x7672,x7674)) % 186.05/186.63 [768]~E(x7681,x7682)+E(f636(x7683,x7684,x7681),f636(x7683,x7684,x7682)) % 186.05/186.63 [769]~E(x7691,x7692)+E(f246(x7691,x7693,x7694),f246(x7692,x7693,x7694)) % 186.05/186.63 [770]~E(x7701,x7702)+E(f246(x7703,x7701,x7704),f246(x7703,x7702,x7704)) % 186.05/186.63 [771]~E(x7711,x7712)+E(f246(x7713,x7714,x7711),f246(x7713,x7714,x7712)) % 186.05/186.63 [772]~E(x7721,x7722)+E(f156(x7721,x7723,x7724),f156(x7722,x7723,x7724)) % 186.05/186.63 [773]~E(x7731,x7732)+E(f156(x7733,x7731,x7734),f156(x7733,x7732,x7734)) % 186.05/186.63 [774]~E(x7741,x7742)+E(f156(x7743,x7744,x7741),f156(x7743,x7744,x7742)) % 186.05/186.63 [775]~E(x7751,x7752)+E(f606(x7751,x7753),f606(x7752,x7753)) % 186.05/186.63 [776]~E(x7761,x7762)+E(f606(x7763,x7761),f606(x7763,x7762)) % 186.05/186.63 [777]~E(x7771,x7772)+E(f712(x7771,x7773,x7774,x7775),f712(x7772,x7773,x7774,x7775)) % 186.05/186.63 [778]~E(x7781,x7782)+E(f712(x7783,x7781,x7784,x7785),f712(x7783,x7782,x7784,x7785)) % 186.05/186.63 [779]~E(x7791,x7792)+E(f712(x7793,x7794,x7791,x7795),f712(x7793,x7794,x7792,x7795)) % 186.05/186.63 [780]~E(x7801,x7802)+E(f712(x7803,x7804,x7805,x7801),f712(x7803,x7804,x7805,x7802)) % 186.05/186.63 [781]~E(x7811,x7812)+E(f516(x7811,x7813),f516(x7812,x7813)) % 186.05/186.63 [782]~E(x7821,x7822)+E(f516(x7823,x7821),f516(x7823,x7822)) % 186.05/186.63 [783]~E(x7831,x7832)+E(f231(x7831),f231(x7832)) % 186.05/186.63 [784]~E(x7841,x7842)+E(f681(x7841,x7843),f681(x7842,x7843)) % 186.05/186.63 [785]~E(x7851,x7852)+E(f681(x7853,x7851),f681(x7853,x7852)) % 186.05/186.63 [786]~E(x7861,x7862)+E(f564(x7861,x7863,x7864,x7865,x7866,x7867),f564(x7862,x7863,x7864,x7865,x7866,x7867)) % 186.05/186.63 [787]~E(x7871,x7872)+E(f564(x7873,x7871,x7874,x7875,x7876,x7877),f564(x7873,x7872,x7874,x7875,x7876,x7877)) % 186.05/186.63 [788]~E(x7881,x7882)+E(f564(x7883,x7884,x7881,x7885,x7886,x7887),f564(x7883,x7884,x7882,x7885,x7886,x7887)) % 186.05/186.63 [789]~E(x7891,x7892)+E(f564(x7893,x7894,x7895,x7891,x7896,x7897),f564(x7893,x7894,x7895,x7892,x7896,x7897)) % 186.05/186.63 [790]~E(x7901,x7902)+E(f564(x7903,x7904,x7905,x7906,x7901,x7907),f564(x7903,x7904,x7905,x7906,x7902,x7907)) % 186.05/186.63 [791]~E(x7911,x7912)+E(f564(x7913,x7914,x7915,x7916,x7917,x7911),f564(x7913,x7914,x7915,x7916,x7917,x7912)) % 186.05/186.63 [792]~E(x7921,x7922)+E(f138(x7921,x7923,x7924),f138(x7922,x7923,x7924)) % 186.05/186.63 [793]~E(x7931,x7932)+E(f138(x7933,x7931,x7934),f138(x7933,x7932,x7934)) % 186.05/186.63 [794]~E(x7941,x7942)+E(f138(x7943,x7944,x7941),f138(x7943,x7944,x7942)) % 186.05/186.63 [795]~E(x7951,x7952)+E(f661(x7951,x7953,x7954,x7955,x7956),f661(x7952,x7953,x7954,x7955,x7956)) % 186.05/186.63 [796]~E(x7961,x7962)+E(f661(x7963,x7961,x7964,x7965,x7966),f661(x7963,x7962,x7964,x7965,x7966)) % 186.05/186.63 [797]~E(x7971,x7972)+E(f661(x7973,x7974,x7971,x7975,x7976),f661(x7973,x7974,x7972,x7975,x7976)) % 186.05/186.63 [798]~E(x7981,x7982)+E(f661(x7983,x7984,x7985,x7981,x7986),f661(x7983,x7984,x7985,x7982,x7986)) % 186.05/186.63 [799]~E(x7991,x7992)+E(f661(x7993,x7994,x7995,x7996,x7991),f661(x7993,x7994,x7995,x7996,x7992)) % 186.05/186.63 [800]~E(x8001,x8002)+E(f801(x8001,x8003,x8004),f801(x8002,x8003,x8004)) % 186.05/186.64 [801]~E(x8011,x8012)+E(f801(x8013,x8011,x8014),f801(x8013,x8012,x8014)) % 186.05/186.64 [802]~E(x8021,x8022)+E(f801(x8023,x8024,x8021),f801(x8023,x8024,x8022)) % 186.05/186.64 [803]~E(x8031,x8032)+E(f643(x8031,x8033,x8034,x8035,x8036),f643(x8032,x8033,x8034,x8035,x8036)) % 186.05/186.64 [804]~E(x8041,x8042)+E(f643(x8043,x8041,x8044,x8045,x8046),f643(x8043,x8042,x8044,x8045,x8046)) % 186.05/186.64 [805]~E(x8051,x8052)+E(f643(x8053,x8054,x8051,x8055,x8056),f643(x8053,x8054,x8052,x8055,x8056)) % 186.05/186.64 [806]~E(x8061,x8062)+E(f643(x8063,x8064,x8065,x8061,x8066),f643(x8063,x8064,x8065,x8062,x8066)) % 186.05/186.64 [807]~E(x8071,x8072)+E(f643(x8073,x8074,x8075,x8076,x8071),f643(x8073,x8074,x8075,x8076,x8072)) % 186.05/186.64 [808]~E(x8081,x8082)+E(f64(x8081,x8083,x8084),f64(x8082,x8083,x8084)) % 186.05/186.64 [809]~E(x8091,x8092)+E(f64(x8093,x8091,x8094),f64(x8093,x8092,x8094)) % 186.05/186.64 [810]~E(x8101,x8102)+E(f64(x8103,x8104,x8101),f64(x8103,x8104,x8102)) % 186.05/186.64 [811]~E(x8111,x8112)+E(f188(x8111,x8113),f188(x8112,x8113)) % 186.05/186.64 [812]~E(x8121,x8122)+E(f188(x8123,x8121),f188(x8123,x8122)) % 186.05/186.64 [813]~E(x8131,x8132)+E(f296(x8131),f296(x8132)) % 186.05/186.64 [814]~E(x8141,x8142)+E(f425(x8141,x8143,x8144),f425(x8142,x8143,x8144)) % 186.05/186.64 [815]~E(x8151,x8152)+E(f425(x8153,x8151,x8154),f425(x8153,x8152,x8154)) % 186.05/186.64 [816]~E(x8161,x8162)+E(f425(x8163,x8164,x8161),f425(x8163,x8164,x8162)) % 186.05/186.64 [817]~E(x8171,x8172)+E(f37(x8171,x8173,x8174,x8175,x8176,x8177,x8178,x8179,x81710,x81711),f37(x8172,x8173,x8174,x8175,x8176,x8177,x8178,x8179,x81710,x81711)) % 186.05/186.64 [818]~E(x8181,x8182)+E(f37(x8183,x8181,x8184,x8185,x8186,x8187,x8188,x8189,x81810,x81811),f37(x8183,x8182,x8184,x8185,x8186,x8187,x8188,x8189,x81810,x81811)) % 186.05/186.64 [819]~E(x8191,x8192)+E(f37(x8193,x8194,x8191,x8195,x8196,x8197,x8198,x8199,x81910,x81911),f37(x8193,x8194,x8192,x8195,x8196,x8197,x8198,x8199,x81910,x81911)) % 186.05/186.64 [820]~E(x8201,x8202)+E(f37(x8203,x8204,x8205,x8201,x8206,x8207,x8208,x8209,x82010,x82011),f37(x8203,x8204,x8205,x8202,x8206,x8207,x8208,x8209,x82010,x82011)) % 186.05/186.64 [821]~E(x8211,x8212)+E(f37(x8213,x8214,x8215,x8216,x8211,x8217,x8218,x8219,x82110,x82111),f37(x8213,x8214,x8215,x8216,x8212,x8217,x8218,x8219,x82110,x82111)) % 186.05/186.64 [822]~E(x8221,x8222)+E(f37(x8223,x8224,x8225,x8226,x8227,x8221,x8228,x8229,x82210,x82211),f37(x8223,x8224,x8225,x8226,x8227,x8222,x8228,x8229,x82210,x82211)) % 186.05/186.64 [823]~E(x8231,x8232)+E(f37(x8233,x8234,x8235,x8236,x8237,x8238,x8231,x8239,x82310,x82311),f37(x8233,x8234,x8235,x8236,x8237,x8238,x8232,x8239,x82310,x82311)) % 186.05/186.64 [824]~E(x8241,x8242)+E(f37(x8243,x8244,x8245,x8246,x8247,x8248,x8249,x8241,x82410,x82411),f37(x8243,x8244,x8245,x8246,x8247,x8248,x8249,x8242,x82410,x82411)) % 186.05/186.64 [825]~E(x8251,x8252)+E(f37(x8253,x8254,x8255,x8256,x8257,x8258,x8259,x82510,x8251,x82511),f37(x8253,x8254,x8255,x8256,x8257,x8258,x8259,x82510,x8252,x82511)) % 186.05/186.64 [826]~E(x8261,x8262)+E(f37(x8263,x8264,x8265,x8266,x8267,x8268,x8269,x82610,x82611,x8261),f37(x8263,x8264,x8265,x8266,x8267,x8268,x8269,x82610,x82611,x8262)) % 186.05/186.64 [827]~E(x8271,x8272)+E(f768(x8271,x8273,x8274),f768(x8272,x8273,x8274)) % 186.05/186.64 [828]~E(x8281,x8282)+E(f768(x8283,x8281,x8284),f768(x8283,x8282,x8284)) % 186.05/186.64 [829]~E(x8291,x8292)+E(f768(x8293,x8294,x8291),f768(x8293,x8294,x8292)) % 186.05/186.64 [830]~E(x8301,x8302)+E(f424(x8301,x8303,x8304,x8305),f424(x8302,x8303,x8304,x8305)) % 186.05/186.64 [831]~E(x8311,x8312)+E(f424(x8313,x8311,x8314,x8315),f424(x8313,x8312,x8314,x8315)) % 186.05/186.64 [832]~E(x8321,x8322)+E(f424(x8323,x8324,x8321,x8325),f424(x8323,x8324,x8322,x8325)) % 186.05/186.64 [833]~E(x8331,x8332)+E(f424(x8333,x8334,x8335,x8331),f424(x8333,x8334,x8335,x8332)) % 186.05/186.64 [834]~E(x8341,x8342)+E(f654(x8341,x8343),f654(x8342,x8343)) % 186.05/186.64 [835]~E(x8351,x8352)+E(f654(x8353,x8351),f654(x8353,x8352)) % 186.05/186.64 [836]~E(x8361,x8362)+E(f483(x8361,x8363,x8364),f483(x8362,x8363,x8364)) % 186.05/186.64 [837]~E(x8371,x8372)+E(f483(x8373,x8371,x8374),f483(x8373,x8372,x8374)) % 186.05/186.64 [838]~E(x8381,x8382)+E(f483(x8383,x8384,x8381),f483(x8383,x8384,x8382)) % 186.05/186.64 [839]~E(x8391,x8392)+E(f720(x8391,x8393,x8394,x8395,x8396),f720(x8392,x8393,x8394,x8395,x8396)) % 186.05/186.64 [840]~E(x8401,x8402)+E(f720(x8403,x8401,x8404,x8405,x8406),f720(x8403,x8402,x8404,x8405,x8406)) % 186.05/186.64 [841]~E(x8411,x8412)+E(f720(x8413,x8414,x8411,x8415,x8416),f720(x8413,x8414,x8412,x8415,x8416)) % 186.05/186.64 [842]~E(x8421,x8422)+E(f720(x8423,x8424,x8425,x8421,x8426),f720(x8423,x8424,x8425,x8422,x8426)) % 186.05/186.64 [843]~E(x8431,x8432)+E(f720(x8433,x8434,x8435,x8436,x8431),f720(x8433,x8434,x8435,x8436,x8432)) % 186.05/186.64 [844]~E(x8441,x8442)+E(f601(x8441),f601(x8442)) % 186.05/186.64 [845]~E(x8451,x8452)+E(f265(x8451,x8453),f265(x8452,x8453)) % 186.05/186.64 [846]~E(x8461,x8462)+E(f265(x8463,x8461),f265(x8463,x8462)) % 186.05/186.64 [847]~E(x8471,x8472)+E(f441(x8471,x8473,x8474,x8475,x8476),f441(x8472,x8473,x8474,x8475,x8476)) % 186.05/186.64 [848]~E(x8481,x8482)+E(f441(x8483,x8481,x8484,x8485,x8486),f441(x8483,x8482,x8484,x8485,x8486)) % 186.05/186.64 [849]~E(x8491,x8492)+E(f441(x8493,x8494,x8491,x8495,x8496),f441(x8493,x8494,x8492,x8495,x8496)) % 186.05/186.64 [850]~E(x8501,x8502)+E(f441(x8503,x8504,x8505,x8501,x8506),f441(x8503,x8504,x8505,x8502,x8506)) % 186.05/186.64 [851]~E(x8511,x8512)+E(f441(x8513,x8514,x8515,x8516,x8511),f441(x8513,x8514,x8515,x8516,x8512)) % 186.05/186.64 [852]~E(x8521,x8522)+E(f379(x8521,x8523,x8524,x8525),f379(x8522,x8523,x8524,x8525)) % 186.05/186.64 [853]~E(x8531,x8532)+E(f379(x8533,x8531,x8534,x8535),f379(x8533,x8532,x8534,x8535)) % 186.05/186.64 [854]~E(x8541,x8542)+E(f379(x8543,x8544,x8541,x8545),f379(x8543,x8544,x8542,x8545)) % 186.05/186.64 [855]~E(x8551,x8552)+E(f379(x8553,x8554,x8555,x8551),f379(x8553,x8554,x8555,x8552)) % 186.05/186.64 [856]~E(x8561,x8562)+E(f384(x8561,x8563,x8564,x8565),f384(x8562,x8563,x8564,x8565)) % 186.05/186.64 [857]~E(x8571,x8572)+E(f384(x8573,x8571,x8574,x8575),f384(x8573,x8572,x8574,x8575)) % 186.05/186.64 [858]~E(x8581,x8582)+E(f384(x8583,x8584,x8581,x8585),f384(x8583,x8584,x8582,x8585)) % 186.05/186.64 [859]~E(x8591,x8592)+E(f384(x8593,x8594,x8595,x8591),f384(x8593,x8594,x8595,x8592)) % 186.05/186.64 [860]~E(x8601,x8602)+E(f693(x8601,x8603,x8604,x8605),f693(x8602,x8603,x8604,x8605)) % 186.05/186.64 [861]~E(x8611,x8612)+E(f693(x8613,x8611,x8614,x8615),f693(x8613,x8612,x8614,x8615)) % 186.05/186.64 [862]~E(x8621,x8622)+E(f693(x8623,x8624,x8621,x8625),f693(x8623,x8624,x8622,x8625)) % 186.05/186.64 [863]~E(x8631,x8632)+E(f693(x8633,x8634,x8635,x8631),f693(x8633,x8634,x8635,x8632)) % 186.05/186.64 [864]~E(x8641,x8642)+E(f656(x8641,x8643,x8644,x8645),f656(x8642,x8643,x8644,x8645)) % 186.05/186.64 [865]~E(x8651,x8652)+E(f656(x8653,x8651,x8654,x8655),f656(x8653,x8652,x8654,x8655)) % 186.05/186.64 [866]~E(x8661,x8662)+E(f656(x8663,x8664,x8661,x8665),f656(x8663,x8664,x8662,x8665)) % 186.05/186.64 [867]~E(x8671,x8672)+E(f656(x8673,x8674,x8675,x8671),f656(x8673,x8674,x8675,x8672)) % 186.05/186.64 [868]~E(x8681,x8682)+E(f263(x8681,x8683),f263(x8682,x8683)) % 186.05/186.64 [869]~E(x8691,x8692)+E(f263(x8693,x8691),f263(x8693,x8692)) % 186.05/186.64 [870]~E(x8701,x8702)+E(f460(x8701,x8703,x8704),f460(x8702,x8703,x8704)) % 186.05/186.64 [871]~E(x8711,x8712)+E(f460(x8713,x8711,x8714),f460(x8713,x8712,x8714)) % 186.05/186.64 [872]~E(x8721,x8722)+E(f460(x8723,x8724,x8721),f460(x8723,x8724,x8722)) % 186.05/186.64 [873]~E(x8731,x8732)+E(f667(x8731,x8733,x8734,x8735,x8736),f667(x8732,x8733,x8734,x8735,x8736)) % 186.05/186.64 [874]~E(x8741,x8742)+E(f667(x8743,x8741,x8744,x8745,x8746),f667(x8743,x8742,x8744,x8745,x8746)) % 186.05/186.64 [875]~E(x8751,x8752)+E(f667(x8753,x8754,x8751,x8755,x8756),f667(x8753,x8754,x8752,x8755,x8756)) % 186.05/186.64 [876]~E(x8761,x8762)+E(f667(x8763,x8764,x8765,x8761,x8766),f667(x8763,x8764,x8765,x8762,x8766)) % 186.05/186.64 [877]~E(x8771,x8772)+E(f667(x8773,x8774,x8775,x8776,x8771),f667(x8773,x8774,x8775,x8776,x8772)) % 186.05/186.64 [878]~E(x8781,x8782)+E(f341(x8781,x8783,x8784),f341(x8782,x8783,x8784)) % 186.05/186.64 [879]~E(x8791,x8792)+E(f341(x8793,x8791,x8794),f341(x8793,x8792,x8794)) % 186.05/186.64 [880]~E(x8801,x8802)+E(f341(x8803,x8804,x8801),f341(x8803,x8804,x8802)) % 186.05/186.64 [881]~E(x8811,x8812)+E(f833(x8811,x8813,x8814),f833(x8812,x8813,x8814)) % 186.05/186.64 [882]~E(x8821,x8822)+E(f833(x8823,x8821,x8824),f833(x8823,x8822,x8824)) % 186.05/186.64 [883]~E(x8831,x8832)+E(f833(x8833,x8834,x8831),f833(x8833,x8834,x8832)) % 186.05/186.64 [884]~E(x8841,x8842)+E(f840(x8841,x8843,x8844),f840(x8842,x8843,x8844)) % 186.05/186.64 [885]~E(x8851,x8852)+E(f840(x8853,x8851,x8854),f840(x8853,x8852,x8854)) % 186.05/186.64 [886]~E(x8861,x8862)+E(f840(x8863,x8864,x8861),f840(x8863,x8864,x8862)) % 186.05/186.64 [887]~E(x8871,x8872)+E(f662(x8871,x8873,x8874,x8875,x8876),f662(x8872,x8873,x8874,x8875,x8876)) % 186.05/186.64 [888]~E(x8881,x8882)+E(f662(x8883,x8881,x8884,x8885,x8886),f662(x8883,x8882,x8884,x8885,x8886)) % 186.05/186.64 [889]~E(x8891,x8892)+E(f662(x8893,x8894,x8891,x8895,x8896),f662(x8893,x8894,x8892,x8895,x8896)) % 186.05/186.64 [890]~E(x8901,x8902)+E(f662(x8903,x8904,x8905,x8901,x8906),f662(x8903,x8904,x8905,x8902,x8906)) % 186.05/186.64 [891]~E(x8911,x8912)+E(f662(x8913,x8914,x8915,x8916,x8911),f662(x8913,x8914,x8915,x8916,x8912)) % 186.05/186.64 [892]~E(x8921,x8922)+E(f210(x8921,x8923),f210(x8922,x8923)) % 186.05/186.64 [893]~E(x8931,x8932)+E(f210(x8933,x8931),f210(x8933,x8932)) % 186.05/186.64 [894]~E(x8941,x8942)+E(f492(x8941,x8943),f492(x8942,x8943)) % 186.05/186.64 [895]~E(x8951,x8952)+E(f492(x8953,x8951),f492(x8953,x8952)) % 186.05/186.64 [896]~E(x8961,x8962)+E(f766(x8961,x8963,x8964),f766(x8962,x8963,x8964)) % 186.05/186.64 [897]~E(x8971,x8972)+E(f766(x8973,x8971,x8974),f766(x8973,x8972,x8974)) % 186.05/186.64 [898]~E(x8981,x8982)+E(f766(x8983,x8984,x8981),f766(x8983,x8984,x8982)) % 186.05/186.64 [899]~E(x8991,x8992)+E(f185(x8991,x8993),f185(x8992,x8993)) % 186.05/186.64 [900]~E(x9001,x9002)+E(f185(x9003,x9001),f185(x9003,x9002)) % 186.05/186.64 [901]~E(x9011,x9012)+E(f788(x9011,x9013,x9014),f788(x9012,x9013,x9014)) % 186.05/186.64 [902]~E(x9021,x9022)+E(f788(x9023,x9021,x9024),f788(x9023,x9022,x9024)) % 186.05/186.64 [903]~E(x9031,x9032)+E(f788(x9033,x9034,x9031),f788(x9033,x9034,x9032)) % 186.05/186.64 [904]~E(x9041,x9042)+E(f120(x9041,x9043),f120(x9042,x9043)) % 186.05/186.64 [905]~E(x9051,x9052)+E(f120(x9053,x9051),f120(x9053,x9052)) % 186.05/186.64 [906]~E(x9061,x9062)+E(f194(x9061,x9063),f194(x9062,x9063)) % 186.05/186.64 [907]~E(x9071,x9072)+E(f194(x9073,x9071),f194(x9073,x9072)) % 186.05/186.64 [908]~E(x9081,x9082)+E(f220(x9081,x9083,x9084,x9085,x9086),f220(x9082,x9083,x9084,x9085,x9086)) % 186.05/186.64 [909]~E(x9091,x9092)+E(f220(x9093,x9091,x9094,x9095,x9096),f220(x9093,x9092,x9094,x9095,x9096)) % 186.05/186.64 [910]~E(x9101,x9102)+E(f220(x9103,x9104,x9101,x9105,x9106),f220(x9103,x9104,x9102,x9105,x9106)) % 186.05/186.64 [911]~E(x9111,x9112)+E(f220(x9113,x9114,x9115,x9111,x9116),f220(x9113,x9114,x9115,x9112,x9116)) % 186.05/186.64 [912]~E(x9121,x9122)+E(f220(x9123,x9124,x9125,x9126,x9121),f220(x9123,x9124,x9125,x9126,x9122)) % 186.05/186.64 [913]~E(x9131,x9132)+E(f123(x9131,x9133),f123(x9132,x9133)) % 186.05/186.64 [914]~E(x9141,x9142)+E(f123(x9143,x9141),f123(x9143,x9142)) % 186.05/186.64 [915]~E(x9151,x9152)+E(f497(x9151,x9153,x9154),f497(x9152,x9153,x9154)) % 186.05/186.64 [916]~E(x9161,x9162)+E(f497(x9163,x9161,x9164),f497(x9163,x9162,x9164)) % 186.05/186.64 [917]~E(x9171,x9172)+E(f497(x9173,x9174,x9171),f497(x9173,x9174,x9172)) % 186.05/186.64 [918]~E(x9181,x9182)+E(f810(x9181,x9183,x9184),f810(x9182,x9183,x9184)) % 186.05/186.64 [919]~E(x9191,x9192)+E(f810(x9193,x9191,x9194),f810(x9193,x9192,x9194)) % 186.05/186.64 [920]~E(x9201,x9202)+E(f810(x9203,x9204,x9201),f810(x9203,x9204,x9202)) % 186.05/186.64 [921]~E(x9211,x9212)+E(f634(x9211,x9213,x9214),f634(x9212,x9213,x9214)) % 186.05/186.64 [922]~E(x9221,x9222)+E(f634(x9223,x9221,x9224),f634(x9223,x9222,x9224)) % 186.05/186.64 [923]~E(x9231,x9232)+E(f634(x9233,x9234,x9231),f634(x9233,x9234,x9232)) % 186.05/186.64 [924]~E(x9241,x9242)+E(f797(x9241,x9243,x9244),f797(x9242,x9243,x9244)) % 186.05/186.64 [925]~E(x9251,x9252)+E(f797(x9253,x9251,x9254),f797(x9253,x9252,x9254)) % 186.05/186.64 [926]~E(x9261,x9262)+E(f797(x9263,x9264,x9261),f797(x9263,x9264,x9262)) % 186.05/186.64 [927]~E(x9271,x9272)+E(f570(x9271,x9273,x9274,x9275,x9276),f570(x9272,x9273,x9274,x9275,x9276)) % 186.05/186.64 [928]~E(x9281,x9282)+E(f570(x9283,x9281,x9284,x9285,x9286),f570(x9283,x9282,x9284,x9285,x9286)) % 186.05/186.64 [929]~E(x9291,x9292)+E(f570(x9293,x9294,x9291,x9295,x9296),f570(x9293,x9294,x9292,x9295,x9296)) % 186.05/186.64 [930]~E(x9301,x9302)+E(f570(x9303,x9304,x9305,x9301,x9306),f570(x9303,x9304,x9305,x9302,x9306)) % 186.05/186.64 [931]~E(x9311,x9312)+E(f570(x9313,x9314,x9315,x9316,x9311),f570(x9313,x9314,x9315,x9316,x9312)) % 186.05/186.64 [932]~E(x9321,x9322)+E(f368(x9321,x9323,x9324,x9325,x9326),f368(x9322,x9323,x9324,x9325,x9326)) % 186.05/186.64 [933]~E(x9331,x9332)+E(f368(x9333,x9331,x9334,x9335,x9336),f368(x9333,x9332,x9334,x9335,x9336)) % 186.05/186.64 [934]~E(x9341,x9342)+E(f368(x9343,x9344,x9341,x9345,x9346),f368(x9343,x9344,x9342,x9345,x9346)) % 186.05/186.64 [935]~E(x9351,x9352)+E(f368(x9353,x9354,x9355,x9351,x9356),f368(x9353,x9354,x9355,x9352,x9356)) % 186.05/186.64 [936]~E(x9361,x9362)+E(f368(x9363,x9364,x9365,x9366,x9361),f368(x9363,x9364,x9365,x9366,x9362)) % 186.05/186.64 [937]~E(x9371,x9372)+E(f78(x9371,x9373,x9374,x9375,x9376),f78(x9372,x9373,x9374,x9375,x9376)) % 186.05/186.64 [938]~E(x9381,x9382)+E(f78(x9383,x9381,x9384,x9385,x9386),f78(x9383,x9382,x9384,x9385,x9386)) % 186.05/186.64 [939]~E(x9391,x9392)+E(f78(x9393,x9394,x9391,x9395,x9396),f78(x9393,x9394,x9392,x9395,x9396)) % 186.05/186.64 [940]~E(x9401,x9402)+E(f78(x9403,x9404,x9405,x9401,x9406),f78(x9403,x9404,x9405,x9402,x9406)) % 186.05/186.64 [941]~E(x9411,x9412)+E(f78(x9413,x9414,x9415,x9416,x9411),f78(x9413,x9414,x9415,x9416,x9412)) % 186.05/186.64 [942]~E(x9421,x9422)+E(f430(x9421,x9423,x9424,x9425,x9426,x9427,x9428),f430(x9422,x9423,x9424,x9425,x9426,x9427,x9428)) % 186.05/186.64 [943]~E(x9431,x9432)+E(f430(x9433,x9431,x9434,x9435,x9436,x9437,x9438),f430(x9433,x9432,x9434,x9435,x9436,x9437,x9438)) % 186.05/186.64 [944]~E(x9441,x9442)+E(f430(x9443,x9444,x9441,x9445,x9446,x9447,x9448),f430(x9443,x9444,x9442,x9445,x9446,x9447,x9448)) % 186.05/186.64 [945]~E(x9451,x9452)+E(f430(x9453,x9454,x9455,x9451,x9456,x9457,x9458),f430(x9453,x9454,x9455,x9452,x9456,x9457,x9458)) % 186.05/186.64 [946]~E(x9461,x9462)+E(f430(x9463,x9464,x9465,x9466,x9461,x9467,x9468),f430(x9463,x9464,x9465,x9466,x9462,x9467,x9468)) % 186.05/186.64 [947]~E(x9471,x9472)+E(f430(x9473,x9474,x9475,x9476,x9477,x9471,x9478),f430(x9473,x9474,x9475,x9476,x9477,x9472,x9478)) % 186.05/186.64 [948]~E(x9481,x9482)+E(f430(x9483,x9484,x9485,x9486,x9487,x9488,x9481),f430(x9483,x9484,x9485,x9486,x9487,x9488,x9482)) % 186.05/186.64 [949]~E(x9491,x9492)+E(f286(x9491,x9493,x9494),f286(x9492,x9493,x9494)) % 186.05/186.64 [950]~E(x9501,x9502)+E(f286(x9503,x9501,x9504),f286(x9503,x9502,x9504)) % 186.05/186.64 [951]~E(x9511,x9512)+E(f286(x9513,x9514,x9511),f286(x9513,x9514,x9512)) % 186.05/186.64 [952]~E(x9521,x9522)+E(f507(x9521,x9523,x9524),f507(x9522,x9523,x9524)) % 186.05/186.64 [953]~E(x9531,x9532)+E(f507(x9533,x9531,x9534),f507(x9533,x9532,x9534)) % 186.05/186.64 [954]~E(x9541,x9542)+E(f507(x9543,x9544,x9541),f507(x9543,x9544,x9542)) % 186.05/186.64 [955]~E(x9551,x9552)+E(f676(x9551,x9553,x9554),f676(x9552,x9553,x9554)) % 186.05/186.64 [956]~E(x9561,x9562)+E(f676(x9563,x9561,x9564),f676(x9563,x9562,x9564)) % 186.05/186.64 [957]~E(x9571,x9572)+E(f676(x9573,x9574,x9571),f676(x9573,x9574,x9572)) % 186.05/186.64 [958]~E(x9581,x9582)+E(f765(x9581,x9583,x9584),f765(x9582,x9583,x9584)) % 186.05/186.64 [959]~E(x9591,x9592)+E(f765(x9593,x9591,x9594),f765(x9593,x9592,x9594)) % 186.05/186.64 [960]~E(x9601,x9602)+E(f765(x9603,x9604,x9601),f765(x9603,x9604,x9602)) % 186.05/186.64 [961]~E(x9611,x9612)+E(f684(x9611),f684(x9612)) % 186.05/186.64 [962]~E(x9621,x9622)+E(f206(x9621,x9623,x9624,x9625,x9626,x9627,x9628),f206(x9622,x9623,x9624,x9625,x9626,x9627,x9628)) % 186.05/186.64 [963]~E(x9631,x9632)+E(f206(x9633,x9631,x9634,x9635,x9636,x9637,x9638),f206(x9633,x9632,x9634,x9635,x9636,x9637,x9638)) % 186.05/186.64 [964]~E(x9641,x9642)+E(f206(x9643,x9644,x9641,x9645,x9646,x9647,x9648),f206(x9643,x9644,x9642,x9645,x9646,x9647,x9648)) % 186.05/186.64 [965]~E(x9651,x9652)+E(f206(x9653,x9654,x9655,x9651,x9656,x9657,x9658),f206(x9653,x9654,x9655,x9652,x9656,x9657,x9658)) % 186.05/186.64 [966]~E(x9661,x9662)+E(f206(x9663,x9664,x9665,x9666,x9661,x9667,x9668),f206(x9663,x9664,x9665,x9666,x9662,x9667,x9668)) % 186.05/186.64 [967]~E(x9671,x9672)+E(f206(x9673,x9674,x9675,x9676,x9677,x9671,x9678),f206(x9673,x9674,x9675,x9676,x9677,x9672,x9678)) % 186.05/186.64 [968]~E(x9681,x9682)+E(f206(x9683,x9684,x9685,x9686,x9687,x9688,x9681),f206(x9683,x9684,x9685,x9686,x9687,x9688,x9682)) % 186.05/186.64 [969]~E(x9691,x9692)+E(f90(x9691),f90(x9692)) % 186.05/186.64 [970]~E(x9701,x9702)+E(f36(x9701,x9703),f36(x9702,x9703)) % 186.05/186.64 [971]~E(x9711,x9712)+E(f36(x9713,x9711),f36(x9713,x9712)) % 186.05/186.64 [972]~E(x9721,x9722)+E(f461(x9721,x9723,x9724,x9725),f461(x9722,x9723,x9724,x9725)) % 186.05/186.64 [973]~E(x9731,x9732)+E(f461(x9733,x9731,x9734,x9735),f461(x9733,x9732,x9734,x9735)) % 186.05/186.64 [974]~E(x9741,x9742)+E(f461(x9743,x9744,x9741,x9745),f461(x9743,x9744,x9742,x9745)) % 186.05/186.64 [975]~E(x9751,x9752)+E(f461(x9753,x9754,x9755,x9751),f461(x9753,x9754,x9755,x9752)) % 186.05/186.64 [976]~E(x9761,x9762)+E(f487(x9761,x9763,x9764,x9765),f487(x9762,x9763,x9764,x9765)) % 186.05/186.64 [977]~E(x9771,x9772)+E(f487(x9773,x9771,x9774,x9775),f487(x9773,x9772,x9774,x9775)) % 186.05/186.64 [978]~E(x9781,x9782)+E(f487(x9783,x9784,x9781,x9785),f487(x9783,x9784,x9782,x9785)) % 186.05/186.64 [979]~E(x9791,x9792)+E(f487(x9793,x9794,x9795,x9791),f487(x9793,x9794,x9795,x9792)) % 186.05/186.64 [980]~E(x9801,x9802)+E(f539(x9801,x9803,x9804,x9805),f539(x9802,x9803,x9804,x9805)) % 186.05/186.64 [981]~E(x9811,x9812)+E(f539(x9813,x9811,x9814,x9815),f539(x9813,x9812,x9814,x9815)) % 186.05/186.64 [982]~E(x9821,x9822)+E(f539(x9823,x9824,x9821,x9825),f539(x9823,x9824,x9822,x9825)) % 186.05/186.64 [983]~E(x9831,x9832)+E(f539(x9833,x9834,x9835,x9831),f539(x9833,x9834,x9835,x9832)) % 186.05/186.64 [984]~E(x9841,x9842)+E(f486(x9841,x9843,x9844,x9845),f486(x9842,x9843,x9844,x9845)) % 186.05/186.64 [985]~E(x9851,x9852)+E(f486(x9853,x9851,x9854,x9855),f486(x9853,x9852,x9854,x9855)) % 186.05/186.64 [986]~E(x9861,x9862)+E(f486(x9863,x9864,x9861,x9865),f486(x9863,x9864,x9862,x9865)) % 186.05/186.64 [987]~E(x9871,x9872)+E(f486(x9873,x9874,x9875,x9871),f486(x9873,x9874,x9875,x9872)) % 186.05/186.64 [988]~E(x9881,x9882)+E(f534(x9881,x9883,x9884,x9885,x9886),f534(x9882,x9883,x9884,x9885,x9886)) % 186.05/186.64 [989]~E(x9891,x9892)+E(f534(x9893,x9891,x9894,x9895,x9896),f534(x9893,x9892,x9894,x9895,x9896)) % 186.05/186.64 [990]~E(x9901,x9902)+E(f534(x9903,x9904,x9901,x9905,x9906),f534(x9903,x9904,x9902,x9905,x9906)) % 186.05/186.64 [991]~E(x9911,x9912)+E(f534(x9913,x9914,x9915,x9911,x9916),f534(x9913,x9914,x9915,x9912,x9916)) % 186.05/186.64 [992]~E(x9921,x9922)+E(f534(x9923,x9924,x9925,x9926,x9921),f534(x9923,x9924,x9925,x9926,x9922)) % 186.05/186.64 [993]~E(x9931,x9932)+E(f429(x9931,x9933,x9934,x9935),f429(x9932,x9933,x9934,x9935)) % 186.05/186.64 [994]~E(x9941,x9942)+E(f429(x9943,x9941,x9944,x9945),f429(x9943,x9942,x9944,x9945)) % 186.05/186.64 [995]~E(x9951,x9952)+E(f429(x9953,x9954,x9951,x9955),f429(x9953,x9954,x9952,x9955)) % 186.05/186.64 [996]~E(x9961,x9962)+E(f429(x9963,x9964,x9965,x9961),f429(x9963,x9964,x9965,x9962)) % 186.05/186.64 [997]~E(x9971,x9972)+E(f711(x9971,x9973,x9974,x9975),f711(x9972,x9973,x9974,x9975)) % 186.05/186.64 [998]~E(x9981,x9982)+E(f711(x9983,x9981,x9984,x9985),f711(x9983,x9982,x9984,x9985)) % 186.05/186.64 [999]~E(x9991,x9992)+E(f711(x9993,x9994,x9991,x9995),f711(x9993,x9994,x9992,x9995)) % 186.05/186.64 [1000]~E(x10001,x10002)+E(f711(x10003,x10004,x10005,x10001),f711(x10003,x10004,x10005,x10002)) % 186.05/186.64 [1001]~E(x10011,x10012)+E(f699(x10011,x10013),f699(x10012,x10013)) % 186.05/186.64 [1002]~E(x10021,x10022)+E(f699(x10023,x10021),f699(x10023,x10022)) % 186.05/186.64 [1003]~E(x10031,x10032)+E(f457(x10031,x10033),f457(x10032,x10033)) % 186.05/186.64 [1004]~E(x10041,x10042)+E(f457(x10043,x10041),f457(x10043,x10042)) % 186.05/186.64 [1005]~E(x10051,x10052)+E(f631(x10051,x10053,x10054,x10055,x10056,x10057),f631(x10052,x10053,x10054,x10055,x10056,x10057)) % 186.05/186.64 [1006]~E(x10061,x10062)+E(f631(x10063,x10061,x10064,x10065,x10066,x10067),f631(x10063,x10062,x10064,x10065,x10066,x10067)) % 186.05/186.64 [1007]~E(x10071,x10072)+E(f631(x10073,x10074,x10071,x10075,x10076,x10077),f631(x10073,x10074,x10072,x10075,x10076,x10077)) % 186.05/186.64 [1008]~E(x10081,x10082)+E(f631(x10083,x10084,x10085,x10081,x10086,x10087),f631(x10083,x10084,x10085,x10082,x10086,x10087)) % 186.05/186.64 [1009]~E(x10091,x10092)+E(f631(x10093,x10094,x10095,x10096,x10091,x10097),f631(x10093,x10094,x10095,x10096,x10092,x10097)) % 186.05/186.64 [1010]~E(x10101,x10102)+E(f631(x10103,x10104,x10105,x10106,x10107,x10101),f631(x10103,x10104,x10105,x10106,x10107,x10102)) % 186.05/186.64 [1011]~E(x10111,x10112)+E(f310(x10111),f310(x10112)) % 186.05/186.64 [1012]~E(x10121,x10122)+E(f602(x10121,x10123),f602(x10122,x10123)) % 186.05/186.64 [1013]~E(x10131,x10132)+E(f602(x10133,x10131),f602(x10133,x10132)) % 186.05/186.64 [1014]~E(x10141,x10142)+E(f420(x10141,x10143,x10144),f420(x10142,x10143,x10144)) % 186.05/186.64 [1015]~E(x10151,x10152)+E(f420(x10153,x10151,x10154),f420(x10153,x10152,x10154)) % 186.05/186.64 [1016]~E(x10161,x10162)+E(f420(x10163,x10164,x10161),f420(x10163,x10164,x10162)) % 186.05/186.64 [1017]~E(x10171,x10172)+E(f203(x10171),f203(x10172)) % 186.05/186.64 [1018]~E(x10181,x10182)+E(f562(x10181,x10183,x10184,x10185),f562(x10182,x10183,x10184,x10185)) % 186.05/186.64 [1019]~E(x10191,x10192)+E(f562(x10193,x10191,x10194,x10195),f562(x10193,x10192,x10194,x10195)) % 186.05/186.64 [1020]~E(x10201,x10202)+E(f562(x10203,x10204,x10201,x10205),f562(x10203,x10204,x10202,x10205)) % 186.05/186.64 [1021]~E(x10211,x10212)+E(f562(x10213,x10214,x10215,x10211),f562(x10213,x10214,x10215,x10212)) % 186.05/186.64 [1022]~E(x10221,x10222)+E(f519(x10221,x10223,x10224,x10225),f519(x10222,x10223,x10224,x10225)) % 186.05/186.64 [1023]~E(x10231,x10232)+E(f519(x10233,x10231,x10234,x10235),f519(x10233,x10232,x10234,x10235)) % 186.05/186.64 [1024]~E(x10241,x10242)+E(f519(x10243,x10244,x10241,x10245),f519(x10243,x10244,x10242,x10245)) % 186.05/186.64 [1025]~E(x10251,x10252)+E(f519(x10253,x10254,x10255,x10251),f519(x10253,x10254,x10255,x10252)) % 186.05/186.64 [1026]~E(x10261,x10262)+E(f800(x10261,x10263),f800(x10262,x10263)) % 186.05/186.64 [1027]~E(x10271,x10272)+E(f800(x10273,x10271),f800(x10273,x10272)) % 186.05/186.64 [1028]~E(x10281,x10282)+E(f421(x10281,x10283,x10284),f421(x10282,x10283,x10284)) % 186.05/186.64 [1029]~E(x10291,x10292)+E(f421(x10293,x10291,x10294),f421(x10293,x10292,x10294)) % 186.05/186.64 [1030]~E(x10301,x10302)+E(f421(x10303,x10304,x10301),f421(x10303,x10304,x10302)) % 186.05/186.64 [1031]~E(x10311,x10312)+E(f538(x10311,x10313,x10314,x10315,x10316),f538(x10312,x10313,x10314,x10315,x10316)) % 186.05/186.64 [1032]~E(x10321,x10322)+E(f538(x10323,x10321,x10324,x10325,x10326),f538(x10323,x10322,x10324,x10325,x10326)) % 186.05/186.64 [1033]~E(x10331,x10332)+E(f538(x10333,x10334,x10331,x10335,x10336),f538(x10333,x10334,x10332,x10335,x10336)) % 186.05/186.64 [1034]~E(x10341,x10342)+E(f538(x10343,x10344,x10345,x10341,x10346),f538(x10343,x10344,x10345,x10342,x10346)) % 186.05/186.64 [1035]~E(x10351,x10352)+E(f538(x10353,x10354,x10355,x10356,x10351),f538(x10353,x10354,x10355,x10356,x10352)) % 186.05/186.64 [1036]~E(x10361,x10362)+E(f617(x10361,x10363),f617(x10362,x10363)) % 186.05/186.64 [1037]~E(x10371,x10372)+E(f617(x10373,x10371),f617(x10373,x10372)) % 186.05/186.64 [1038]~E(x10381,x10382)+E(f834(x10381,x10383,x10384),f834(x10382,x10383,x10384)) % 186.05/186.64 [1039]~E(x10391,x10392)+E(f834(x10393,x10391,x10394),f834(x10393,x10392,x10394)) % 186.05/186.64 [1040]~E(x10401,x10402)+E(f834(x10403,x10404,x10401),f834(x10403,x10404,x10402)) % 186.05/186.64 [1041]~E(x10411,x10412)+E(f372(x10411,x10413,x10414,x10415,x10416,x10417,x10418,x10419),f372(x10412,x10413,x10414,x10415,x10416,x10417,x10418,x10419)) % 186.05/186.64 [1042]~E(x10421,x10422)+E(f372(x10423,x10421,x10424,x10425,x10426,x10427,x10428,x10429),f372(x10423,x10422,x10424,x10425,x10426,x10427,x10428,x10429)) % 186.05/186.64 [1043]~E(x10431,x10432)+E(f372(x10433,x10434,x10431,x10435,x10436,x10437,x10438,x10439),f372(x10433,x10434,x10432,x10435,x10436,x10437,x10438,x10439)) % 186.05/186.64 [1044]~E(x10441,x10442)+E(f372(x10443,x10444,x10445,x10441,x10446,x10447,x10448,x10449),f372(x10443,x10444,x10445,x10442,x10446,x10447,x10448,x10449)) % 186.05/186.64 [1045]~E(x10451,x10452)+E(f372(x10453,x10454,x10455,x10456,x10451,x10457,x10458,x10459),f372(x10453,x10454,x10455,x10456,x10452,x10457,x10458,x10459)) % 186.05/186.64 [1046]~E(x10461,x10462)+E(f372(x10463,x10464,x10465,x10466,x10467,x10461,x10468,x10469),f372(x10463,x10464,x10465,x10466,x10467,x10462,x10468,x10469)) % 186.05/186.64 [1047]~E(x10471,x10472)+E(f372(x10473,x10474,x10475,x10476,x10477,x10478,x10471,x10479),f372(x10473,x10474,x10475,x10476,x10477,x10478,x10472,x10479)) % 186.05/186.64 [1048]~E(x10481,x10482)+E(f372(x10483,x10484,x10485,x10486,x10487,x10488,x10489,x10481),f372(x10483,x10484,x10485,x10486,x10487,x10488,x10489,x10482)) % 186.05/186.64 [1049]~E(x10491,x10492)+E(f610(x10491,x10493,x10494),f610(x10492,x10493,x10494)) % 186.05/186.64 [1050]~E(x10501,x10502)+E(f610(x10503,x10501,x10504),f610(x10503,x10502,x10504)) % 186.05/186.64 [1051]~E(x10511,x10512)+E(f610(x10513,x10514,x10511),f610(x10513,x10514,x10512)) % 186.05/186.64 [1052]~E(x10521,x10522)+E(f244(x10521,x10523,x10524),f244(x10522,x10523,x10524)) % 186.05/186.64 [1053]~E(x10531,x10532)+E(f244(x10533,x10531,x10534),f244(x10533,x10532,x10534)) % 186.05/186.64 [1054]~E(x10541,x10542)+E(f244(x10543,x10544,x10541),f244(x10543,x10544,x10542)) % 186.05/186.64 [1055]~E(x10551,x10552)+E(f611(x10551,x10553,x10554),f611(x10552,x10553,x10554)) % 186.05/186.64 [1056]~E(x10561,x10562)+E(f611(x10563,x10561,x10564),f611(x10563,x10562,x10564)) % 186.05/186.64 [1057]~E(x10571,x10572)+E(f611(x10573,x10574,x10571),f611(x10573,x10574,x10572)) % 186.05/186.64 [1058]~E(x10581,x10582)+E(f689(x10581,x10583,x10584,x10585),f689(x10582,x10583,x10584,x10585)) % 186.05/186.64 [1059]~E(x10591,x10592)+E(f689(x10593,x10591,x10594,x10595),f689(x10593,x10592,x10594,x10595)) % 186.05/186.64 [1060]~E(x10601,x10602)+E(f689(x10603,x10604,x10601,x10605),f689(x10603,x10604,x10602,x10605)) % 186.05/186.64 [1061]~E(x10611,x10612)+E(f689(x10613,x10614,x10615,x10611),f689(x10613,x10614,x10615,x10612)) % 186.05/186.64 [1062]~E(x10621,x10622)+E(f757(x10621,x10623,x10624,x10625),f757(x10622,x10623,x10624,x10625)) % 186.05/186.64 [1063]~E(x10631,x10632)+E(f757(x10633,x10631,x10634,x10635),f757(x10633,x10632,x10634,x10635)) % 186.05/186.64 [1064]~E(x10641,x10642)+E(f757(x10643,x10644,x10641,x10645),f757(x10643,x10644,x10642,x10645)) % 186.05/186.64 [1065]~E(x10651,x10652)+E(f757(x10653,x10654,x10655,x10651),f757(x10653,x10654,x10655,x10652)) % 186.05/186.64 [1066]~E(x10661,x10662)+E(f678(x10661,x10663,x10664),f678(x10662,x10663,x10664)) % 186.05/186.64 [1067]~E(x10671,x10672)+E(f678(x10673,x10671,x10674),f678(x10673,x10672,x10674)) % 186.05/186.64 [1068]~E(x10681,x10682)+E(f678(x10683,x10684,x10681),f678(x10683,x10684,x10682)) % 186.05/186.64 [1069]~E(x10691,x10692)+E(f754(x10691,x10693,x10694,x10695),f754(x10692,x10693,x10694,x10695)) % 186.05/186.64 [1070]~E(x10701,x10702)+E(f754(x10703,x10701,x10704,x10705),f754(x10703,x10702,x10704,x10705)) % 186.05/186.64 [1071]~E(x10711,x10712)+E(f754(x10713,x10714,x10711,x10715),f754(x10713,x10714,x10712,x10715)) % 186.05/186.64 [1072]~E(x10721,x10722)+E(f754(x10723,x10724,x10725,x10721),f754(x10723,x10724,x10725,x10722)) % 186.05/186.64 [1073]~E(x10731,x10732)+E(f437(x10731,x10733,x10734,x10735),f437(x10732,x10733,x10734,x10735)) % 186.05/186.64 [1074]~E(x10741,x10742)+E(f437(x10743,x10741,x10744,x10745),f437(x10743,x10742,x10744,x10745)) % 186.05/186.64 [1075]~E(x10751,x10752)+E(f437(x10753,x10754,x10751,x10755),f437(x10753,x10754,x10752,x10755)) % 186.05/186.64 [1076]~E(x10761,x10762)+E(f437(x10763,x10764,x10765,x10761),f437(x10763,x10764,x10765,x10762)) % 186.05/186.64 [1077]~E(x10771,x10772)+E(f79(x10771,x10773,x10774,x10775),f79(x10772,x10773,x10774,x10775)) % 186.05/186.64 [1078]~E(x10781,x10782)+E(f79(x10783,x10781,x10784,x10785),f79(x10783,x10782,x10784,x10785)) % 186.05/186.64 [1079]~E(x10791,x10792)+E(f79(x10793,x10794,x10791,x10795),f79(x10793,x10794,x10792,x10795)) % 186.05/186.64 [1080]~E(x10801,x10802)+E(f79(x10803,x10804,x10805,x10801),f79(x10803,x10804,x10805,x10802)) % 186.05/186.64 [1081]~E(x10811,x10812)+E(f200(x10811,x10813,x10814,x10815),f200(x10812,x10813,x10814,x10815)) % 186.05/186.64 [1082]~E(x10821,x10822)+E(f200(x10823,x10821,x10824,x10825),f200(x10823,x10822,x10824,x10825)) % 186.05/186.64 [1083]~E(x10831,x10832)+E(f200(x10833,x10834,x10831,x10835),f200(x10833,x10834,x10832,x10835)) % 186.05/186.64 [1084]~E(x10841,x10842)+E(f200(x10843,x10844,x10845,x10841),f200(x10843,x10844,x10845,x10842)) % 186.05/186.64 [1085]~E(x10851,x10852)+E(f409(x10851,x10853,x10854,x10855),f409(x10852,x10853,x10854,x10855)) % 186.05/186.64 [1086]~E(x10861,x10862)+E(f409(x10863,x10861,x10864,x10865),f409(x10863,x10862,x10864,x10865)) % 186.05/186.64 [1087]~E(x10871,x10872)+E(f409(x10873,x10874,x10871,x10875),f409(x10873,x10874,x10872,x10875)) % 186.05/186.64 [1088]~E(x10881,x10882)+E(f409(x10883,x10884,x10885,x10881),f409(x10883,x10884,x10885,x10882)) % 186.05/186.64 [1089]~E(x10891,x10892)+E(f805(x10891,x10893,x10894),f805(x10892,x10893,x10894)) % 186.05/186.64 [1090]~E(x10901,x10902)+E(f805(x10903,x10901,x10904),f805(x10903,x10902,x10904)) % 186.05/186.64 [1091]~E(x10911,x10912)+E(f805(x10913,x10914,x10911),f805(x10913,x10914,x10912)) % 186.05/186.64 [1092]~E(x10921,x10922)+E(f718(x10921,x10923,x10924,x10925,x10926),f718(x10922,x10923,x10924,x10925,x10926)) % 186.05/186.64 [1093]~E(x10931,x10932)+E(f718(x10933,x10931,x10934,x10935,x10936),f718(x10933,x10932,x10934,x10935,x10936)) % 186.05/186.64 [1094]~E(x10941,x10942)+E(f718(x10943,x10944,x10941,x10945,x10946),f718(x10943,x10944,x10942,x10945,x10946)) % 186.05/186.64 [1095]~E(x10951,x10952)+E(f718(x10953,x10954,x10955,x10951,x10956),f718(x10953,x10954,x10955,x10952,x10956)) % 186.05/186.64 [1096]~E(x10961,x10962)+E(f718(x10963,x10964,x10965,x10966,x10961),f718(x10963,x10964,x10965,x10966,x10962)) % 186.05/186.64 [1097]~E(x10971,x10972)+E(f381(x10971,x10973,x10974,x10975),f381(x10972,x10973,x10974,x10975)) % 186.05/186.64 [1098]~E(x10981,x10982)+E(f381(x10983,x10981,x10984,x10985),f381(x10983,x10982,x10984,x10985)) % 186.05/186.64 [1099]~E(x10991,x10992)+E(f381(x10993,x10994,x10991,x10995),f381(x10993,x10994,x10992,x10995)) % 186.05/186.64 [1100]~E(x11001,x11002)+E(f381(x11003,x11004,x11005,x11001),f381(x11003,x11004,x11005,x11002)) % 186.05/186.64 [1101]~E(x11011,x11012)+E(f272(x11011,x11013,x11014,x11015),f272(x11012,x11013,x11014,x11015)) % 186.05/186.64 [1102]~E(x11021,x11022)+E(f272(x11023,x11021,x11024,x11025),f272(x11023,x11022,x11024,x11025)) % 186.05/186.64 [1103]~E(x11031,x11032)+E(f272(x11033,x11034,x11031,x11035),f272(x11033,x11034,x11032,x11035)) % 186.05/186.64 [1104]~E(x11041,x11042)+E(f272(x11043,x11044,x11045,x11041),f272(x11043,x11044,x11045,x11042)) % 186.05/186.64 [1105]~E(x11051,x11052)+E(f223(x11051,x11053,x11054,x11055),f223(x11052,x11053,x11054,x11055)) % 186.05/186.64 [1106]~E(x11061,x11062)+E(f223(x11063,x11061,x11064,x11065),f223(x11063,x11062,x11064,x11065)) % 186.05/186.64 [1107]~E(x11071,x11072)+E(f223(x11073,x11074,x11071,x11075),f223(x11073,x11074,x11072,x11075)) % 186.05/186.64 [1108]~E(x11081,x11082)+E(f223(x11083,x11084,x11085,x11081),f223(x11083,x11084,x11085,x11082)) % 186.05/186.64 [1109]~E(x11091,x11092)+E(f815(x11091,x11093,x11094),f815(x11092,x11093,x11094)) % 186.05/186.64 [1110]~E(x11101,x11102)+E(f815(x11103,x11101,x11104),f815(x11103,x11102,x11104)) % 186.05/186.64 [1111]~E(x11111,x11112)+E(f815(x11113,x11114,x11111),f815(x11113,x11114,x11112)) % 186.05/186.64 [1112]~E(x11121,x11122)+E(f771(x11121,x11123,x11124),f771(x11122,x11123,x11124)) % 186.05/186.64 [1113]~E(x11131,x11132)+E(f771(x11133,x11131,x11134),f771(x11133,x11132,x11134)) % 186.05/186.64 [1114]~E(x11141,x11142)+E(f771(x11143,x11144,x11141),f771(x11143,x11144,x11142)) % 186.05/186.64 [1115]~E(x11151,x11152)+E(f746(x11151,x11153,x11154),f746(x11152,x11153,x11154)) % 186.05/186.64 [1116]~E(x11161,x11162)+E(f746(x11163,x11161,x11164),f746(x11163,x11162,x11164)) % 186.05/186.64 [1117]~E(x11171,x11172)+E(f746(x11173,x11174,x11171),f746(x11173,x11174,x11172)) % 186.05/186.64 [1118]~E(x11181,x11182)+E(f703(x11181,x11183,x11184,x11185,x11186),f703(x11182,x11183,x11184,x11185,x11186)) % 186.05/186.64 [1119]~E(x11191,x11192)+E(f703(x11193,x11191,x11194,x11195,x11196),f703(x11193,x11192,x11194,x11195,x11196)) % 186.05/186.64 [1120]~E(x11201,x11202)+E(f703(x11203,x11204,x11201,x11205,x11206),f703(x11203,x11204,x11202,x11205,x11206)) % 186.05/186.64 [1121]~E(x11211,x11212)+E(f703(x11213,x11214,x11215,x11211,x11216),f703(x11213,x11214,x11215,x11212,x11216)) % 186.05/186.64 [1122]~E(x11221,x11222)+E(f703(x11223,x11224,x11225,x11226,x11221),f703(x11223,x11224,x11225,x11226,x11222)) % 186.05/186.64 [1123]~E(x11231,x11232)+E(f260(x11231,x11233),f260(x11232,x11233)) % 186.05/186.64 [1124]~E(x11241,x11242)+E(f260(x11243,x11241),f260(x11243,x11242)) % 186.05/186.64 [1125]~E(x11251,x11252)+E(f567(x11251,x11253,x11254),f567(x11252,x11253,x11254)) % 186.05/186.64 [1126]~E(x11261,x11262)+E(f567(x11263,x11261,x11264),f567(x11263,x11262,x11264)) % 186.05/186.64 [1127]~E(x11271,x11272)+E(f567(x11273,x11274,x11271),f567(x11273,x11274,x11272)) % 186.05/186.64 [1128]~E(x11281,x11282)+E(f645(x11281,x11283,x11284,x11285,x11286),f645(x11282,x11283,x11284,x11285,x11286)) % 186.05/186.64 [1129]~E(x11291,x11292)+E(f645(x11293,x11291,x11294,x11295,x11296),f645(x11293,x11292,x11294,x11295,x11296)) % 186.05/186.64 [1130]~E(x11301,x11302)+E(f645(x11303,x11304,x11301,x11305,x11306),f645(x11303,x11304,x11302,x11305,x11306)) % 186.05/186.64 [1131]~E(x11311,x11312)+E(f645(x11313,x11314,x11315,x11311,x11316),f645(x11313,x11314,x11315,x11312,x11316)) % 186.05/186.64 [1132]~E(x11321,x11322)+E(f645(x11323,x11324,x11325,x11326,x11321),f645(x11323,x11324,x11325,x11326,x11322)) % 186.05/186.64 [1133]~E(x11331,x11332)+E(f53(x11331,x11333),f53(x11332,x11333)) % 186.05/186.64 [1134]~E(x11341,x11342)+E(f53(x11343,x11341),f53(x11343,x11342)) % 186.05/186.64 [1135]~E(x11351,x11352)+E(f607(x11351,x11353,x11354),f607(x11352,x11353,x11354)) % 186.05/186.64 [1136]~E(x11361,x11362)+E(f607(x11363,x11361,x11364),f607(x11363,x11362,x11364)) % 186.05/186.64 [1137]~E(x11371,x11372)+E(f607(x11373,x11374,x11371),f607(x11373,x11374,x11372)) % 186.05/186.64 [1138]~E(x11381,x11382)+E(f439(x11381,x11383,x11384,x11385),f439(x11382,x11383,x11384,x11385)) % 186.05/186.64 [1139]~E(x11391,x11392)+E(f439(x11393,x11391,x11394,x11395),f439(x11393,x11392,x11394,x11395)) % 186.05/186.64 [1140]~E(x11401,x11402)+E(f439(x11403,x11404,x11401,x11405),f439(x11403,x11404,x11402,x11405)) % 186.05/186.64 [1141]~E(x11411,x11412)+E(f439(x11413,x11414,x11415,x11411),f439(x11413,x11414,x11415,x11412)) % 186.05/186.64 [1142]~E(x11421,x11422)+E(f319(x11421,x11423,x11424,x11425,x11426),f319(x11422,x11423,x11424,x11425,x11426)) % 186.05/186.64 [1143]~E(x11431,x11432)+E(f319(x11433,x11431,x11434,x11435,x11436),f319(x11433,x11432,x11434,x11435,x11436)) % 186.05/186.64 [1144]~E(x11441,x11442)+E(f319(x11443,x11444,x11441,x11445,x11446),f319(x11443,x11444,x11442,x11445,x11446)) % 186.05/186.64 [1145]~E(x11451,x11452)+E(f319(x11453,x11454,x11455,x11451,x11456),f319(x11453,x11454,x11455,x11452,x11456)) % 186.05/186.64 [1146]~E(x11461,x11462)+E(f319(x11463,x11464,x11465,x11466,x11461),f319(x11463,x11464,x11465,x11466,x11462)) % 186.05/186.64 [1147]~E(x11471,x11472)+E(f375(x11471,x11473),f375(x11472,x11473)) % 186.05/186.64 [1148]~E(x11481,x11482)+E(f375(x11483,x11481),f375(x11483,x11482)) % 186.05/186.64 [1149]~E(x11491,x11492)+E(f762(x11491,x11493),f762(x11492,x11493)) % 186.05/186.64 [1150]~E(x11501,x11502)+E(f762(x11503,x11501),f762(x11503,x11502)) % 186.05/186.64 [1151]~E(x11511,x11512)+E(f371(x11511,x11513,x11514,x11515,x11516),f371(x11512,x11513,x11514,x11515,x11516)) % 186.05/186.64 [1152]~E(x11521,x11522)+E(f371(x11523,x11521,x11524,x11525,x11526),f371(x11523,x11522,x11524,x11525,x11526)) % 186.05/186.64 [1153]~E(x11531,x11532)+E(f371(x11533,x11534,x11531,x11535,x11536),f371(x11533,x11534,x11532,x11535,x11536)) % 186.05/186.64 [1154]~E(x11541,x11542)+E(f371(x11543,x11544,x11545,x11541,x11546),f371(x11543,x11544,x11545,x11542,x11546)) % 186.05/186.64 [1155]~E(x11551,x11552)+E(f371(x11553,x11554,x11555,x11556,x11551),f371(x11553,x11554,x11555,x11556,x11552)) % 186.05/186.64 [1156]~E(x11561,x11562)+E(f406(x11561,x11563,x11564),f406(x11562,x11563,x11564)) % 186.05/186.64 [1157]~E(x11571,x11572)+E(f406(x11573,x11571,x11574),f406(x11573,x11572,x11574)) % 186.05/186.64 [1158]~E(x11581,x11582)+E(f406(x11583,x11584,x11581),f406(x11583,x11584,x11582)) % 186.05/186.64 [1159]~E(x11591,x11592)+E(f193(x11591,x11593,x11594,x11595),f193(x11592,x11593,x11594,x11595)) % 186.05/186.64 [1160]~E(x11601,x11602)+E(f193(x11603,x11601,x11604,x11605),f193(x11603,x11602,x11604,x11605)) % 186.05/186.64 [1161]~E(x11611,x11612)+E(f193(x11613,x11614,x11611,x11615),f193(x11613,x11614,x11612,x11615)) % 186.05/186.64 [1162]~E(x11621,x11622)+E(f193(x11623,x11624,x11625,x11621),f193(x11623,x11624,x11625,x11622)) % 186.05/186.64 [1163]~E(x11631,x11632)+E(f280(x11631,x11633),f280(x11632,x11633)) % 186.05/186.64 [1164]~E(x11641,x11642)+E(f280(x11643,x11641),f280(x11643,x11642)) % 186.05/186.64 [1165]~E(x11651,x11652)+E(f671(x11651,x11653,x11654),f671(x11652,x11653,x11654)) % 186.05/186.64 [1166]~E(x11661,x11662)+E(f671(x11663,x11661,x11664),f671(x11663,x11662,x11664)) % 186.05/186.64 [1167]~E(x11671,x11672)+E(f671(x11673,x11674,x11671),f671(x11673,x11674,x11672)) % 186.05/186.64 [1168]~E(x11681,x11682)+E(f644(x11681,x11683,x11684,x11685,x11686),f644(x11682,x11683,x11684,x11685,x11686)) % 186.05/186.64 [1169]~E(x11691,x11692)+E(f644(x11693,x11691,x11694,x11695,x11696),f644(x11693,x11692,x11694,x11695,x11696)) % 186.05/186.64 [1170]~E(x11701,x11702)+E(f644(x11703,x11704,x11701,x11705,x11706),f644(x11703,x11704,x11702,x11705,x11706)) % 186.05/186.64 [1171]~E(x11711,x11712)+E(f644(x11713,x11714,x11715,x11711,x11716),f644(x11713,x11714,x11715,x11712,x11716)) % 186.05/186.64 [1172]~E(x11721,x11722)+E(f644(x11723,x11724,x11725,x11726,x11721),f644(x11723,x11724,x11725,x11726,x11722)) % 186.05/186.64 [1173]~E(x11731,x11732)+E(f476(x11731,x11733,x11734),f476(x11732,x11733,x11734)) % 186.05/186.64 [1174]~E(x11741,x11742)+E(f476(x11743,x11741,x11744),f476(x11743,x11742,x11744)) % 186.05/186.64 [1175]~E(x11751,x11752)+E(f476(x11753,x11754,x11751),f476(x11753,x11754,x11752)) % 186.05/186.64 [1176]~E(x11761,x11762)+E(f622(x11761,x11763,x11764),f622(x11762,x11763,x11764)) % 186.05/186.64 [1177]~E(x11771,x11772)+E(f622(x11773,x11771,x11774),f622(x11773,x11772,x11774)) % 186.05/186.64 [1178]~E(x11781,x11782)+E(f622(x11783,x11784,x11781),f622(x11783,x11784,x11782)) % 186.05/186.64 [1179]~E(x11791,x11792)+E(f400(x11791,x11793),f400(x11792,x11793)) % 186.05/186.64 [1180]~E(x11801,x11802)+E(f400(x11803,x11801),f400(x11803,x11802)) % 186.05/186.64 [1181]~E(x11811,x11812)+E(f748(x11811),f748(x11812)) % 186.05/186.64 [1182]~E(x11821,x11822)+E(f628(x11821,x11823,x11824),f628(x11822,x11823,x11824)) % 186.05/186.64 [1183]~E(x11831,x11832)+E(f628(x11833,x11831,x11834),f628(x11833,x11832,x11834)) % 186.05/186.64 [1184]~E(x11841,x11842)+E(f628(x11843,x11844,x11841),f628(x11843,x11844,x11842)) % 186.05/186.64 [1185]~E(x11851,x11852)+E(f581(x11851,x11853),f581(x11852,x11853)) % 186.05/186.64 [1186]~E(x11861,x11862)+E(f581(x11863,x11861),f581(x11863,x11862)) % 186.05/186.64 [1187]~E(x11871,x11872)+E(f659(x11871,x11873,x11874,x11875,x11876),f659(x11872,x11873,x11874,x11875,x11876)) % 186.05/186.64 [1188]~E(x11881,x11882)+E(f659(x11883,x11881,x11884,x11885,x11886),f659(x11883,x11882,x11884,x11885,x11886)) % 186.05/186.64 [1189]~E(x11891,x11892)+E(f659(x11893,x11894,x11891,x11895,x11896),f659(x11893,x11894,x11892,x11895,x11896)) % 186.05/186.64 [1190]~E(x11901,x11902)+E(f659(x11903,x11904,x11905,x11901,x11906),f659(x11903,x11904,x11905,x11902,x11906)) % 186.05/186.64 [1191]~E(x11911,x11912)+E(f659(x11913,x11914,x11915,x11916,x11911),f659(x11913,x11914,x11915,x11916,x11912)) % 186.05/186.64 [1192]~E(x11921,x11922)+E(f234(x11921,x11923),f234(x11922,x11923)) % 186.05/186.64 [1193]~E(x11931,x11932)+E(f234(x11933,x11931),f234(x11933,x11932)) % 186.05/186.64 [1194]~E(x11941,x11942)+E(f767(x11941,x11943,x11944),f767(x11942,x11943,x11944)) % 186.05/186.64 [1195]~E(x11951,x11952)+E(f767(x11953,x11951,x11954),f767(x11953,x11952,x11954)) % 186.05/186.64 [1196]~E(x11961,x11962)+E(f767(x11963,x11964,x11961),f767(x11963,x11964,x11962)) % 186.05/186.64 [1197]~E(x11971,x11972)+E(f475(x11971,x11973,x11974),f475(x11972,x11973,x11974)) % 186.05/186.64 [1198]~E(x11981,x11982)+E(f475(x11983,x11981,x11984),f475(x11983,x11982,x11984)) % 186.05/186.64 [1199]~E(x11991,x11992)+E(f475(x11993,x11994,x11991),f475(x11993,x11994,x11992)) % 186.05/186.64 [1200]~E(x12001,x12002)+E(f21(x12001,x12003,x12004,x12005),f21(x12002,x12003,x12004,x12005)) % 186.05/186.64 [1201]~E(x12011,x12012)+E(f21(x12013,x12011,x12014,x12015),f21(x12013,x12012,x12014,x12015)) % 186.05/186.64 [1202]~E(x12021,x12022)+E(f21(x12023,x12024,x12021,x12025),f21(x12023,x12024,x12022,x12025)) % 186.05/186.64 [1203]~E(x12031,x12032)+E(f21(x12033,x12034,x12035,x12031),f21(x12033,x12034,x12035,x12032)) % 186.05/186.64 [1204]~E(x12041,x12042)+E(f817(x12041,x12043,x12044),f817(x12042,x12043,x12044)) % 186.05/186.64 [1205]~E(x12051,x12052)+E(f817(x12053,x12051,x12054),f817(x12053,x12052,x12054)) % 186.05/186.64 [1206]~E(x12061,x12062)+E(f817(x12063,x12064,x12061),f817(x12063,x12064,x12062)) % 186.05/186.64 [1207]~E(x12071,x12072)+E(f514(x12071,x12073,x12074,x12075,x12076),f514(x12072,x12073,x12074,x12075,x12076)) % 186.05/186.64 [1208]~E(x12081,x12082)+E(f514(x12083,x12081,x12084,x12085,x12086),f514(x12083,x12082,x12084,x12085,x12086)) % 186.05/186.64 [1209]~E(x12091,x12092)+E(f514(x12093,x12094,x12091,x12095,x12096),f514(x12093,x12094,x12092,x12095,x12096)) % 186.05/186.64 [1210]~E(x12101,x12102)+E(f514(x12103,x12104,x12105,x12101,x12106),f514(x12103,x12104,x12105,x12102,x12106)) % 186.05/186.64 [1211]~E(x12111,x12112)+E(f514(x12113,x12114,x12115,x12116,x12111),f514(x12113,x12114,x12115,x12116,x12112)) % 186.05/186.64 [1212]~E(x12121,x12122)+E(f528(x12121,x12123,x12124,x12125),f528(x12122,x12123,x12124,x12125)) % 186.05/186.64 [1213]~E(x12131,x12132)+E(f528(x12133,x12131,x12134,x12135),f528(x12133,x12132,x12134,x12135)) % 186.05/186.64 [1214]~E(x12141,x12142)+E(f528(x12143,x12144,x12141,x12145),f528(x12143,x12144,x12142,x12145)) % 186.05/186.64 [1215]~E(x12151,x12152)+E(f528(x12153,x12154,x12155,x12151),f528(x12153,x12154,x12155,x12152)) % 186.05/186.64 [1216]~E(x12161,x12162)+E(f426(x12161,x12163,x12164,x12165,x12166,x12167,x12168,x12169,x121610),f426(x12162,x12163,x12164,x12165,x12166,x12167,x12168,x12169,x121610)) % 186.05/186.64 [1217]~E(x12171,x12172)+E(f426(x12173,x12171,x12174,x12175,x12176,x12177,x12178,x12179,x121710),f426(x12173,x12172,x12174,x12175,x12176,x12177,x12178,x12179,x121710)) % 186.05/186.64 [1218]~E(x12181,x12182)+E(f426(x12183,x12184,x12181,x12185,x12186,x12187,x12188,x12189,x121810),f426(x12183,x12184,x12182,x12185,x12186,x12187,x12188,x12189,x121810)) % 186.05/186.64 [1219]~E(x12191,x12192)+E(f426(x12193,x12194,x12195,x12191,x12196,x12197,x12198,x12199,x121910),f426(x12193,x12194,x12195,x12192,x12196,x12197,x12198,x12199,x121910)) % 186.05/186.64 [1220]~E(x12201,x12202)+E(f426(x12203,x12204,x12205,x12206,x12201,x12207,x12208,x12209,x122010),f426(x12203,x12204,x12205,x12206,x12202,x12207,x12208,x12209,x122010)) % 186.05/186.64 [1221]~E(x12211,x12212)+E(f426(x12213,x12214,x12215,x12216,x12217,x12211,x12218,x12219,x122110),f426(x12213,x12214,x12215,x12216,x12217,x12212,x12218,x12219,x122110)) % 186.05/186.64 [1222]~E(x12221,x12222)+E(f426(x12223,x12224,x12225,x12226,x12227,x12228,x12221,x12229,x122210),f426(x12223,x12224,x12225,x12226,x12227,x12228,x12222,x12229,x122210)) % 186.05/186.64 [1223]~E(x12231,x12232)+E(f426(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12231,x122310),f426(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12232,x122310)) % 186.05/186.64 [1224]~E(x12241,x12242)+E(f426(x12243,x12244,x12245,x12246,x12247,x12248,x12249,x122410,x12241),f426(x12243,x12244,x12245,x12246,x12247,x12248,x12249,x122410,x12242)) % 186.05/186.64 [1225]~E(x12251,x12252)+E(f569(x12251,x12253,x12254,x12255,x12256),f569(x12252,x12253,x12254,x12255,x12256)) % 186.05/186.64 [1226]~E(x12261,x12262)+E(f569(x12263,x12261,x12264,x12265,x12266),f569(x12263,x12262,x12264,x12265,x12266)) % 186.05/186.64 [1227]~E(x12271,x12272)+E(f569(x12273,x12274,x12271,x12275,x12276),f569(x12273,x12274,x12272,x12275,x12276)) % 186.05/186.64 [1228]~E(x12281,x12282)+E(f569(x12283,x12284,x12285,x12281,x12286),f569(x12283,x12284,x12285,x12282,x12286)) % 186.05/186.64 [1229]~E(x12291,x12292)+E(f569(x12293,x12294,x12295,x12296,x12291),f569(x12293,x12294,x12295,x12296,x12292)) % 186.05/186.64 [1230]~E(x12301,x12302)+E(f481(x12301,x12303,x12304,x12305,x12306),f481(x12302,x12303,x12304,x12305,x12306)) % 186.05/186.64 [1231]~E(x12311,x12312)+E(f481(x12313,x12311,x12314,x12315,x12316),f481(x12313,x12312,x12314,x12315,x12316)) % 186.05/186.64 [1232]~E(x12321,x12322)+E(f481(x12323,x12324,x12321,x12325,x12326),f481(x12323,x12324,x12322,x12325,x12326)) % 186.05/186.64 [1233]~E(x12331,x12332)+E(f481(x12333,x12334,x12335,x12331,x12336),f481(x12333,x12334,x12335,x12332,x12336)) % 186.05/186.64 [1234]~E(x12341,x12342)+E(f481(x12343,x12344,x12345,x12346,x12341),f481(x12343,x12344,x12345,x12346,x12342)) % 186.05/186.64 [1235]~E(x12351,x12352)+E(f702(x12351,x12353,x12354,x12355),f702(x12352,x12353,x12354,x12355)) % 186.05/186.64 [1236]~E(x12361,x12362)+E(f702(x12363,x12361,x12364,x12365),f702(x12363,x12362,x12364,x12365)) % 186.05/186.64 [1237]~E(x12371,x12372)+E(f702(x12373,x12374,x12371,x12375),f702(x12373,x12374,x12372,x12375)) % 186.05/186.64 [1238]~E(x12381,x12382)+E(f702(x12383,x12384,x12385,x12381),f702(x12383,x12384,x12385,x12382)) % 186.05/186.64 [1239]~E(x12391,x12392)+E(f360(x12391,x12393,x12394,x12395,x12396),f360(x12392,x12393,x12394,x12395,x12396)) % 186.05/186.64 [1240]~E(x12401,x12402)+E(f360(x12403,x12401,x12404,x12405,x12406),f360(x12403,x12402,x12404,x12405,x12406)) % 186.05/186.64 [1241]~E(x12411,x12412)+E(f360(x12413,x12414,x12411,x12415,x12416),f360(x12413,x12414,x12412,x12415,x12416)) % 186.05/186.64 [1242]~E(x12421,x12422)+E(f360(x12423,x12424,x12425,x12421,x12426),f360(x12423,x12424,x12425,x12422,x12426)) % 186.05/186.64 [1243]~E(x12431,x12432)+E(f360(x12433,x12434,x12435,x12436,x12431),f360(x12433,x12434,x12435,x12436,x12432)) % 186.05/186.64 [1244]~E(x12441,x12442)+E(f513(x12441,x12443,x12444,x12445,x12446),f513(x12442,x12443,x12444,x12445,x12446)) % 186.05/186.64 [1245]~E(x12451,x12452)+E(f513(x12453,x12451,x12454,x12455,x12456),f513(x12453,x12452,x12454,x12455,x12456)) % 186.05/186.64 [1246]~E(x12461,x12462)+E(f513(x12463,x12464,x12461,x12465,x12466),f513(x12463,x12464,x12462,x12465,x12466)) % 186.05/186.64 [1247]~E(x12471,x12472)+E(f513(x12473,x12474,x12475,x12471,x12476),f513(x12473,x12474,x12475,x12472,x12476)) % 186.05/186.64 [1248]~E(x12481,x12482)+E(f513(x12483,x12484,x12485,x12486,x12481),f513(x12483,x12484,x12485,x12486,x12482)) % 186.05/186.64 [1249]~E(x12491,x12492)+E(f593(x12491,x12493,x12494,x12495),f593(x12492,x12493,x12494,x12495)) % 186.05/186.64 [1250]~E(x12501,x12502)+E(f593(x12503,x12501,x12504,x12505),f593(x12503,x12502,x12504,x12505)) % 186.05/186.64 [1251]~E(x12511,x12512)+E(f593(x12513,x12514,x12511,x12515),f593(x12513,x12514,x12512,x12515)) % 186.05/186.64 [1252]~E(x12521,x12522)+E(f593(x12523,x12524,x12525,x12521),f593(x12523,x12524,x12525,x12522)) % 186.05/186.64 [1253]~E(x12531,x12532)+E(f48(x12531),f48(x12532)) % 186.05/186.64 [1254]~E(x12541,x12542)+E(f576(x12541,x12543,x12544,x12545,x12546),f576(x12542,x12543,x12544,x12545,x12546)) % 186.05/186.64 [1255]~E(x12551,x12552)+E(f576(x12553,x12551,x12554,x12555,x12556),f576(x12553,x12552,x12554,x12555,x12556)) % 186.05/186.64 [1256]~E(x12561,x12562)+E(f576(x12563,x12564,x12561,x12565,x12566),f576(x12563,x12564,x12562,x12565,x12566)) % 186.05/186.64 [1257]~E(x12571,x12572)+E(f576(x12573,x12574,x12575,x12571,x12576),f576(x12573,x12574,x12575,x12572,x12576)) % 186.05/186.64 [1258]~E(x12581,x12582)+E(f576(x12583,x12584,x12585,x12586,x12581),f576(x12583,x12584,x12585,x12586,x12582)) % 186.05/186.64 [1259]~E(x12591,x12592)+E(f819(x12591,x12593,x12594,x12595),f819(x12592,x12593,x12594,x12595)) % 186.05/186.64 [1260]~E(x12601,x12602)+E(f819(x12603,x12601,x12604,x12605),f819(x12603,x12602,x12604,x12605)) % 186.05/186.64 [1261]~E(x12611,x12612)+E(f819(x12613,x12614,x12611,x12615),f819(x12613,x12614,x12612,x12615)) % 186.05/186.64 [1262]~E(x12621,x12622)+E(f819(x12623,x12624,x12625,x12621),f819(x12623,x12624,x12625,x12622)) % 186.05/186.64 [1263]~E(x12631,x12632)+E(f416(x12631,x12633,x12634,x12635),f416(x12632,x12633,x12634,x12635)) % 186.05/186.64 [1264]~E(x12641,x12642)+E(f416(x12643,x12641,x12644,x12645),f416(x12643,x12642,x12644,x12645)) % 186.05/186.64 [1265]~E(x12651,x12652)+E(f416(x12653,x12654,x12651,x12655),f416(x12653,x12654,x12652,x12655)) % 186.05/186.64 [1266]~E(x12661,x12662)+E(f416(x12663,x12664,x12665,x12661),f416(x12663,x12664,x12665,x12662)) % 186.05/186.64 [1267]~E(x12671,x12672)+E(f820(x12671,x12673,x12674),f820(x12672,x12673,x12674)) % 186.05/186.64 [1268]~E(x12681,x12682)+E(f820(x12683,x12681,x12684),f820(x12683,x12682,x12684)) % 186.05/186.64 [1269]~E(x12691,x12692)+E(f820(x12693,x12694,x12691),f820(x12693,x12694,x12692)) % 186.05/186.64 [1270]~E(x12701,x12702)+E(f537(x12701,x12703,x12704,x12705),f537(x12702,x12703,x12704,x12705)) % 186.05/186.64 [1271]~E(x12711,x12712)+E(f537(x12713,x12711,x12714,x12715),f537(x12713,x12712,x12714,x12715)) % 186.05/186.64 [1272]~E(x12721,x12722)+E(f537(x12723,x12724,x12721,x12725),f537(x12723,x12724,x12722,x12725)) % 186.05/186.64 [1273]~E(x12731,x12732)+E(f537(x12733,x12734,x12735,x12731),f537(x12733,x12734,x12735,x12732)) % 186.05/186.64 [1274]~E(x12741,x12742)+E(f701(x12741,x12743,x12744,x12745),f701(x12742,x12743,x12744,x12745)) % 186.05/186.64 [1275]~E(x12751,x12752)+E(f701(x12753,x12751,x12754,x12755),f701(x12753,x12752,x12754,x12755)) % 186.05/186.64 [1276]~E(x12761,x12762)+E(f701(x12763,x12764,x12761,x12765),f701(x12763,x12764,x12762,x12765)) % 186.05/186.64 [1277]~E(x12771,x12772)+E(f701(x12773,x12774,x12775,x12771),f701(x12773,x12774,x12775,x12772)) % 186.05/186.64 [1278]~E(x12781,x12782)+E(f512(x12781,x12783,x12784,x12785,x12786),f512(x12782,x12783,x12784,x12785,x12786)) % 186.05/186.64 [1279]~E(x12791,x12792)+E(f512(x12793,x12791,x12794,x12795,x12796),f512(x12793,x12792,x12794,x12795,x12796)) % 186.05/186.64 [1280]~E(x12801,x12802)+E(f512(x12803,x12804,x12801,x12805,x12806),f512(x12803,x12804,x12802,x12805,x12806)) % 186.05/186.64 [1281]~E(x12811,x12812)+E(f512(x12813,x12814,x12815,x12811,x12816),f512(x12813,x12814,x12815,x12812,x12816)) % 186.05/186.64 [1282]~E(x12821,x12822)+E(f512(x12823,x12824,x12825,x12826,x12821),f512(x12823,x12824,x12825,x12826,x12822)) % 186.05/186.64 [1283]~E(x12831,x12832)+E(f822(x12831,x12833,x12834),f822(x12832,x12833,x12834)) % 186.05/186.64 [1284]~E(x12841,x12842)+E(f822(x12843,x12841,x12844),f822(x12843,x12842,x12844)) % 186.05/186.64 [1285]~E(x12851,x12852)+E(f822(x12853,x12854,x12851),f822(x12853,x12854,x12852)) % 186.05/186.64 [1286]~E(x12861,x12862)+E(f594(x12861,x12863,x12864,x12865),f594(x12862,x12863,x12864,x12865)) % 186.05/186.64 [1287]~E(x12871,x12872)+E(f594(x12873,x12871,x12874,x12875),f594(x12873,x12872,x12874,x12875)) % 186.05/186.64 [1288]~E(x12881,x12882)+E(f594(x12883,x12884,x12881,x12885),f594(x12883,x12884,x12882,x12885)) % 186.05/186.64 [1289]~E(x12891,x12892)+E(f594(x12893,x12894,x12895,x12891),f594(x12893,x12894,x12895,x12892)) % 186.05/186.64 [1290]~E(x12901,x12902)+E(f818(x12901,x12903,x12904,x12905),f818(x12902,x12903,x12904,x12905)) % 186.05/186.64 [1291]~E(x12911,x12912)+E(f818(x12913,x12911,x12914,x12915),f818(x12913,x12912,x12914,x12915)) % 186.05/186.64 [1292]~E(x12921,x12922)+E(f818(x12923,x12924,x12921,x12925),f818(x12923,x12924,x12922,x12925)) % 186.05/186.64 [1293]~E(x12931,x12932)+E(f818(x12933,x12934,x12935,x12931),f818(x12933,x12934,x12935,x12932)) % 186.05/186.64 [1294]~E(x12941,x12942)+E(f761(x12941,x12943),f761(x12942,x12943)) % 186.05/186.64 [1295]~E(x12951,x12952)+E(f761(x12953,x12951),f761(x12953,x12952)) % 186.05/186.64 [1296]~E(x12961,x12962)+E(f267(x12961,x12963),f267(x12962,x12963)) % 186.05/186.64 [1297]~E(x12971,x12972)+E(f267(x12973,x12971),f267(x12973,x12972)) % 186.05/186.64 [1298]~E(x12981,x12982)+E(f225(x12981,x12983,x12984,x12985),f225(x12982,x12983,x12984,x12985)) % 186.05/186.64 [1299]~E(x12991,x12992)+E(f225(x12993,x12991,x12994,x12995),f225(x12993,x12992,x12994,x12995)) % 186.05/186.64 [1300]~E(x13001,x13002)+E(f225(x13003,x13004,x13001,x13005),f225(x13003,x13004,x13002,x13005)) % 186.05/186.64 [1301]~E(x13011,x13012)+E(f225(x13013,x13014,x13015,x13011),f225(x13013,x13014,x13015,x13012)) % 186.05/186.64 [1302]~E(x13021,x13022)+E(f414(x13021,x13023,x13024),f414(x13022,x13023,x13024)) % 186.05/186.64 [1303]~E(x13031,x13032)+E(f414(x13033,x13031,x13034),f414(x13033,x13032,x13034)) % 186.05/186.64 [1304]~E(x13041,x13042)+E(f414(x13043,x13044,x13041),f414(x13043,x13044,x13042)) % 186.05/186.64 [1305]~E(x13051,x13052)+E(f814(x13051,x13053,x13054),f814(x13052,x13053,x13054)) % 186.05/186.64 [1306]~E(x13061,x13062)+E(f814(x13063,x13061,x13064),f814(x13063,x13062,x13064)) % 186.05/186.64 [1307]~E(x13071,x13072)+E(f814(x13073,x13074,x13071),f814(x13073,x13074,x13072)) % 186.05/186.64 [1308]~E(x13081,x13082)+E(f789(x13081,x13083),f789(x13082,x13083)) % 186.05/186.64 [1309]~E(x13091,x13092)+E(f789(x13093,x13091),f789(x13093,x13092)) % 186.05/186.64 [1310]~E(x13101,x13102)+E(f541(x13101,x13103,x13104,x13105,x13106,x13107),f541(x13102,x13103,x13104,x13105,x13106,x13107)) % 186.05/186.64 [1311]~E(x13111,x13112)+E(f541(x13113,x13111,x13114,x13115,x13116,x13117),f541(x13113,x13112,x13114,x13115,x13116,x13117)) % 186.05/186.64 [1312]~E(x13121,x13122)+E(f541(x13123,x13124,x13121,x13125,x13126,x13127),f541(x13123,x13124,x13122,x13125,x13126,x13127)) % 186.05/186.64 [1313]~E(x13131,x13132)+E(f541(x13133,x13134,x13135,x13131,x13136,x13137),f541(x13133,x13134,x13135,x13132,x13136,x13137)) % 186.05/186.64 [1314]~E(x13141,x13142)+E(f541(x13143,x13144,x13145,x13146,x13141,x13147),f541(x13143,x13144,x13145,x13146,x13142,x13147)) % 186.05/186.64 [1315]~E(x13151,x13152)+E(f541(x13153,x13154,x13155,x13156,x13157,x13151),f541(x13153,x13154,x13155,x13156,x13157,x13152)) % 186.05/186.64 [1316]~E(x13161,x13162)+E(f209(x13161,x13163),f209(x13162,x13163)) % 186.05/186.64 [1317]~E(x13171,x13172)+E(f209(x13173,x13171),f209(x13173,x13172)) % 186.05/186.64 [1318]~E(x13181,x13182)+E(f390(x13181,x13183,x13184,x13185,x13186),f390(x13182,x13183,x13184,x13185,x13186)) % 186.05/186.64 [1319]~E(x13191,x13192)+E(f390(x13193,x13191,x13194,x13195,x13196),f390(x13193,x13192,x13194,x13195,x13196)) % 186.05/186.64 [1320]~E(x13201,x13202)+E(f390(x13203,x13204,x13201,x13205,x13206),f390(x13203,x13204,x13202,x13205,x13206)) % 186.05/186.64 [1321]~E(x13211,x13212)+E(f390(x13213,x13214,x13215,x13211,x13216),f390(x13213,x13214,x13215,x13212,x13216)) % 186.05/186.64 [1322]~E(x13221,x13222)+E(f390(x13223,x13224,x13225,x13226,x13221),f390(x13223,x13224,x13225,x13226,x13222)) % 186.05/186.64 [1323]~E(x13231,x13232)+E(f641(x13231,x13233,x13234),f641(x13232,x13233,x13234)) % 186.05/186.64 [1324]~E(x13241,x13242)+E(f641(x13243,x13241,x13244),f641(x13243,x13242,x13244)) % 186.05/186.64 [1325]~E(x13251,x13252)+E(f641(x13253,x13254,x13251),f641(x13253,x13254,x13252)) % 186.05/186.64 [1326]~E(x13261,x13262)+E(f744(x13261,x13263,x13264,x13265),f744(x13262,x13263,x13264,x13265)) % 186.05/186.64 [1327]~E(x13271,x13272)+E(f744(x13273,x13271,x13274,x13275),f744(x13273,x13272,x13274,x13275)) % 186.05/186.64 [1328]~E(x13281,x13282)+E(f744(x13283,x13284,x13281,x13285),f744(x13283,x13284,x13282,x13285)) % 186.05/186.64 [1329]~E(x13291,x13292)+E(f744(x13293,x13294,x13295,x13291),f744(x13293,x13294,x13295,x13292)) % 186.05/186.64 [1330]~E(x13301,x13302)+E(f351(x13301,x13303),f351(x13302,x13303)) % 186.05/186.64 [1331]~E(x13311,x13312)+E(f351(x13313,x13311),f351(x13313,x13312)) % 186.05/186.64 [1332]~E(x13321,x13322)+E(f591(x13321,x13323,x13324,x13325),f591(x13322,x13323,x13324,x13325)) % 186.05/186.64 [1333]~E(x13331,x13332)+E(f591(x13333,x13331,x13334,x13335),f591(x13333,x13332,x13334,x13335)) % 186.05/186.64 [1334]~E(x13341,x13342)+E(f591(x13343,x13344,x13341,x13345),f591(x13343,x13344,x13342,x13345)) % 186.05/186.64 [1335]~E(x13351,x13352)+E(f591(x13353,x13354,x13355,x13351),f591(x13353,x13354,x13355,x13352)) % 186.05/186.64 [1336]~E(x13361,x13362)+E(f446(x13361,x13363),f446(x13362,x13363)) % 186.05/186.64 [1337]~E(x13371,x13372)+E(f446(x13373,x13371),f446(x13373,x13372)) % 186.05/186.64 [1338]~E(x13381,x13382)+E(f555(x13381,x13383,x13384),f555(x13382,x13383,x13384)) % 186.05/186.64 [1339]~E(x13391,x13392)+E(f555(x13393,x13391,x13394),f555(x13393,x13392,x13394)) % 186.05/186.64 [1340]~E(x13401,x13402)+E(f555(x13403,x13404,x13401),f555(x13403,x13404,x13402)) % 186.05/186.64 [1341]~E(x13411,x13412)+E(f535(x13411,x13413,x13414,x13415,x13416,x13417,x13418,x13419),f535(x13412,x13413,x13414,x13415,x13416,x13417,x13418,x13419)) % 186.05/186.64 [1342]~E(x13421,x13422)+E(f535(x13423,x13421,x13424,x13425,x13426,x13427,x13428,x13429),f535(x13423,x13422,x13424,x13425,x13426,x13427,x13428,x13429)) % 186.05/186.64 [1343]~E(x13431,x13432)+E(f535(x13433,x13434,x13431,x13435,x13436,x13437,x13438,x13439),f535(x13433,x13434,x13432,x13435,x13436,x13437,x13438,x13439)) % 186.05/186.64 [1344]~E(x13441,x13442)+E(f535(x13443,x13444,x13445,x13441,x13446,x13447,x13448,x13449),f535(x13443,x13444,x13445,x13442,x13446,x13447,x13448,x13449)) % 186.05/186.64 [1345]~E(x13451,x13452)+E(f535(x13453,x13454,x13455,x13456,x13451,x13457,x13458,x13459),f535(x13453,x13454,x13455,x13456,x13452,x13457,x13458,x13459)) % 186.05/186.64 [1346]~E(x13461,x13462)+E(f535(x13463,x13464,x13465,x13466,x13467,x13461,x13468,x13469),f535(x13463,x13464,x13465,x13466,x13467,x13462,x13468,x13469)) % 186.05/186.64 [1347]~E(x13471,x13472)+E(f535(x13473,x13474,x13475,x13476,x13477,x13478,x13471,x13479),f535(x13473,x13474,x13475,x13476,x13477,x13478,x13472,x13479)) % 186.05/186.64 [1348]~E(x13481,x13482)+E(f535(x13483,x13484,x13485,x13486,x13487,x13488,x13489,x13481),f535(x13483,x13484,x13485,x13486,x13487,x13488,x13489,x13482)) % 186.05/186.64 [1349]~E(x13491,x13492)+E(f755(x13491,x13493,x13494),f755(x13492,x13493,x13494)) % 186.05/186.64 [1350]~E(x13501,x13502)+E(f755(x13503,x13501,x13504),f755(x13503,x13502,x13504)) % 186.05/186.64 [1351]~E(x13511,x13512)+E(f755(x13513,x13514,x13511),f755(x13513,x13514,x13512)) % 186.05/186.64 [1352]~E(x13521,x13522)+E(f466(x13521,x13523,x13524),f466(x13522,x13523,x13524)) % 186.05/186.64 [1353]~E(x13531,x13532)+E(f466(x13533,x13531,x13534),f466(x13533,x13532,x13534)) % 186.05/186.64 [1354]~E(x13541,x13542)+E(f466(x13543,x13544,x13541),f466(x13543,x13544,x13542)) % 186.05/186.64 [1355]~E(x13551,x13552)+E(f394(x13551,x13553,x13554),f394(x13552,x13553,x13554)) % 186.05/186.64 [1356]~E(x13561,x13562)+E(f394(x13563,x13561,x13564),f394(x13563,x13562,x13564)) % 186.05/186.64 [1357]~E(x13571,x13572)+E(f394(x13573,x13574,x13571),f394(x13573,x13574,x13572)) % 186.05/186.64 [1358]~E(x13581,x13582)+E(f646(x13581,x13583,x13584,x13585,x13586),f646(x13582,x13583,x13584,x13585,x13586)) % 186.05/186.64 [1359]~E(x13591,x13592)+E(f646(x13593,x13591,x13594,x13595,x13596),f646(x13593,x13592,x13594,x13595,x13596)) % 186.05/186.64 [1360]~E(x13601,x13602)+E(f646(x13603,x13604,x13601,x13605,x13606),f646(x13603,x13604,x13602,x13605,x13606)) % 186.05/186.64 [1361]~E(x13611,x13612)+E(f646(x13613,x13614,x13615,x13611,x13616),f646(x13613,x13614,x13615,x13612,x13616)) % 186.05/186.64 [1362]~E(x13621,x13622)+E(f646(x13623,x13624,x13625,x13626,x13621),f646(x13623,x13624,x13625,x13626,x13622)) % 186.05/186.64 [1363]~E(x13631,x13632)+E(f366(x13631,x13633,x13634,x13635,x13636),f366(x13632,x13633,x13634,x13635,x13636)) % 186.05/186.64 [1364]~E(x13641,x13642)+E(f366(x13643,x13641,x13644,x13645,x13646),f366(x13643,x13642,x13644,x13645,x13646)) % 186.05/186.64 [1365]~E(x13651,x13652)+E(f366(x13653,x13654,x13651,x13655,x13656),f366(x13653,x13654,x13652,x13655,x13656)) % 186.05/186.64 [1366]~E(x13661,x13662)+E(f366(x13663,x13664,x13665,x13661,x13666),f366(x13663,x13664,x13665,x13662,x13666)) % 186.05/186.64 [1367]~E(x13671,x13672)+E(f366(x13673,x13674,x13675,x13676,x13671),f366(x13673,x13674,x13675,x13676,x13672)) % 186.05/186.64 [1368]~E(x13681,x13682)+E(f526(x13681,x13683,x13684),f526(x13682,x13683,x13684)) % 186.05/186.64 [1369]~E(x13691,x13692)+E(f526(x13693,x13691,x13694),f526(x13693,x13692,x13694)) % 186.05/186.64 [1370]~E(x13701,x13702)+E(f526(x13703,x13704,x13701),f526(x13703,x13704,x13702)) % 186.05/186.64 [1371]~E(x13711,x13712)+E(f504(x13711),f504(x13712)) % 186.05/186.64 [1372]~E(x13721,x13722)+E(f530(x13721,x13723,x13724),f530(x13722,x13723,x13724)) % 186.05/186.64 [1373]~E(x13731,x13732)+E(f530(x13733,x13731,x13734),f530(x13733,x13732,x13734)) % 186.05/186.64 [1374]~E(x13741,x13742)+E(f530(x13743,x13744,x13741),f530(x13743,x13744,x13742)) % 186.05/186.64 [1375]~E(x13751,x13752)+E(f827(x13751,x13753,x13754),f827(x13752,x13753,x13754)) % 186.05/186.64 [1376]~E(x13761,x13762)+E(f827(x13763,x13761,x13764),f827(x13763,x13762,x13764)) % 186.05/186.64 [1377]~E(x13771,x13772)+E(f827(x13773,x13774,x13771),f827(x13773,x13774,x13772)) % 186.05/186.64 [1378]~E(x13781,x13782)+E(f721(x13781,x13783,x13784,x13785,x13786),f721(x13782,x13783,x13784,x13785,x13786)) % 186.05/186.64 [1379]~E(x13791,x13792)+E(f721(x13793,x13791,x13794,x13795,x13796),f721(x13793,x13792,x13794,x13795,x13796)) % 186.05/186.64 [1380]~E(x13801,x13802)+E(f721(x13803,x13804,x13801,x13805,x13806),f721(x13803,x13804,x13802,x13805,x13806)) % 186.05/186.64 [1381]~E(x13811,x13812)+E(f721(x13813,x13814,x13815,x13811,x13816),f721(x13813,x13814,x13815,x13812,x13816)) % 186.05/186.64 [1382]~E(x13821,x13822)+E(f721(x13823,x13824,x13825,x13826,x13821),f721(x13823,x13824,x13825,x13826,x13822)) % 186.05/186.64 [1383]~E(x13831,x13832)+E(f777(x13831),f777(x13832)) % 186.05/186.64 [1384]~E(x13841,x13842)+E(f24(x13841,x13843),f24(x13842,x13843)) % 186.05/186.64 [1385]~E(x13851,x13852)+E(f24(x13853,x13851),f24(x13853,x13852)) % 186.05/186.64 [1386]~E(x13861,x13862)+E(f553(x13861,x13863,x13864),f553(x13862,x13863,x13864)) % 186.05/186.64 [1387]~E(x13871,x13872)+E(f553(x13873,x13871,x13874),f553(x13873,x13872,x13874)) % 186.05/186.64 [1388]~E(x13881,x13882)+E(f553(x13883,x13884,x13881),f553(x13883,x13884,x13882)) % 186.05/186.64 [1389]~E(x13891,x13892)+E(f542(x13891,x13893,x13894,x13895,x13896,x13897),f542(x13892,x13893,x13894,x13895,x13896,x13897)) % 186.05/186.64 [1390]~E(x13901,x13902)+E(f542(x13903,x13901,x13904,x13905,x13906,x13907),f542(x13903,x13902,x13904,x13905,x13906,x13907)) % 186.05/186.64 [1391]~E(x13911,x13912)+E(f542(x13913,x13914,x13911,x13915,x13916,x13917),f542(x13913,x13914,x13912,x13915,x13916,x13917)) % 186.05/186.64 [1392]~E(x13921,x13922)+E(f542(x13923,x13924,x13925,x13921,x13926,x13927),f542(x13923,x13924,x13925,x13922,x13926,x13927)) % 186.05/186.64 [1393]~E(x13931,x13932)+E(f542(x13933,x13934,x13935,x13936,x13931,x13937),f542(x13933,x13934,x13935,x13936,x13932,x13937)) % 186.05/186.64 [1394]~E(x13941,x13942)+E(f542(x13943,x13944,x13945,x13946,x13947,x13941),f542(x13943,x13944,x13945,x13946,x13947,x13942)) % 186.05/186.64 [1395]~E(x13951,x13952)+E(f353(x13951,x13953),f353(x13952,x13953)) % 186.05/186.64 [1396]~E(x13961,x13962)+E(f353(x13963,x13961),f353(x13963,x13962)) % 186.05/186.64 [1397]~E(x13971,x13972)+E(f485(x13971,x13973,x13974,x13975,x13976),f485(x13972,x13973,x13974,x13975,x13976)) % 186.05/186.64 [1398]~E(x13981,x13982)+E(f485(x13983,x13981,x13984,x13985,x13986),f485(x13983,x13982,x13984,x13985,x13986)) % 186.05/186.64 [1399]~E(x13991,x13992)+E(f485(x13993,x13994,x13991,x13995,x13996),f485(x13993,x13994,x13992,x13995,x13996)) % 186.05/186.64 [1400]~E(x14001,x14002)+E(f485(x14003,x14004,x14005,x14001,x14006),f485(x14003,x14004,x14005,x14002,x14006)) % 186.05/186.64 [1401]~E(x14011,x14012)+E(f485(x14013,x14014,x14015,x14016,x14011),f485(x14013,x14014,x14015,x14016,x14012)) % 186.05/186.64 [1402]~E(x14021,x14022)+E(f431(x14021,x14023,x14024,x14025),f431(x14022,x14023,x14024,x14025)) % 186.05/186.64 [1403]~E(x14031,x14032)+E(f431(x14033,x14031,x14034,x14035),f431(x14033,x14032,x14034,x14035)) % 186.05/186.64 [1404]~E(x14041,x14042)+E(f431(x14043,x14044,x14041,x14045),f431(x14043,x14044,x14042,x14045)) % 186.05/186.64 [1405]~E(x14051,x14052)+E(f431(x14053,x14054,x14055,x14051),f431(x14053,x14054,x14055,x14052)) % 186.05/186.64 [1406]~E(x14061,x14062)+E(f228(x14061,x14063,x14064),f228(x14062,x14063,x14064)) % 186.05/186.64 [1407]~E(x14071,x14072)+E(f228(x14073,x14071,x14074),f228(x14073,x14072,x14074)) % 186.05/186.64 [1408]~E(x14081,x14082)+E(f228(x14083,x14084,x14081),f228(x14083,x14084,x14082)) % 186.05/186.64 [1409]~E(x14091,x14092)+E(f621(x14091,x14093,x14094,x14095,x14096,x14097),f621(x14092,x14093,x14094,x14095,x14096,x14097)) % 186.05/186.64 [1410]~E(x14101,x14102)+E(f621(x14103,x14101,x14104,x14105,x14106,x14107),f621(x14103,x14102,x14104,x14105,x14106,x14107)) % 186.05/186.64 [1411]~E(x14111,x14112)+E(f621(x14113,x14114,x14111,x14115,x14116,x14117),f621(x14113,x14114,x14112,x14115,x14116,x14117)) % 186.05/186.64 [1412]~E(x14121,x14122)+E(f621(x14123,x14124,x14125,x14121,x14126,x14127),f621(x14123,x14124,x14125,x14122,x14126,x14127)) % 186.05/186.64 [1413]~E(x14131,x14132)+E(f621(x14133,x14134,x14135,x14136,x14131,x14137),f621(x14133,x14134,x14135,x14136,x14132,x14137)) % 186.05/186.64 [1414]~E(x14141,x14142)+E(f621(x14143,x14144,x14145,x14146,x14147,x14141),f621(x14143,x14144,x14145,x14146,x14147,x14142)) % 186.05/186.64 [1415]~E(x14151,x14152)+E(f482(x14151,x14153,x14154),f482(x14152,x14153,x14154)) % 186.05/186.64 [1416]~E(x14161,x14162)+E(f482(x14163,x14161,x14164),f482(x14163,x14162,x14164)) % 186.05/186.64 [1417]~E(x14171,x14172)+E(f482(x14173,x14174,x14171),f482(x14173,x14174,x14172)) % 186.05/186.64 [1418]~E(x14181,x14182)+E(f707(x14181,x14183,x14184,x14185,x14186,x14187),f707(x14182,x14183,x14184,x14185,x14186,x14187)) % 186.05/186.64 [1419]~E(x14191,x14192)+E(f707(x14193,x14191,x14194,x14195,x14196,x14197),f707(x14193,x14192,x14194,x14195,x14196,x14197)) % 186.05/186.64 [1420]~E(x14201,x14202)+E(f707(x14203,x14204,x14201,x14205,x14206,x14207),f707(x14203,x14204,x14202,x14205,x14206,x14207)) % 186.05/186.64 [1421]~E(x14211,x14212)+E(f707(x14213,x14214,x14215,x14211,x14216,x14217),f707(x14213,x14214,x14215,x14212,x14216,x14217)) % 186.05/186.64 [1422]~E(x14221,x14222)+E(f707(x14223,x14224,x14225,x14226,x14221,x14227),f707(x14223,x14224,x14225,x14226,x14222,x14227)) % 186.05/186.64 [1423]~E(x14231,x14232)+E(f707(x14233,x14234,x14235,x14236,x14237,x14231),f707(x14233,x14234,x14235,x14236,x14237,x14232)) % 186.05/186.64 [1424]~E(x14241,x14242)+E(f386(x14241,x14243,x14244,x14245,x14246),f386(x14242,x14243,x14244,x14245,x14246)) % 186.05/186.64 [1425]~E(x14251,x14252)+E(f386(x14253,x14251,x14254,x14255,x14256),f386(x14253,x14252,x14254,x14255,x14256)) % 186.05/186.64 [1426]~E(x14261,x14262)+E(f386(x14263,x14264,x14261,x14265,x14266),f386(x14263,x14264,x14262,x14265,x14266)) % 186.05/186.64 [1427]~E(x14271,x14272)+E(f386(x14273,x14274,x14275,x14271,x14276),f386(x14273,x14274,x14275,x14272,x14276)) % 186.05/186.64 [1428]~E(x14281,x14282)+E(f386(x14283,x14284,x14285,x14286,x14281),f386(x14283,x14284,x14285,x14286,x14282)) % 186.05/186.64 [1429]~E(x14291,x14292)+E(f495(x14291,x14293,x14294,x14295,x14296,x14297),f495(x14292,x14293,x14294,x14295,x14296,x14297)) % 186.05/186.64 [1430]~E(x14301,x14302)+E(f495(x14303,x14301,x14304,x14305,x14306,x14307),f495(x14303,x14302,x14304,x14305,x14306,x14307)) % 186.05/186.64 [1431]~E(x14311,x14312)+E(f495(x14313,x14314,x14311,x14315,x14316,x14317),f495(x14313,x14314,x14312,x14315,x14316,x14317)) % 186.05/186.64 [1432]~E(x14321,x14322)+E(f495(x14323,x14324,x14325,x14321,x14326,x14327),f495(x14323,x14324,x14325,x14322,x14326,x14327)) % 186.05/186.64 [1433]~E(x14331,x14332)+E(f495(x14333,x14334,x14335,x14336,x14331,x14337),f495(x14333,x14334,x14335,x14336,x14332,x14337)) % 186.05/186.64 [1434]~E(x14341,x14342)+E(f495(x14343,x14344,x14345,x14346,x14347,x14341),f495(x14343,x14344,x14345,x14346,x14347,x14342)) % 186.05/186.64 [1435]~E(x14351,x14352)+E(f445(x14351,x14353),f445(x14352,x14353)) % 186.05/186.64 [1436]~E(x14361,x14362)+E(f445(x14363,x14361),f445(x14363,x14362)) % 186.05/186.64 [1437]~E(x14371,x14372)+E(f435(x14371,x14373,x14374,x14375),f435(x14372,x14373,x14374,x14375)) % 186.05/186.64 [1438]~E(x14381,x14382)+E(f435(x14383,x14381,x14384,x14385),f435(x14383,x14382,x14384,x14385)) % 186.05/186.64 [1439]~E(x14391,x14392)+E(f435(x14393,x14394,x14391,x14395),f435(x14393,x14394,x14392,x14395)) % 186.05/186.64 [1440]~E(x14401,x14402)+E(f435(x14403,x14404,x14405,x14401),f435(x14403,x14404,x14405,x14402)) % 186.05/186.64 [1441]~E(x14411,x14412)+E(f605(x14411,x14413),f605(x14412,x14413)) % 186.05/186.64 [1442]~E(x14421,x14422)+E(f605(x14423,x14421),f605(x14423,x14422)) % 186.05/186.64 [1443]~E(x14431,x14432)+E(f191(x14431,x14433,x14434,x14435),f191(x14432,x14433,x14434,x14435)) % 186.05/186.64 [1444]~E(x14441,x14442)+E(f191(x14443,x14441,x14444,x14445),f191(x14443,x14442,x14444,x14445)) % 186.05/186.64 [1445]~E(x14451,x14452)+E(f191(x14453,x14454,x14451,x14455),f191(x14453,x14454,x14452,x14455)) % 186.05/186.64 [1446]~E(x14461,x14462)+E(f191(x14463,x14464,x14465,x14461),f191(x14463,x14464,x14465,x14462)) % 186.05/186.64 [1447]~E(x14471,x14472)+E(f462(x14471,x14473,x14474),f462(x14472,x14473,x14474)) % 186.05/186.64 [1448]~E(x14481,x14482)+E(f462(x14483,x14481,x14484),f462(x14483,x14482,x14484)) % 186.05/186.64 [1449]~E(x14491,x14492)+E(f462(x14493,x14494,x14491),f462(x14493,x14494,x14492)) % 186.05/186.64 [1450]~E(x14501,x14502)+E(f391(x14501,x14503,x14504,x14505,x14506),f391(x14502,x14503,x14504,x14505,x14506)) % 186.05/186.64 [1451]~E(x14511,x14512)+E(f391(x14513,x14511,x14514,x14515,x14516),f391(x14513,x14512,x14514,x14515,x14516)) % 186.05/186.64 [1452]~E(x14521,x14522)+E(f391(x14523,x14524,x14521,x14525,x14526),f391(x14523,x14524,x14522,x14525,x14526)) % 186.05/186.64 [1453]~E(x14531,x14532)+E(f391(x14533,x14534,x14535,x14531,x14536),f391(x14533,x14534,x14535,x14532,x14536)) % 186.05/186.64 [1454]~E(x14541,x14542)+E(f391(x14543,x14544,x14545,x14546,x14541),f391(x14543,x14544,x14545,x14546,x14542)) % 186.05/186.64 [1455]~E(x14551,x14552)+E(f465(x14551,x14553,x14554),f465(x14552,x14553,x14554)) % 186.05/186.64 [1456]~E(x14561,x14562)+E(f465(x14563,x14561,x14564),f465(x14563,x14562,x14564)) % 186.05/186.64 [1457]~E(x14571,x14572)+E(f465(x14573,x14574,x14571),f465(x14573,x14574,x14572)) % 186.05/186.64 [1458]~E(x14581,x14582)+E(f520(x14581),f520(x14582)) % 186.05/186.64 [1459]~E(x14591,x14592)+E(f724(x14591),f724(x14592)) % 186.05/186.64 [1460]~E(x14601,x14602)+E(f150(x14601,x14603),f150(x14602,x14603)) % 186.05/186.64 [1461]~E(x14611,x14612)+E(f150(x14613,x14611),f150(x14613,x14612)) % 186.05/186.64 [1462]~E(x14621,x14622)+E(f563(x14621,x14623,x14624,x14625,x14626,x14627),f563(x14622,x14623,x14624,x14625,x14626,x14627)) % 186.05/186.64 [1463]~E(x14631,x14632)+E(f563(x14633,x14631,x14634,x14635,x14636,x14637),f563(x14633,x14632,x14634,x14635,x14636,x14637)) % 186.05/186.64 [1464]~E(x14641,x14642)+E(f563(x14643,x14644,x14641,x14645,x14646,x14647),f563(x14643,x14644,x14642,x14645,x14646,x14647)) % 186.05/186.64 [1465]~E(x14651,x14652)+E(f563(x14653,x14654,x14655,x14651,x14656,x14657),f563(x14653,x14654,x14655,x14652,x14656,x14657)) % 186.05/186.64 [1466]~E(x14661,x14662)+E(f563(x14663,x14664,x14665,x14666,x14661,x14667),f563(x14663,x14664,x14665,x14666,x14662,x14667)) % 186.05/186.64 [1467]~E(x14671,x14672)+E(f563(x14673,x14674,x14675,x14676,x14677,x14671),f563(x14673,x14674,x14675,x14676,x14677,x14672)) % 186.05/186.64 [1468]~E(x14681,x14682)+E(f318(x14681,x14683,x14684,x14685,x14686),f318(x14682,x14683,x14684,x14685,x14686)) % 186.05/186.64 [1469]~E(x14691,x14692)+E(f318(x14693,x14691,x14694,x14695,x14696),f318(x14693,x14692,x14694,x14695,x14696)) % 186.05/186.64 [1470]~E(x14701,x14702)+E(f318(x14703,x14704,x14701,x14705,x14706),f318(x14703,x14704,x14702,x14705,x14706)) % 186.05/186.64 [1471]~E(x14711,x14712)+E(f318(x14713,x14714,x14715,x14711,x14716),f318(x14713,x14714,x14715,x14712,x14716)) % 186.05/186.64 [1472]~E(x14721,x14722)+E(f318(x14723,x14724,x14725,x14726,x14721),f318(x14723,x14724,x14725,x14726,x14722)) % 186.05/186.64 [1473]~E(x14731,x14732)+E(f340(x14731,x14733),f340(x14732,x14733)) % 186.05/186.64 [1474]~E(x14741,x14742)+E(f340(x14743,x14741),f340(x14743,x14742)) % 186.05/186.64 [1475]~E(x14751,x14752)+E(f124(x14751),f124(x14752)) % 186.05/186.64 [1476]~E(x14761,x14762)+E(f824(x14761,x14763,x14764),f824(x14762,x14763,x14764)) % 186.05/186.64 [1477]~E(x14771,x14772)+E(f824(x14773,x14771,x14774),f824(x14773,x14772,x14774)) % 186.05/186.64 [1478]~E(x14781,x14782)+E(f824(x14783,x14784,x14781),f824(x14783,x14784,x14782)) % 186.05/186.64 [1479]~E(x14791,x14792)+E(f633(x14791,x14793,x14794),f633(x14792,x14793,x14794)) % 186.05/186.64 [1480]~E(x14801,x14802)+E(f633(x14803,x14801,x14804),f633(x14803,x14802,x14804)) % 186.05/186.64 [1481]~E(x14811,x14812)+E(f633(x14813,x14814,x14811),f633(x14813,x14814,x14812)) % 186.05/186.64 [1482]~E(x14821,x14822)+E(f837(x14821,x14823,x14824,x14825,x14826,x14827,x14828),f837(x14822,x14823,x14824,x14825,x14826,x14827,x14828)) % 186.05/186.64 [1483]~E(x14831,x14832)+E(f837(x14833,x14831,x14834,x14835,x14836,x14837,x14838),f837(x14833,x14832,x14834,x14835,x14836,x14837,x14838)) % 186.05/186.64 [1484]~E(x14841,x14842)+E(f837(x14843,x14844,x14841,x14845,x14846,x14847,x14848),f837(x14843,x14844,x14842,x14845,x14846,x14847,x14848)) % 186.05/186.64 [1485]~E(x14851,x14852)+E(f837(x14853,x14854,x14855,x14851,x14856,x14857,x14858),f837(x14853,x14854,x14855,x14852,x14856,x14857,x14858)) % 186.05/186.64 [1486]~E(x14861,x14862)+E(f837(x14863,x14864,x14865,x14866,x14861,x14867,x14868),f837(x14863,x14864,x14865,x14866,x14862,x14867,x14868)) % 186.05/186.64 [1487]~E(x14871,x14872)+E(f837(x14873,x14874,x14875,x14876,x14877,x14871,x14878),f837(x14873,x14874,x14875,x14876,x14877,x14872,x14878)) % 186.05/186.64 [1488]~E(x14881,x14882)+E(f837(x14883,x14884,x14885,x14886,x14887,x14888,x14881),f837(x14883,x14884,x14885,x14886,x14887,x14888,x14882)) % 186.05/186.64 [1489]~E(x14891,x14892)+E(f454(x14891,x14893,x14894,x14895,x14896,x14897,x14898),f454(x14892,x14893,x14894,x14895,x14896,x14897,x14898)) % 186.05/186.64 [1490]~E(x14901,x14902)+E(f454(x14903,x14901,x14904,x14905,x14906,x14907,x14908),f454(x14903,x14902,x14904,x14905,x14906,x14907,x14908)) % 186.05/186.64 [1491]~E(x14911,x14912)+E(f454(x14913,x14914,x14911,x14915,x14916,x14917,x14918),f454(x14913,x14914,x14912,x14915,x14916,x14917,x14918)) % 186.05/186.64 [1492]~E(x14921,x14922)+E(f454(x14923,x14924,x14925,x14921,x14926,x14927,x14928),f454(x14923,x14924,x14925,x14922,x14926,x14927,x14928)) % 186.05/186.64 [1493]~E(x14931,x14932)+E(f454(x14933,x14934,x14935,x14936,x14931,x14937,x14938),f454(x14933,x14934,x14935,x14936,x14932,x14937,x14938)) % 186.05/186.64 [1494]~E(x14941,x14942)+E(f454(x14943,x14944,x14945,x14946,x14947,x14941,x14948),f454(x14943,x14944,x14945,x14946,x14947,x14942,x14948)) % 186.05/186.64 [1495]~E(x14951,x14952)+E(f454(x14953,x14954,x14955,x14956,x14957,x14958,x14951),f454(x14953,x14954,x14955,x14956,x14957,x14958,x14952)) % 186.05/186.64 [1496]~E(x14961,x14962)+E(f708(x14961,x14963,x14964,x14965),f708(x14962,x14963,x14964,x14965)) % 186.05/186.64 [1497]~E(x14971,x14972)+E(f708(x14973,x14971,x14974,x14975),f708(x14973,x14972,x14974,x14975)) % 186.05/186.64 [1498]~E(x14981,x14982)+E(f708(x14983,x14984,x14981,x14985),f708(x14983,x14984,x14982,x14985)) % 186.05/186.64 [1499]~E(x14991,x14992)+E(f708(x14993,x14994,x14995,x14991),f708(x14993,x14994,x14995,x14992)) % 186.05/186.64 [1500]~E(x15001,x15002)+E(f614(x15001,x15003,x15004,x15005,x15006,x15007),f614(x15002,x15003,x15004,x15005,x15006,x15007)) % 186.05/186.64 [1501]~E(x15011,x15012)+E(f614(x15013,x15011,x15014,x15015,x15016,x15017),f614(x15013,x15012,x15014,x15015,x15016,x15017)) % 186.05/186.64 [1502]~E(x15021,x15022)+E(f614(x15023,x15024,x15021,x15025,x15026,x15027),f614(x15023,x15024,x15022,x15025,x15026,x15027)) % 186.05/186.64 [1503]~E(x15031,x15032)+E(f614(x15033,x15034,x15035,x15031,x15036,x15037),f614(x15033,x15034,x15035,x15032,x15036,x15037)) % 186.05/186.64 [1504]~E(x15041,x15042)+E(f614(x15043,x15044,x15045,x15046,x15041,x15047),f614(x15043,x15044,x15045,x15046,x15042,x15047)) % 186.05/186.64 [1505]~E(x15051,x15052)+E(f614(x15053,x15054,x15055,x15056,x15057,x15051),f614(x15053,x15054,x15055,x15056,x15057,x15052)) % 186.05/186.64 [1506]~E(x15061,x15062)+E(f615(x15061,x15063,x15064,x15065,x15066,x15067),f615(x15062,x15063,x15064,x15065,x15066,x15067)) % 186.05/186.64 [1507]~E(x15071,x15072)+E(f615(x15073,x15071,x15074,x15075,x15076,x15077),f615(x15073,x15072,x15074,x15075,x15076,x15077)) % 186.05/186.64 [1508]~E(x15081,x15082)+E(f615(x15083,x15084,x15081,x15085,x15086,x15087),f615(x15083,x15084,x15082,x15085,x15086,x15087)) % 186.05/186.64 [1509]~E(x15091,x15092)+E(f615(x15093,x15094,x15095,x15091,x15096,x15097),f615(x15093,x15094,x15095,x15092,x15096,x15097)) % 186.05/186.64 [1510]~E(x15101,x15102)+E(f615(x15103,x15104,x15105,x15106,x15101,x15107),f615(x15103,x15104,x15105,x15106,x15102,x15107)) % 186.05/186.64 [1511]~E(x15111,x15112)+E(f615(x15113,x15114,x15115,x15116,x15117,x15111),f615(x15113,x15114,x15115,x15116,x15117,x15112)) % 186.05/186.64 [1512]~E(x15121,x15122)+E(f269(x15121,x15123,x15124),f269(x15122,x15123,x15124)) % 186.05/186.64 [1513]~E(x15131,x15132)+E(f269(x15133,x15131,x15134),f269(x15133,x15132,x15134)) % 186.05/186.64 [1514]~E(x15141,x15142)+E(f269(x15143,x15144,x15141),f269(x15143,x15144,x15142)) % 186.05/186.64 [1515]~E(x15151,x15152)+E(f794(x15151,x15153,x15154),f794(x15152,x15153,x15154)) % 186.05/186.64 [1516]~E(x15161,x15162)+E(f794(x15163,x15161,x15164),f794(x15163,x15162,x15164)) % 186.05/186.64 [1517]~E(x15171,x15172)+E(f794(x15173,x15174,x15171),f794(x15173,x15174,x15172)) % 186.05/186.64 [1518]~E(x15181,x15182)+E(f565(x15181,x15183),f565(x15182,x15183)) % 186.05/186.64 [1519]~E(x15191,x15192)+E(f565(x15193,x15191),f565(x15193,x15192)) % 186.05/186.64 [1520]~E(x15201,x15202)+E(f826(x15201,x15203,x15204),f826(x15202,x15203,x15204)) % 186.05/186.64 [1521]~E(x15211,x15212)+E(f826(x15213,x15211,x15214),f826(x15213,x15212,x15214)) % 186.05/186.64 [1522]~E(x15221,x15222)+E(f826(x15223,x15224,x15221),f826(x15223,x15224,x15222)) % 186.05/186.64 [1523]~E(x15231,x15232)+E(f404(x15231,x15233,x15234),f404(x15232,x15233,x15234)) % 186.05/186.64 [1524]~E(x15241,x15242)+E(f404(x15243,x15241,x15244),f404(x15243,x15242,x15244)) % 186.05/186.64 [1525]~E(x15251,x15252)+E(f404(x15253,x15254,x15251),f404(x15253,x15254,x15252)) % 186.05/186.64 [1526]~E(x15261,x15262)+E(f204(x15261,x15263,x15264,x15265),f204(x15262,x15263,x15264,x15265)) % 186.05/186.64 [1527]~E(x15271,x15272)+E(f204(x15273,x15271,x15274,x15275),f204(x15273,x15272,x15274,x15275)) % 186.05/186.64 [1528]~E(x15281,x15282)+E(f204(x15283,x15284,x15281,x15285),f204(x15283,x15284,x15282,x15285)) % 186.05/186.64 [1529]~E(x15291,x15292)+E(f204(x15293,x15294,x15295,x15291),f204(x15293,x15294,x15295,x15292)) % 186.05/186.64 [1530]~E(x15301,x15302)+E(f385(x15301,x15303,x15304,x15305),f385(x15302,x15303,x15304,x15305)) % 186.05/186.64 [1531]~E(x15311,x15312)+E(f385(x15313,x15311,x15314,x15315),f385(x15313,x15312,x15314,x15315)) % 186.05/186.64 [1532]~E(x15321,x15322)+E(f385(x15323,x15324,x15321,x15325),f385(x15323,x15324,x15322,x15325)) % 186.05/186.64 [1533]~E(x15331,x15332)+E(f385(x15333,x15334,x15335,x15331),f385(x15333,x15334,x15335,x15332)) % 186.05/186.64 [1534]~E(x15341,x15342)+E(f609(x15341,x15343,x15344,x15345),f609(x15342,x15343,x15344,x15345)) % 186.05/186.64 [1535]~E(x15351,x15352)+E(f609(x15353,x15351,x15354,x15355),f609(x15353,x15352,x15354,x15355)) % 186.05/186.64 [1536]~E(x15361,x15362)+E(f609(x15363,x15364,x15361,x15365),f609(x15363,x15364,x15362,x15365)) % 186.05/186.64 [1537]~E(x15371,x15372)+E(f609(x15373,x15374,x15375,x15371),f609(x15373,x15374,x15375,x15372)) % 186.05/186.64 [1538]~E(x15381,x15382)+E(f154(x15381,x15383,x15384,x15385),f154(x15382,x15383,x15384,x15385)) % 186.05/186.64 [1539]~E(x15391,x15392)+E(f154(x15393,x15391,x15394,x15395),f154(x15393,x15392,x15394,x15395)) % 186.05/186.64 [1540]~E(x15401,x15402)+E(f154(x15403,x15404,x15401,x15405),f154(x15403,x15404,x15402,x15405)) % 186.05/186.64 [1541]~E(x15411,x15412)+E(f154(x15413,x15414,x15415,x15411),f154(x15413,x15414,x15415,x15412)) % 186.05/186.64 [1542]~E(x15421,x15422)+E(f730(x15421,x15423,x15424),f730(x15422,x15423,x15424)) % 186.05/186.64 [1543]~E(x15431,x15432)+E(f730(x15433,x15431,x15434),f730(x15433,x15432,x15434)) % 186.05/186.64 [1544]~E(x15441,x15442)+E(f730(x15443,x15444,x15441),f730(x15443,x15444,x15442)) % 186.05/186.64 [1545]~E(x15451,x15452)+E(f655(x15451,x15453,x15454,x15455),f655(x15452,x15453,x15454,x15455)) % 186.05/186.64 [1546]~E(x15461,x15462)+E(f655(x15463,x15461,x15464,x15465),f655(x15463,x15462,x15464,x15465)) % 186.05/186.64 [1547]~E(x15471,x15472)+E(f655(x15473,x15474,x15471,x15475),f655(x15473,x15474,x15472,x15475)) % 186.05/186.64 [1548]~E(x15481,x15482)+E(f655(x15483,x15484,x15485,x15481),f655(x15483,x15484,x15485,x15482)) % 186.05/186.64 [1549]~E(x15491,x15492)+E(f447(x15491,x15493),f447(x15492,x15493)) % 186.05/186.64 [1550]~E(x15501,x15502)+E(f447(x15503,x15501),f447(x15503,x15502)) % 186.05/186.64 [1551]~E(x15511,x15512)+E(f590(x15511,x15513,x15514),f590(x15512,x15513,x15514)) % 186.05/186.64 [1552]~E(x15521,x15522)+E(f590(x15523,x15521,x15524),f590(x15523,x15522,x15524)) % 186.05/186.64 [1553]~E(x15531,x15532)+E(f590(x15533,x15534,x15531),f590(x15533,x15534,x15532)) % 186.05/186.64 [1554]~E(x15541,x15542)+E(f836(x15541,x15543,x15544,x15545,x15546,x15547,x15548),f836(x15542,x15543,x15544,x15545,x15546,x15547,x15548)) % 186.05/186.64 [1555]~E(x15551,x15552)+E(f836(x15553,x15551,x15554,x15555,x15556,x15557,x15558),f836(x15553,x15552,x15554,x15555,x15556,x15557,x15558)) % 186.05/186.64 [1556]~E(x15561,x15562)+E(f836(x15563,x15564,x15561,x15565,x15566,x15567,x15568),f836(x15563,x15564,x15562,x15565,x15566,x15567,x15568)) % 186.05/186.64 [1557]~E(x15571,x15572)+E(f836(x15573,x15574,x15575,x15571,x15576,x15577,x15578),f836(x15573,x15574,x15575,x15572,x15576,x15577,x15578)) % 186.05/186.64 [1558]~E(x15581,x15582)+E(f836(x15583,x15584,x15585,x15586,x15581,x15587,x15588),f836(x15583,x15584,x15585,x15586,x15582,x15587,x15588)) % 186.05/186.64 [1559]~E(x15591,x15592)+E(f836(x15593,x15594,x15595,x15596,x15597,x15591,x15598),f836(x15593,x15594,x15595,x15596,x15597,x15592,x15598)) % 186.05/186.64 [1560]~E(x15601,x15602)+E(f836(x15603,x15604,x15605,x15606,x15607,x15608,x15601),f836(x15603,x15604,x15605,x15606,x15607,x15608,x15602)) % 186.05/186.64 [1561]~E(x15611,x15612)+E(f51(x15611),f51(x15612)) % 186.05/186.64 [1562]~E(x15621,x15622)+E(f704(x15621,x15623,x15624,x15625,x15626),f704(x15622,x15623,x15624,x15625,x15626)) % 186.05/186.64 [1563]~E(x15631,x15632)+E(f704(x15633,x15631,x15634,x15635,x15636),f704(x15633,x15632,x15634,x15635,x15636)) % 186.05/186.64 [1564]~E(x15641,x15642)+E(f704(x15643,x15644,x15641,x15645,x15646),f704(x15643,x15644,x15642,x15645,x15646)) % 186.05/186.64 [1565]~E(x15651,x15652)+E(f704(x15653,x15654,x15655,x15651,x15656),f704(x15653,x15654,x15655,x15652,x15656)) % 186.05/186.64 [1566]~E(x15661,x15662)+E(f704(x15663,x15664,x15665,x15666,x15661),f704(x15663,x15664,x15665,x15666,x15662)) % 186.05/186.64 [1567]~E(x15671,x15672)+E(f772(x15671,x15673,x15674),f772(x15672,x15673,x15674)) % 186.05/186.64 [1568]~E(x15681,x15682)+E(f772(x15683,x15681,x15684),f772(x15683,x15682,x15684)) % 186.05/186.64 [1569]~E(x15691,x15692)+E(f772(x15693,x15694,x15691),f772(x15693,x15694,x15692)) % 186.05/186.64 [1570]~E(x15701,x15702)+E(f76(x15701,x15703),f76(x15702,x15703)) % 186.05/186.64 [1571]~E(x15711,x15712)+E(f76(x15713,x15711),f76(x15713,x15712)) % 186.05/186.64 [1572]~E(x15721,x15722)+E(f769(x15721,x15723),f769(x15722,x15723)) % 186.05/186.64 [1573]~E(x15731,x15732)+E(f769(x15733,x15731),f769(x15733,x15732)) % 186.05/186.64 [1574]~E(x15741,x15742)+E(f427(x15741,x15743),f427(x15742,x15743)) % 186.05/186.64 [1575]~E(x15751,x15752)+E(f427(x15753,x15751),f427(x15753,x15752)) % 186.05/186.64 [1576]~E(x15761,x15762)+E(f369(x15761,x15763),f369(x15762,x15763)) % 186.05/186.64 [1577]~E(x15771,x15772)+E(f369(x15773,x15771),f369(x15773,x15772)) % 186.05/186.64 [1578]~E(x15781,x15782)+E(f192(x15781,x15783,x15784,x15785),f192(x15782,x15783,x15784,x15785)) % 186.05/186.64 [1579]~E(x15791,x15792)+E(f192(x15793,x15791,x15794,x15795),f192(x15793,x15792,x15794,x15795)) % 186.05/186.64 [1580]~E(x15801,x15802)+E(f192(x15803,x15804,x15801,x15805),f192(x15803,x15804,x15802,x15805)) % 186.05/186.64 [1581]~E(x15811,x15812)+E(f192(x15813,x15814,x15815,x15811),f192(x15813,x15814,x15815,x15812)) % 186.05/186.64 [1582]~E(x15821,x15822)+E(f342(x15821,x15823),f342(x15822,x15823)) % 186.05/186.64 [1583]~E(x15831,x15832)+E(f342(x15833,x15831),f342(x15833,x15832)) % 186.05/186.64 [1584]~E(x15841,x15842)+E(f558(x15841),f558(x15842)) % 186.05/186.64 [1585]~E(x15851,x15852)+E(f230(x15851,x15853,x15854,x15855,x15856),f230(x15852,x15853,x15854,x15855,x15856)) % 186.05/186.64 [1586]~E(x15861,x15862)+E(f230(x15863,x15861,x15864,x15865,x15866),f230(x15863,x15862,x15864,x15865,x15866)) % 186.05/186.64 [1587]~E(x15871,x15872)+E(f230(x15873,x15874,x15871,x15875,x15876),f230(x15873,x15874,x15872,x15875,x15876)) % 186.05/186.64 [1588]~E(x15881,x15882)+E(f230(x15883,x15884,x15885,x15881,x15886),f230(x15883,x15884,x15885,x15882,x15886)) % 186.05/186.64 [1589]~E(x15891,x15892)+E(f230(x15893,x15894,x15895,x15896,x15891),f230(x15893,x15894,x15895,x15896,x15892)) % 186.05/186.64 [1590]~E(x15901,x15902)+E(f365(x15901,x15903,x15904,x15905,x15906),f365(x15902,x15903,x15904,x15905,x15906)) % 186.05/186.64 [1591]~E(x15911,x15912)+E(f365(x15913,x15911,x15914,x15915,x15916),f365(x15913,x15912,x15914,x15915,x15916)) % 186.05/186.64 [1592]~E(x15921,x15922)+E(f365(x15923,x15924,x15921,x15925,x15926),f365(x15923,x15924,x15922,x15925,x15926)) % 186.05/186.64 [1593]~E(x15931,x15932)+E(f365(x15933,x15934,x15935,x15931,x15936),f365(x15933,x15934,x15935,x15932,x15936)) % 186.05/186.64 [1594]~E(x15941,x15942)+E(f365(x15943,x15944,x15945,x15946,x15941),f365(x15943,x15944,x15945,x15946,x15942)) % 186.05/186.64 [1595]~E(x15951,x15952)+E(f838(x15951,x15953,x15954),f838(x15952,x15953,x15954)) % 186.05/186.64 [1596]~E(x15961,x15962)+E(f838(x15963,x15961,x15964),f838(x15963,x15962,x15964)) % 186.05/186.64 [1597]~E(x15971,x15972)+E(f838(x15973,x15974,x15971),f838(x15973,x15974,x15972)) % 186.05/186.64 [1598]~E(x15981,x15982)+E(f551(x15981,x15983,x15984,x15985,x15986),f551(x15982,x15983,x15984,x15985,x15986)) % 186.05/186.64 [1599]~E(x15991,x15992)+E(f551(x15993,x15991,x15994,x15995,x15996),f551(x15993,x15992,x15994,x15995,x15996)) % 186.05/186.64 [1600]~E(x16001,x16002)+E(f551(x16003,x16004,x16001,x16005,x16006),f551(x16003,x16004,x16002,x16005,x16006)) % 186.05/186.64 [1601]~E(x16011,x16012)+E(f551(x16013,x16014,x16015,x16011,x16016),f551(x16013,x16014,x16015,x16012,x16016)) % 186.05/186.64 [1602]~E(x16021,x16022)+E(f551(x16023,x16024,x16025,x16026,x16021),f551(x16023,x16024,x16025,x16026,x16022)) % 186.05/186.64 [1603]~E(x16031,x16032)+E(f604(x16031,x16033),f604(x16032,x16033)) % 186.05/186.64 [1604]~E(x16041,x16042)+E(f604(x16043,x16041),f604(x16043,x16042)) % 186.05/186.64 [1605]~E(x16051,x16052)+E(f749(x16051,x16053,x16054),f749(x16052,x16053,x16054)) % 186.05/186.64 [1606]~E(x16061,x16062)+E(f749(x16063,x16061,x16064),f749(x16063,x16062,x16064)) % 186.05/186.64 [1607]~E(x16071,x16072)+E(f749(x16073,x16074,x16071),f749(x16073,x16074,x16072)) % 186.05/186.64 [1608]~E(x16081,x16082)+E(f49(x16081),f49(x16082)) % 186.05/186.64 [1609]~E(x16091,x16092)+E(f415(x16091,x16093,x16094),f415(x16092,x16093,x16094)) % 186.05/186.64 [1610]~E(x16101,x16102)+E(f415(x16103,x16101,x16104),f415(x16103,x16102,x16104)) % 186.05/186.64 [1611]~E(x16111,x16112)+E(f415(x16113,x16114,x16111),f415(x16113,x16114,x16112)) % 186.05/186.64 [1612]~E(x16121,x16122)+E(f456(x16121,x16123),f456(x16122,x16123)) % 186.05/186.64 [1613]~E(x16131,x16132)+E(f456(x16133,x16131),f456(x16133,x16132)) % 186.05/186.64 [1614]~E(x16141,x16142)+E(f738(x16141,x16143,x16144,x16145),f738(x16142,x16143,x16144,x16145)) % 186.05/186.64 [1615]~E(x16151,x16152)+E(f738(x16153,x16151,x16154,x16155),f738(x16153,x16152,x16154,x16155)) % 186.05/186.64 [1616]~E(x16161,x16162)+E(f738(x16163,x16164,x16161,x16165),f738(x16163,x16164,x16162,x16165)) % 186.05/186.64 [1617]~E(x16171,x16172)+E(f738(x16173,x16174,x16175,x16171),f738(x16173,x16174,x16175,x16172)) % 186.05/186.64 [1618]~E(x16181,x16182)+E(f442(x16181,x16183,x16184,x16185),f442(x16182,x16183,x16184,x16185)) % 186.05/186.64 [1619]~E(x16191,x16192)+E(f442(x16193,x16191,x16194,x16195),f442(x16193,x16192,x16194,x16195)) % 186.05/186.64 [1620]~E(x16201,x16202)+E(f442(x16203,x16204,x16201,x16205),f442(x16203,x16204,x16202,x16205)) % 186.05/186.64 [1621]~E(x16211,x16212)+E(f442(x16213,x16214,x16215,x16211),f442(x16213,x16214,x16215,x16212)) % 186.05/186.64 [1622]~E(x16221,x16222)+E(f152(x16221,x16223),f152(x16222,x16223)) % 186.05/186.64 [1623]~E(x16231,x16232)+E(f152(x16233,x16231),f152(x16233,x16232)) % 186.05/186.64 [1624]~E(x16241,x16242)+E(f726(x16241,x16243,x16244),f726(x16242,x16243,x16244)) % 186.05/186.64 [1625]~E(x16251,x16252)+E(f726(x16253,x16251,x16254),f726(x16253,x16252,x16254)) % 186.05/186.64 [1626]~E(x16261,x16262)+E(f726(x16263,x16264,x16261),f726(x16263,x16264,x16262)) % 186.05/186.64 [1627]~E(x16271,x16272)+E(f830(x16271,x16273,x16274),f830(x16272,x16273,x16274)) % 186.05/186.64 [1628]~E(x16281,x16282)+E(f830(x16283,x16281,x16284),f830(x16283,x16282,x16284)) % 186.05/186.64 [1629]~E(x16291,x16292)+E(f830(x16293,x16294,x16291),f830(x16293,x16294,x16292)) % 186.05/186.64 [1630]~E(x16301,x16302)+E(f380(x16301,x16303,x16304,x16305,x16306),f380(x16302,x16303,x16304,x16305,x16306)) % 186.05/186.64 [1631]~E(x16311,x16312)+E(f380(x16313,x16311,x16314,x16315,x16316),f380(x16313,x16312,x16314,x16315,x16316)) % 186.05/186.64 [1632]~E(x16321,x16322)+E(f380(x16323,x16324,x16321,x16325,x16326),f380(x16323,x16324,x16322,x16325,x16326)) % 186.05/186.64 [1633]~E(x16331,x16332)+E(f380(x16333,x16334,x16335,x16331,x16336),f380(x16333,x16334,x16335,x16332,x16336)) % 186.05/186.64 [1634]~E(x16341,x16342)+E(f380(x16343,x16344,x16345,x16346,x16341),f380(x16343,x16344,x16345,x16346,x16342)) % 186.05/186.64 [1635]~E(x16351,x16352)+E(f658(x16351,x16353,x16354,x16355,x16356),f658(x16352,x16353,x16354,x16355,x16356)) % 186.05/186.64 [1636]~E(x16361,x16362)+E(f658(x16363,x16361,x16364,x16365,x16366),f658(x16363,x16362,x16364,x16365,x16366)) % 186.05/186.64 [1637]~E(x16371,x16372)+E(f658(x16373,x16374,x16371,x16375,x16376),f658(x16373,x16374,x16372,x16375,x16376)) % 186.05/186.64 [1638]~E(x16381,x16382)+E(f658(x16383,x16384,x16385,x16381,x16386),f658(x16383,x16384,x16385,x16382,x16386)) % 186.05/186.64 [1639]~E(x16391,x16392)+E(f658(x16393,x16394,x16395,x16396,x16391),f658(x16393,x16394,x16395,x16396,x16392)) % 186.05/186.64 [1640]~E(x16401,x16402)+E(f728(x16401),f728(x16402)) % 186.05/186.64 [1641]~E(x16411,x16412)+E(f670(x16411,x16413),f670(x16412,x16413)) % 186.05/186.64 [1642]~E(x16421,x16422)+E(f670(x16423,x16421),f670(x16423,x16422)) % 186.05/186.64 [1643]~E(x16431,x16432)+E(f598(x16431,x16433,x16434,x16435),f598(x16432,x16433,x16434,x16435)) % 186.05/186.64 [1644]~E(x16441,x16442)+E(f598(x16443,x16441,x16444,x16445),f598(x16443,x16442,x16444,x16445)) % 186.05/186.64 [1645]~E(x16451,x16452)+E(f598(x16453,x16454,x16451,x16455),f598(x16453,x16454,x16452,x16455)) % 186.05/186.64 [1646]~E(x16461,x16462)+E(f598(x16463,x16464,x16465,x16461),f598(x16463,x16464,x16465,x16462)) % 186.05/186.64 [1647]~E(x16471,x16472)+E(f595(x16471,x16473,x16474,x16475),f595(x16472,x16473,x16474,x16475)) % 186.05/186.64 [1648]~E(x16481,x16482)+E(f595(x16483,x16481,x16484,x16485),f595(x16483,x16482,x16484,x16485)) % 186.05/186.64 [1649]~E(x16491,x16492)+E(f595(x16493,x16494,x16491,x16495),f595(x16493,x16494,x16492,x16495)) % 186.05/186.64 [1650]~E(x16501,x16502)+E(f595(x16503,x16504,x16505,x16501),f595(x16503,x16504,x16505,x16502)) % 186.05/186.64 [1651]~E(x16511,x16512)+E(f566(x16511,x16513),f566(x16512,x16513)) % 186.05/186.64 [1652]~E(x16521,x16522)+E(f566(x16523,x16521),f566(x16523,x16522)) % 186.05/186.64 [1653]~E(x16531,x16532)+E(f550(x16531,x16533,x16534),f550(x16532,x16533,x16534)) % 186.05/186.64 [1654]~E(x16541,x16542)+E(f550(x16543,x16541,x16544),f550(x16543,x16542,x16544)) % 186.05/186.64 [1655]~E(x16551,x16552)+E(f550(x16553,x16554,x16551),f550(x16553,x16554,x16552)) % 186.05/186.64 [1656]~E(x16561,x16562)+E(f649(x16561,x16563,x16564,x16565,x16566),f649(x16562,x16563,x16564,x16565,x16566)) % 186.05/186.64 [1657]~E(x16571,x16572)+E(f649(x16573,x16571,x16574,x16575,x16576),f649(x16573,x16572,x16574,x16575,x16576)) % 186.05/186.64 [1658]~E(x16581,x16582)+E(f649(x16583,x16584,x16581,x16585,x16586),f649(x16583,x16584,x16582,x16585,x16586)) % 186.05/186.64 [1659]~E(x16591,x16592)+E(f649(x16593,x16594,x16595,x16591,x16596),f649(x16593,x16594,x16595,x16592,x16596)) % 186.05/186.64 [1660]~E(x16601,x16602)+E(f649(x16603,x16604,x16605,x16606,x16601),f649(x16603,x16604,x16605,x16606,x16602)) % 186.05/186.64 [1661]~E(x16611,x16612)+E(f733(x16611,x16613,x16614,x16615),f733(x16612,x16613,x16614,x16615)) % 186.05/186.64 [1662]~E(x16621,x16622)+E(f733(x16623,x16621,x16624,x16625),f733(x16623,x16622,x16624,x16625)) % 186.05/186.64 [1663]~E(x16631,x16632)+E(f733(x16633,x16634,x16631,x16635),f733(x16633,x16634,x16632,x16635)) % 186.05/186.64 [1664]~E(x16641,x16642)+E(f733(x16643,x16644,x16645,x16641),f733(x16643,x16644,x16645,x16642)) % 186.05/186.64 [1665]~E(x16651,x16652)+E(f290(x16651,x16653,x16654),f290(x16652,x16653,x16654)) % 186.05/186.64 [1666]~E(x16661,x16662)+E(f290(x16663,x16661,x16664),f290(x16663,x16662,x16664)) % 186.05/186.64 [1667]~E(x16671,x16672)+E(f290(x16673,x16674,x16671),f290(x16673,x16674,x16672)) % 186.05/186.64 [1668]~E(x16681,x16682)+E(f455(x16681,x16683),f455(x16682,x16683)) % 186.05/186.64 [1669]~E(x16691,x16692)+E(f455(x16693,x16691),f455(x16693,x16692)) % 186.05/186.64 [1670]~E(x16701,x16702)+E(f532(x16701,x16703,x16704),f532(x16702,x16703,x16704)) % 186.05/186.64 [1671]~E(x16711,x16712)+E(f532(x16713,x16711,x16714),f532(x16713,x16712,x16714)) % 186.05/186.64 [1672]~E(x16721,x16722)+E(f532(x16723,x16724,x16721),f532(x16723,x16724,x16722)) % 186.05/186.64 [1673]~E(x16731,x16732)+E(f470(x16731,x16733,x16734),f470(x16732,x16733,x16734)) % 186.05/186.64 [1674]~E(x16741,x16742)+E(f470(x16743,x16741,x16744),f470(x16743,x16742,x16744)) % 186.05/186.64 [1675]~E(x16751,x16752)+E(f470(x16753,x16754,x16751),f470(x16753,x16754,x16752)) % 186.05/186.64 [1676]~E(x16761,x16762)+E(f498(x16761,x16763,x16764,x16765),f498(x16762,x16763,x16764,x16765)) % 186.05/186.64 [1677]~E(x16771,x16772)+E(f498(x16773,x16771,x16774,x16775),f498(x16773,x16772,x16774,x16775)) % 186.05/186.64 [1678]~E(x16781,x16782)+E(f498(x16783,x16784,x16781,x16785),f498(x16783,x16784,x16782,x16785)) % 186.05/186.64 [1679]~E(x16791,x16792)+E(f498(x16793,x16794,x16795,x16791),f498(x16793,x16794,x16795,x16792)) % 186.05/186.64 [1680]~E(x16801,x16802)+E(f347(x16801,x16803,x16804,x16805),f347(x16802,x16803,x16804,x16805)) % 186.05/186.64 [1681]~E(x16811,x16812)+E(f347(x16813,x16811,x16814,x16815),f347(x16813,x16812,x16814,x16815)) % 186.05/186.64 [1682]~E(x16821,x16822)+E(f347(x16823,x16824,x16821,x16825),f347(x16823,x16824,x16822,x16825)) % 186.05/186.64 [1683]~E(x16831,x16832)+E(f347(x16833,x16834,x16835,x16831),f347(x16833,x16834,x16835,x16832)) % 186.05/186.64 [1684]~E(x16841,x16842)+E(f763(x16841,x16843,x16844),f763(x16842,x16843,x16844)) % 186.05/186.64 [1685]~E(x16851,x16852)+E(f763(x16853,x16851,x16854),f763(x16853,x16852,x16854)) % 186.05/186.64 [1686]~E(x16861,x16862)+E(f763(x16863,x16864,x16861),f763(x16863,x16864,x16862)) % 186.05/186.64 [1687]~E(x16871,x16872)+E(f422(x16871,x16873,x16874,x16875),f422(x16872,x16873,x16874,x16875)) % 186.05/186.64 [1688]~E(x16881,x16882)+E(f422(x16883,x16881,x16884,x16885),f422(x16883,x16882,x16884,x16885)) % 186.05/186.64 [1689]~E(x16891,x16892)+E(f422(x16893,x16894,x16891,x16895),f422(x16893,x16894,x16892,x16895)) % 186.05/186.64 [1690]~E(x16901,x16902)+E(f422(x16903,x16904,x16905,x16901),f422(x16903,x16904,x16905,x16902)) % 186.05/186.64 [1691]~E(x16911,x16912)+E(f630(x16911,x16913,x16914),f630(x16912,x16913,x16914)) % 186.05/186.64 [1692]~E(x16921,x16922)+E(f630(x16923,x16921,x16924),f630(x16923,x16922,x16924)) % 186.05/186.64 [1693]~E(x16931,x16932)+E(f630(x16933,x16934,x16931),f630(x16933,x16934,x16932)) % 186.05/186.64 [1694]~E(x16941,x16942)+E(f499(x16941,x16943,x16944,x16945,x16946,x16947,x16948),f499(x16942,x16943,x16944,x16945,x16946,x16947,x16948)) % 186.05/186.64 [1695]~E(x16951,x16952)+E(f499(x16953,x16951,x16954,x16955,x16956,x16957,x16958),f499(x16953,x16952,x16954,x16955,x16956,x16957,x16958)) % 186.05/186.64 [1696]~E(x16961,x16962)+E(f499(x16963,x16964,x16961,x16965,x16966,x16967,x16968),f499(x16963,x16964,x16962,x16965,x16966,x16967,x16968)) % 186.05/186.64 [1697]~E(x16971,x16972)+E(f499(x16973,x16974,x16975,x16971,x16976,x16977,x16978),f499(x16973,x16974,x16975,x16972,x16976,x16977,x16978)) % 186.05/186.64 [1698]~E(x16981,x16982)+E(f499(x16983,x16984,x16985,x16986,x16981,x16987,x16988),f499(x16983,x16984,x16985,x16986,x16982,x16987,x16988)) % 186.05/186.64 [1699]~E(x16991,x16992)+E(f499(x16993,x16994,x16995,x16996,x16997,x16991,x16998),f499(x16993,x16994,x16995,x16996,x16997,x16992,x16998)) % 186.05/186.64 [1700]~E(x17001,x17002)+E(f499(x17003,x17004,x17005,x17006,x17007,x17008,x17001),f499(x17003,x17004,x17005,x17006,x17007,x17008,x17002)) % 186.05/186.64 [1701]~E(x17011,x17012)+E(f373(x17011,x17013),f373(x17012,x17013)) % 186.05/186.64 [1702]~E(x17021,x17022)+E(f373(x17023,x17021),f373(x17023,x17022)) % 186.05/186.64 [1703]~E(x17031,x17032)+E(f518(x17031,x17033),f518(x17032,x17033)) % 186.05/186.64 [1704]~E(x17041,x17042)+E(f518(x17043,x17041),f518(x17043,x17042)) % 186.05/186.64 [1705]~E(x17051,x17052)+E(f213(x17051,x17053),f213(x17052,x17053)) % 186.05/186.64 [1706]~E(x17061,x17062)+E(f213(x17063,x17061),f213(x17063,x17062)) % 186.05/186.64 [1707]~E(x17071,x17072)+E(f383(x17071,x17073,x17074,x17075,x17076),f383(x17072,x17073,x17074,x17075,x17076)) % 186.05/186.64 [1708]~E(x17081,x17082)+E(f383(x17083,x17081,x17084,x17085,x17086),f383(x17083,x17082,x17084,x17085,x17086)) % 186.05/186.64 [1709]~E(x17091,x17092)+E(f383(x17093,x17094,x17091,x17095,x17096),f383(x17093,x17094,x17092,x17095,x17096)) % 186.05/186.64 [1710]~E(x17101,x17102)+E(f383(x17103,x17104,x17105,x17101,x17106),f383(x17103,x17104,x17105,x17102,x17106)) % 186.05/186.64 [1711]~E(x17111,x17112)+E(f383(x17113,x17114,x17115,x17116,x17111),f383(x17113,x17114,x17115,x17116,x17112)) % 186.05/186.64 [1712]~E(x17121,x17122)+E(f350(x17121,x17123,x17124),f350(x17122,x17123,x17124)) % 186.05/186.64 [1713]~E(x17131,x17132)+E(f350(x17133,x17131,x17134),f350(x17133,x17132,x17134)) % 186.05/186.64 [1714]~E(x17141,x17142)+E(f350(x17143,x17144,x17141),f350(x17143,x17144,x17142)) % 186.05/186.64 [1715]~E(x17151,x17152)+E(f803(x17151,x17153,x17154),f803(x17152,x17153,x17154)) % 186.05/186.64 [1716]~E(x17161,x17162)+E(f803(x17163,x17161,x17164),f803(x17163,x17162,x17164)) % 186.05/186.64 [1717]~E(x17171,x17172)+E(f803(x17173,x17174,x17171),f803(x17173,x17174,x17172)) % 186.05/186.64 [1718]~E(x17181,x17182)+E(f697(x17181,x17183,x17184),f697(x17182,x17183,x17184)) % 186.05/186.64 [1719]~E(x17191,x17192)+E(f697(x17193,x17191,x17194),f697(x17193,x17192,x17194)) % 186.05/186.64 [1720]~E(x17201,x17202)+E(f697(x17203,x17204,x17201),f697(x17203,x17204,x17202)) % 186.05/186.64 [1721]~E(x17211,x17212)+E(f398(x17211,x17213,x17214,x17215),f398(x17212,x17213,x17214,x17215)) % 186.05/186.64 [1722]~E(x17221,x17222)+E(f398(x17223,x17221,x17224,x17225),f398(x17223,x17222,x17224,x17225)) % 186.05/186.64 [1723]~E(x17231,x17232)+E(f398(x17233,x17234,x17231,x17235),f398(x17233,x17234,x17232,x17235)) % 186.05/186.64 [1724]~E(x17241,x17242)+E(f398(x17243,x17244,x17245,x17241),f398(x17243,x17244,x17245,x17242)) % 186.05/186.64 [1725]~E(x17251,x17252)+E(f639(x17251,x17253,x17254),f639(x17252,x17253,x17254)) % 186.05/186.64 [1726]~E(x17261,x17262)+E(f639(x17263,x17261,x17264),f639(x17263,x17262,x17264)) % 186.05/186.64 [1727]~E(x17271,x17272)+E(f639(x17273,x17274,x17271),f639(x17273,x17274,x17272)) % 186.05/186.64 [1728]~E(x17281,x17282)+E(f832(x17281,x17283,x17284),f832(x17282,x17283,x17284)) % 186.05/186.64 [1729]~E(x17291,x17292)+E(f832(x17293,x17291,x17294),f832(x17293,x17292,x17294)) % 186.05/186.64 [1730]~E(x17301,x17302)+E(f832(x17303,x17304,x17301),f832(x17303,x17304,x17302)) % 186.05/186.64 [1731]~E(x17311,x17312)+E(f521(x17311,x17313,x17314),f521(x17312,x17313,x17314)) % 186.05/186.64 [1732]~E(x17321,x17322)+E(f521(x17323,x17321,x17324),f521(x17323,x17322,x17324)) % 186.05/186.64 [1733]~E(x17331,x17332)+E(f521(x17333,x17334,x17331),f521(x17333,x17334,x17332)) % 186.05/186.64 [1734]~E(x17341,x17342)+E(f397(x17341,x17343,x17344),f397(x17342,x17343,x17344)) % 186.05/186.64 [1735]~E(x17351,x17352)+E(f397(x17353,x17351,x17354),f397(x17353,x17352,x17354)) % 186.05/186.64 [1736]~E(x17361,x17362)+E(f397(x17363,x17364,x17361),f397(x17363,x17364,x17362)) % 186.05/186.64 [1737]~E(x17371,x17372)+E(f413(x17371,x17373,x17374,x17375,x17376),f413(x17372,x17373,x17374,x17375,x17376)) % 186.05/186.64 [1738]~E(x17381,x17382)+E(f413(x17383,x17381,x17384,x17385,x17386),f413(x17383,x17382,x17384,x17385,x17386)) % 186.05/186.64 [1739]~E(x17391,x17392)+E(f413(x17393,x17394,x17391,x17395,x17396),f413(x17393,x17394,x17392,x17395,x17396)) % 186.05/186.64 [1740]~E(x17401,x17402)+E(f413(x17403,x17404,x17405,x17401,x17406),f413(x17403,x17404,x17405,x17402,x17406)) % 186.05/186.64 [1741]~E(x17411,x17412)+E(f413(x17413,x17414,x17415,x17416,x17411),f413(x17413,x17414,x17415,x17416,x17412)) % 186.05/186.64 [1742]~E(x17421,x17422)+E(f433(x17421,x17423,x17424,x17425),f433(x17422,x17423,x17424,x17425)) % 186.05/186.64 [1743]~E(x17431,x17432)+E(f433(x17433,x17431,x17434,x17435),f433(x17433,x17432,x17434,x17435)) % 186.05/186.64 [1744]~E(x17441,x17442)+E(f433(x17443,x17444,x17441,x17445),f433(x17443,x17444,x17442,x17445)) % 186.05/186.64 [1745]~E(x17451,x17452)+E(f433(x17453,x17454,x17455,x17451),f433(x17453,x17454,x17455,x17452)) % 186.05/186.64 [1746]~E(x17461,x17462)+E(f444(x17461,x17463),f444(x17462,x17463)) % 186.05/186.64 [1747]~E(x17471,x17472)+E(f444(x17473,x17471),f444(x17473,x17472)) % 186.05/186.64 [1748]~E(x17481,x17482)+E(f544(x17481,x17483,x17484,x17485,x17486,x17487),f544(x17482,x17483,x17484,x17485,x17486,x17487)) % 186.05/186.64 [1749]~E(x17491,x17492)+E(f544(x17493,x17491,x17494,x17495,x17496,x17497),f544(x17493,x17492,x17494,x17495,x17496,x17497)) % 186.05/186.64 [1750]~E(x17501,x17502)+E(f544(x17503,x17504,x17501,x17505,x17506,x17507),f544(x17503,x17504,x17502,x17505,x17506,x17507)) % 186.05/186.64 [1751]~E(x17511,x17512)+E(f544(x17513,x17514,x17515,x17511,x17516,x17517),f544(x17513,x17514,x17515,x17512,x17516,x17517)) % 186.05/186.64 [1752]~E(x17521,x17522)+E(f544(x17523,x17524,x17525,x17526,x17521,x17527),f544(x17523,x17524,x17525,x17526,x17522,x17527)) % 186.05/186.64 [1753]~E(x17531,x17532)+E(f544(x17533,x17534,x17535,x17536,x17537,x17531),f544(x17533,x17534,x17535,x17536,x17537,x17532)) % 186.05/186.64 [1754]~E(x17541,x17542)+E(f448(x17541,x17543),f448(x17542,x17543)) % 186.05/186.64 [1755]~E(x17551,x17552)+E(f448(x17553,x17551),f448(x17553,x17552)) % 186.05/186.64 [1756]~E(x17561,x17562)+E(f627(x17561,x17563,x17564),f627(x17562,x17563,x17564)) % 186.05/186.64 [1757]~E(x17571,x17572)+E(f627(x17573,x17571,x17574),f627(x17573,x17572,x17574)) % 186.05/186.64 [1758]~E(x17581,x17582)+E(f627(x17583,x17584,x17581),f627(x17583,x17584,x17582)) % 186.05/186.64 [1759]~E(x17591,x17592)+E(f816(x17591,x17593,x17594),f816(x17592,x17593,x17594)) % 186.05/186.64 [1760]~E(x17601,x17602)+E(f816(x17603,x17601,x17604),f816(x17603,x17602,x17604)) % 186.05/186.64 [1761]~E(x17611,x17612)+E(f816(x17613,x17614,x17611),f816(x17613,x17614,x17612)) % 186.05/186.64 [1762]~E(x17621,x17622)+E(f578(x17621,x17623,x17624,x17625,x17626,x17627,x17628),f578(x17622,x17623,x17624,x17625,x17626,x17627,x17628)) % 186.05/186.64 [1763]~E(x17631,x17632)+E(f578(x17633,x17631,x17634,x17635,x17636,x17637,x17638),f578(x17633,x17632,x17634,x17635,x17636,x17637,x17638)) % 186.05/186.64 [1764]~E(x17641,x17642)+E(f578(x17643,x17644,x17641,x17645,x17646,x17647,x17648),f578(x17643,x17644,x17642,x17645,x17646,x17647,x17648)) % 186.05/186.64 [1765]~E(x17651,x17652)+E(f578(x17653,x17654,x17655,x17651,x17656,x17657,x17658),f578(x17653,x17654,x17655,x17652,x17656,x17657,x17658)) % 186.05/186.64 [1766]~E(x17661,x17662)+E(f578(x17663,x17664,x17665,x17666,x17661,x17667,x17668),f578(x17663,x17664,x17665,x17666,x17662,x17667,x17668)) % 186.05/186.64 [1767]~E(x17671,x17672)+E(f578(x17673,x17674,x17675,x17676,x17677,x17671,x17678),f578(x17673,x17674,x17675,x17676,x17677,x17672,x17678)) % 186.05/186.64 [1768]~E(x17681,x17682)+E(f578(x17683,x17684,x17685,x17686,x17687,x17688,x17681),f578(x17683,x17684,x17685,x17686,x17687,x17688,x17682)) % 186.05/186.64 [1769]~E(x17691,x17692)+E(f524(x17691,x17693,x17694,x17695,x17696),f524(x17692,x17693,x17694,x17695,x17696)) % 186.05/186.64 [1770]~E(x17701,x17702)+E(f524(x17703,x17701,x17704,x17705,x17706),f524(x17703,x17702,x17704,x17705,x17706)) % 186.05/186.64 [1771]~E(x17711,x17712)+E(f524(x17713,x17714,x17711,x17715,x17716),f524(x17713,x17714,x17712,x17715,x17716)) % 186.05/186.64 [1772]~E(x17721,x17722)+E(f524(x17723,x17724,x17725,x17721,x17726),f524(x17723,x17724,x17725,x17722,x17726)) % 186.05/186.64 [1773]~E(x17731,x17732)+E(f524(x17733,x17734,x17735,x17736,x17731),f524(x17733,x17734,x17735,x17736,x17732)) % 186.05/186.64 [1774]~E(x17741,x17742)+E(f660(x17741,x17743,x17744,x17745,x17746),f660(x17742,x17743,x17744,x17745,x17746)) % 186.05/186.64 [1775]~E(x17751,x17752)+E(f660(x17753,x17751,x17754,x17755,x17756),f660(x17753,x17752,x17754,x17755,x17756)) % 186.05/186.64 [1776]~E(x17761,x17762)+E(f660(x17763,x17764,x17761,x17765,x17766),f660(x17763,x17764,x17762,x17765,x17766)) % 186.05/186.64 [1777]~E(x17771,x17772)+E(f660(x17773,x17774,x17775,x17771,x17776),f660(x17773,x17774,x17775,x17772,x17776)) % 186.05/186.64 [1778]~E(x17781,x17782)+E(f660(x17783,x17784,x17785,x17786,x17781),f660(x17783,x17784,x17785,x17786,x17782)) % 186.05/186.64 [1779]~E(x17791,x17792)+E(f97(x17791,x17793,x17794,x17795),f97(x17792,x17793,x17794,x17795)) % 186.05/186.64 [1780]~E(x17801,x17802)+E(f97(x17803,x17801,x17804,x17805),f97(x17803,x17802,x17804,x17805)) % 186.05/186.64 [1781]~E(x17811,x17812)+E(f97(x17813,x17814,x17811,x17815),f97(x17813,x17814,x17812,x17815)) % 186.05/186.64 [1782]~E(x17821,x17822)+E(f97(x17823,x17824,x17825,x17821),f97(x17823,x17824,x17825,x17822)) % 186.05/186.64 [1783]~E(x17831,x17832)+E(f664(x17831,x17833,x17834,x17835,x17836,x17837,x17838),f664(x17832,x17833,x17834,x17835,x17836,x17837,x17838)) % 186.05/186.64 [1784]~E(x17841,x17842)+E(f664(x17843,x17841,x17844,x17845,x17846,x17847,x17848),f664(x17843,x17842,x17844,x17845,x17846,x17847,x17848)) % 186.05/186.64 [1785]~E(x17851,x17852)+E(f664(x17853,x17854,x17851,x17855,x17856,x17857,x17858),f664(x17853,x17854,x17852,x17855,x17856,x17857,x17858)) % 186.05/186.64 [1786]~E(x17861,x17862)+E(f664(x17863,x17864,x17865,x17861,x17866,x17867,x17868),f664(x17863,x17864,x17865,x17862,x17866,x17867,x17868)) % 186.05/186.64 [1787]~E(x17871,x17872)+E(f664(x17873,x17874,x17875,x17876,x17871,x17877,x17878),f664(x17873,x17874,x17875,x17876,x17872,x17877,x17878)) % 186.05/186.64 [1788]~E(x17881,x17882)+E(f664(x17883,x17884,x17885,x17886,x17887,x17881,x17888),f664(x17883,x17884,x17885,x17886,x17887,x17882,x17888)) % 186.05/186.64 [1789]~E(x17891,x17892)+E(f664(x17893,x17894,x17895,x17896,x17897,x17898,x17891),f664(x17893,x17894,x17895,x17896,x17897,x17898,x17892)) % 186.05/186.64 [1790]~E(x17901,x17902)+E(f393(x17901,x17903),f393(x17902,x17903)) % 186.05/186.64 [1791]~E(x17911,x17912)+E(f393(x17913,x17911),f393(x17913,x17912)) % 186.05/186.64 [1792]~E(x17921,x17922)+E(f679(x17921,x17923,x17924,x17925,x17926,x17927,x17928,x17929),f679(x17922,x17923,x17924,x17925,x17926,x17927,x17928,x17929)) % 186.05/186.64 [1793]~E(x17931,x17932)+E(f679(x17933,x17931,x17934,x17935,x17936,x17937,x17938,x17939),f679(x17933,x17932,x17934,x17935,x17936,x17937,x17938,x17939)) % 186.05/186.64 [1794]~E(x17941,x17942)+E(f679(x17943,x17944,x17941,x17945,x17946,x17947,x17948,x17949),f679(x17943,x17944,x17942,x17945,x17946,x17947,x17948,x17949)) % 186.05/186.64 [1795]~E(x17951,x17952)+E(f679(x17953,x17954,x17955,x17951,x17956,x17957,x17958,x17959),f679(x17953,x17954,x17955,x17952,x17956,x17957,x17958,x17959)) % 186.05/186.64 [1796]~E(x17961,x17962)+E(f679(x17963,x17964,x17965,x17966,x17961,x17967,x17968,x17969),f679(x17963,x17964,x17965,x17966,x17962,x17967,x17968,x17969)) % 186.05/186.64 [1797]~E(x17971,x17972)+E(f679(x17973,x17974,x17975,x17976,x17977,x17971,x17978,x17979),f679(x17973,x17974,x17975,x17976,x17977,x17972,x17978,x17979)) % 186.05/186.64 [1798]~E(x17981,x17982)+E(f679(x17983,x17984,x17985,x17986,x17987,x17988,x17981,x17989),f679(x17983,x17984,x17985,x17986,x17987,x17988,x17982,x17989)) % 186.05/186.64 [1799]~E(x17991,x17992)+E(f679(x17993,x17994,x17995,x17996,x17997,x17998,x17999,x17991),f679(x17993,x17994,x17995,x17996,x17997,x17998,x17999,x17992)) % 186.05/186.64 [1800]~E(x18001,x18002)+E(f224(x18001,x18003,x18004),f224(x18002,x18003,x18004)) % 186.05/186.64 [1801]~E(x18011,x18012)+E(f224(x18013,x18011,x18014),f224(x18013,x18012,x18014)) % 186.05/186.64 [1802]~E(x18021,x18022)+E(f224(x18023,x18024,x18021),f224(x18023,x18024,x18022)) % 186.05/186.64 [1803]~E(x18031,x18032)+E(f453(x18031,x18033,x18034,x18035,x18036,x18037,x18038),f453(x18032,x18033,x18034,x18035,x18036,x18037,x18038)) % 186.05/186.64 [1804]~E(x18041,x18042)+E(f453(x18043,x18041,x18044,x18045,x18046,x18047,x18048),f453(x18043,x18042,x18044,x18045,x18046,x18047,x18048)) % 186.05/186.64 [1805]~E(x18051,x18052)+E(f453(x18053,x18054,x18051,x18055,x18056,x18057,x18058),f453(x18053,x18054,x18052,x18055,x18056,x18057,x18058)) % 186.05/186.64 [1806]~E(x18061,x18062)+E(f453(x18063,x18064,x18065,x18061,x18066,x18067,x18068),f453(x18063,x18064,x18065,x18062,x18066,x18067,x18068)) % 186.05/186.64 [1807]~E(x18071,x18072)+E(f453(x18073,x18074,x18075,x18076,x18071,x18077,x18078),f453(x18073,x18074,x18075,x18076,x18072,x18077,x18078)) % 186.05/186.64 [1808]~E(x18081,x18082)+E(f453(x18083,x18084,x18085,x18086,x18087,x18081,x18088),f453(x18083,x18084,x18085,x18086,x18087,x18082,x18088)) % 186.05/186.64 [1809]~E(x18091,x18092)+E(f453(x18093,x18094,x18095,x18096,x18097,x18098,x18091),f453(x18093,x18094,x18095,x18096,x18097,x18098,x18092)) % 186.05/186.64 [1810]~E(x18101,x18102)+E(f270(x18101,x18103),f270(x18102,x18103)) % 186.05/186.64 [1811]~E(x18111,x18112)+E(f270(x18113,x18111),f270(x18113,x18112)) % 186.05/186.64 [1812]~E(x18121,x18122)+E(f411(x18121,x18123,x18124,x18125),f411(x18122,x18123,x18124,x18125)) % 186.05/186.64 [1813]~E(x18131,x18132)+E(f411(x18133,x18131,x18134,x18135),f411(x18133,x18132,x18134,x18135)) % 186.05/186.64 [1814]~E(x18141,x18142)+E(f411(x18143,x18144,x18141,x18145),f411(x18143,x18144,x18142,x18145)) % 186.05/186.64 [1815]~E(x18151,x18152)+E(f411(x18153,x18154,x18155,x18151),f411(x18153,x18154,x18155,x18152)) % 186.05/186.64 [1816]~E(x18161,x18162)+E(f468(x18161,x18163,x18164),f468(x18162,x18163,x18164)) % 186.05/186.64 [1817]~E(x18171,x18172)+E(f468(x18173,x18171,x18174),f468(x18173,x18172,x18174)) % 186.05/186.64 [1818]~E(x18181,x18182)+E(f468(x18183,x18184,x18181),f468(x18183,x18184,x18182)) % 186.05/186.64 [1819]~E(x18191,x18192)+E(f287(x18191,x18193,x18194),f287(x18192,x18193,x18194)) % 186.05/186.64 [1820]~E(x18201,x18202)+E(f287(x18203,x18201,x18204),f287(x18203,x18202,x18204)) % 186.05/186.64 [1821]~E(x18211,x18212)+E(f287(x18213,x18214,x18211),f287(x18213,x18214,x18212)) % 186.05/186.64 [1822]~E(x18221,x18222)+E(f474(x18221,x18223,x18224),f474(x18222,x18223,x18224)) % 186.05/186.64 [1823]~E(x18231,x18232)+E(f474(x18233,x18231,x18234),f474(x18233,x18232,x18234)) % 186.05/186.64 [1824]~E(x18241,x18242)+E(f474(x18243,x18244,x18241),f474(x18243,x18244,x18242)) % 186.05/186.64 [1825]~E(x18251,x18252)+E(f559(x18251,x18253),f559(x18252,x18253)) % 186.05/186.64 [1826]~E(x18261,x18262)+E(f559(x18263,x18261),f559(x18263,x18262)) % 186.05/186.64 [1827]~E(x18271,x18272)+E(f579(x18271),f579(x18272)) % 186.05/186.64 [1828]~E(x18281,x18282)+E(f478(x18281,x18283,x18284,x18285,x18286),f478(x18282,x18283,x18284,x18285,x18286)) % 186.05/186.64 [1829]~E(x18291,x18292)+E(f478(x18293,x18291,x18294,x18295,x18296),f478(x18293,x18292,x18294,x18295,x18296)) % 186.05/186.64 [1830]~E(x18301,x18302)+E(f478(x18303,x18304,x18301,x18305,x18306),f478(x18303,x18304,x18302,x18305,x18306)) % 186.05/186.64 [1831]~E(x18311,x18312)+E(f478(x18313,x18314,x18315,x18311,x18316),f478(x18313,x18314,x18315,x18312,x18316)) % 186.05/186.64 [1832]~E(x18321,x18322)+E(f478(x18323,x18324,x18325,x18326,x18321),f478(x18323,x18324,x18325,x18326,x18322)) % 186.05/186.64 [1833]~E(x18331,x18332)+E(f399(x18331,x18333,x18334,x18335),f399(x18332,x18333,x18334,x18335)) % 186.05/186.64 [1834]~E(x18341,x18342)+E(f399(x18343,x18341,x18344,x18345),f399(x18343,x18342,x18344,x18345)) % 186.05/186.64 [1835]~E(x18351,x18352)+E(f399(x18353,x18354,x18351,x18355),f399(x18353,x18354,x18352,x18355)) % 186.05/186.64 [1836]~E(x18361,x18362)+E(f399(x18363,x18364,x18365,x18361),f399(x18363,x18364,x18365,x18362)) % 186.05/186.64 [1837]~E(x18371,x18372)+E(f839(x18371,x18373),f839(x18372,x18373)) % 186.05/186.64 [1838]~E(x18381,x18382)+E(f839(x18383,x18381),f839(x18383,x18382)) % 186.05/186.64 [1839]~E(x18391,x18392)+E(f361(x18391,x18393,x18394,x18395),f361(x18392,x18393,x18394,x18395)) % 186.05/186.64 [1840]~E(x18401,x18402)+E(f361(x18403,x18401,x18404,x18405),f361(x18403,x18402,x18404,x18405)) % 186.05/186.64 [1841]~E(x18411,x18412)+E(f361(x18413,x18414,x18411,x18415),f361(x18413,x18414,x18412,x18415)) % 186.05/186.64 [1842]~E(x18421,x18422)+E(f361(x18423,x18424,x18425,x18421),f361(x18423,x18424,x18425,x18422)) % 186.05/186.64 [1843]~E(x18431,x18432)+E(f500(x18431,x18433,x18434,x18435,x18436,x18437,x18438),f500(x18432,x18433,x18434,x18435,x18436,x18437,x18438)) % 186.05/186.64 [1844]~E(x18441,x18442)+E(f500(x18443,x18441,x18444,x18445,x18446,x18447,x18448),f500(x18443,x18442,x18444,x18445,x18446,x18447,x18448)) % 186.05/186.64 [1845]~E(x18451,x18452)+E(f500(x18453,x18454,x18451,x18455,x18456,x18457,x18458),f500(x18453,x18454,x18452,x18455,x18456,x18457,x18458)) % 186.05/186.64 [1846]~E(x18461,x18462)+E(f500(x18463,x18464,x18465,x18461,x18466,x18467,x18468),f500(x18463,x18464,x18465,x18462,x18466,x18467,x18468)) % 186.05/186.64 [1847]~E(x18471,x18472)+E(f500(x18473,x18474,x18475,x18476,x18471,x18477,x18478),f500(x18473,x18474,x18475,x18476,x18472,x18477,x18478)) % 186.05/186.64 [1848]~E(x18481,x18482)+E(f500(x18483,x18484,x18485,x18486,x18487,x18481,x18488),f500(x18483,x18484,x18485,x18486,x18487,x18482,x18488)) % 186.05/186.64 [1849]~E(x18491,x18492)+E(f500(x18493,x18494,x18495,x18496,x18497,x18498,x18491),f500(x18493,x18494,x18495,x18496,x18497,x18498,x18492)) % 186.05/186.64 [1850]~E(x18501,x18502)+E(f574(x18501,x18503,x18504,x18505,x18506,x18507,x18508,x18509),f574(x18502,x18503,x18504,x18505,x18506,x18507,x18508,x18509)) % 186.05/186.64 [1851]~E(x18511,x18512)+E(f574(x18513,x18511,x18514,x18515,x18516,x18517,x18518,x18519),f574(x18513,x18512,x18514,x18515,x18516,x18517,x18518,x18519)) % 186.05/186.64 [1852]~E(x18521,x18522)+E(f574(x18523,x18524,x18521,x18525,x18526,x18527,x18528,x18529),f574(x18523,x18524,x18522,x18525,x18526,x18527,x18528,x18529)) % 186.05/186.64 [1853]~E(x18531,x18532)+E(f574(x18533,x18534,x18535,x18531,x18536,x18537,x18538,x18539),f574(x18533,x18534,x18535,x18532,x18536,x18537,x18538,x18539)) % 186.05/186.64 [1854]~E(x18541,x18542)+E(f574(x18543,x18544,x18545,x18546,x18541,x18547,x18548,x18549),f574(x18543,x18544,x18545,x18546,x18542,x18547,x18548,x18549)) % 186.05/186.64 [1855]~E(x18551,x18552)+E(f574(x18553,x18554,x18555,x18556,x18557,x18551,x18558,x18559),f574(x18553,x18554,x18555,x18556,x18557,x18552,x18558,x18559)) % 186.05/186.64 [1856]~E(x18561,x18562)+E(f574(x18563,x18564,x18565,x18566,x18567,x18568,x18561,x18569),f574(x18563,x18564,x18565,x18566,x18567,x18568,x18562,x18569)) % 186.05/186.64 [1857]~E(x18571,x18572)+E(f574(x18573,x18574,x18575,x18576,x18577,x18578,x18579,x18571),f574(x18573,x18574,x18575,x18576,x18577,x18578,x18579,x18572)) % 186.05/186.64 [1858]~E(x18581,x18582)+E(f370(x18581,x18583),f370(x18582,x18583)) % 186.05/186.64 [1859]~E(x18591,x18592)+E(f370(x18593,x18591),f370(x18593,x18592)) % 186.05/186.64 [1860]~E(x18601,x18602)+E(f288(x18601,x18603,x18604),f288(x18602,x18603,x18604)) % 186.05/186.64 [1861]~E(x18611,x18612)+E(f288(x18613,x18611,x18614),f288(x18613,x18612,x18614)) % 186.05/186.64 [1862]~E(x18621,x18622)+E(f288(x18623,x18624,x18621),f288(x18623,x18624,x18622)) % 186.05/186.64 [1863]~E(x18631,x18632)+E(f247(x18631,x18633,x18634),f247(x18632,x18633,x18634)) % 186.05/186.64 [1864]~E(x18641,x18642)+E(f247(x18643,x18641,x18644),f247(x18643,x18642,x18644)) % 186.05/186.64 [1865]~E(x18651,x18652)+E(f247(x18653,x18654,x18651),f247(x18653,x18654,x18652)) % 186.05/186.64 [1866]~E(x18661,x18662)+E(f572(x18661,x18663,x18664),f572(x18662,x18663,x18664)) % 186.05/186.64 [1867]~E(x18671,x18672)+E(f572(x18673,x18671,x18674),f572(x18673,x18672,x18674)) % 186.05/186.64 [1868]~E(x18681,x18682)+E(f572(x18683,x18684,x18681),f572(x18683,x18684,x18682)) % 186.05/186.64 [1869]~E(x18691,x18692)+E(f531(x18691,x18693,x18694,x18695,x18696),f531(x18692,x18693,x18694,x18695,x18696)) % 186.05/186.64 [1870]~E(x18701,x18702)+E(f531(x18703,x18701,x18704,x18705,x18706),f531(x18703,x18702,x18704,x18705,x18706)) % 186.05/186.64 [1871]~E(x18711,x18712)+E(f531(x18713,x18714,x18711,x18715,x18716),f531(x18713,x18714,x18712,x18715,x18716)) % 186.05/186.64 [1872]~E(x18721,x18722)+E(f531(x18723,x18724,x18725,x18721,x18726),f531(x18723,x18724,x18725,x18722,x18726)) % 186.05/186.64 [1873]~E(x18731,x18732)+E(f531(x18733,x18734,x18735,x18736,x18731),f531(x18733,x18734,x18735,x18736,x18732)) % 186.05/186.64 [1874]~E(x18741,x18742)+E(f417(x18741,x18743,x18744,x18745,x18746),f417(x18742,x18743,x18744,x18745,x18746)) % 186.05/186.64 [1875]~E(x18751,x18752)+E(f417(x18753,x18751,x18754,x18755,x18756),f417(x18753,x18752,x18754,x18755,x18756)) % 186.05/186.64 [1876]~E(x18761,x18762)+E(f417(x18763,x18764,x18761,x18765,x18766),f417(x18763,x18764,x18762,x18765,x18766)) % 186.05/186.64 [1877]~E(x18771,x18772)+E(f417(x18773,x18774,x18775,x18771,x18776),f417(x18773,x18774,x18775,x18772,x18776)) % 186.05/186.64 [1878]~E(x18781,x18782)+E(f417(x18783,x18784,x18785,x18786,x18781),f417(x18783,x18784,x18785,x18786,x18782)) % 186.05/186.64 [1879]~E(x18791,x18792)+E(f419(x18791,x18793,x18794),f419(x18792,x18793,x18794)) % 186.05/186.64 [1880]~E(x18801,x18802)+E(f419(x18803,x18801,x18804),f419(x18803,x18802,x18804)) % 186.05/186.64 [1881]~E(x18811,x18812)+E(f419(x18813,x18814,x18811),f419(x18813,x18814,x18812)) % 186.05/186.64 [1882]~E(x18821,x18822)+E(f387(x18821,x18823,x18824,x18825,x18826),f387(x18822,x18823,x18824,x18825,x18826)) % 186.05/186.64 [1883]~E(x18831,x18832)+E(f387(x18833,x18831,x18834,x18835,x18836),f387(x18833,x18832,x18834,x18835,x18836)) % 186.05/186.64 [1884]~E(x18841,x18842)+E(f387(x18843,x18844,x18841,x18845,x18846),f387(x18843,x18844,x18842,x18845,x18846)) % 186.05/186.64 [1885]~E(x18851,x18852)+E(f387(x18853,x18854,x18855,x18851,x18856),f387(x18853,x18854,x18855,x18852,x18856)) % 186.05/186.64 [1886]~E(x18861,x18862)+E(f387(x18863,x18864,x18865,x18866,x18861),f387(x18863,x18864,x18865,x18866,x18862)) % 186.05/186.64 [1887]~E(x18871,x18872)+E(f327(x18871,x18873,x18874),f327(x18872,x18873,x18874)) % 186.05/186.64 [1888]~E(x18881,x18882)+E(f327(x18883,x18881,x18884),f327(x18883,x18882,x18884)) % 186.05/186.64 [1889]~E(x18891,x18892)+E(f327(x18893,x18894,x18891),f327(x18893,x18894,x18892)) % 186.05/186.64 [1890]~E(x18901,x18902)+E(f469(x18901,x18903,x18904),f469(x18902,x18903,x18904)) % 186.05/186.64 [1891]~E(x18911,x18912)+E(f469(x18913,x18911,x18914),f469(x18913,x18912,x18914)) % 186.05/186.64 [1892]~E(x18921,x18922)+E(f469(x18923,x18924,x18921),f469(x18923,x18924,x18922)) % 186.05/186.64 [1893]~E(x18931,x18932)+E(f790(x18931,x18933),f790(x18932,x18933)) % 186.05/186.64 [1894]~E(x18941,x18942)+E(f790(x18943,x18941),f790(x18943,x18942)) % 186.05/186.64 [1895]~E(x18951,x18952)+E(f717(x18951,x18953,x18954,x18955),f717(x18952,x18953,x18954,x18955)) % 186.05/186.64 [1896]~E(x18961,x18962)+E(f717(x18963,x18961,x18964,x18965),f717(x18963,x18962,x18964,x18965)) % 186.05/186.64 [1897]~E(x18971,x18972)+E(f717(x18973,x18974,x18971,x18975),f717(x18973,x18974,x18972,x18975)) % 186.05/186.64 [1898]~E(x18981,x18982)+E(f717(x18983,x18984,x18985,x18981),f717(x18983,x18984,x18985,x18982)) % 186.05/186.64 [1899]~E(x18991,x18992)+E(f692(x18991,x18993,x18994,x18995,x18996,x18997,x18998),f692(x18992,x18993,x18994,x18995,x18996,x18997,x18998)) % 186.05/186.64 [1900]~E(x19001,x19002)+E(f692(x19003,x19001,x19004,x19005,x19006,x19007,x19008),f692(x19003,x19002,x19004,x19005,x19006,x19007,x19008)) % 186.05/186.64 [1901]~E(x19011,x19012)+E(f692(x19013,x19014,x19011,x19015,x19016,x19017,x19018),f692(x19013,x19014,x19012,x19015,x19016,x19017,x19018)) % 186.05/186.64 [1902]~E(x19021,x19022)+E(f692(x19023,x19024,x19025,x19021,x19026,x19027,x19028),f692(x19023,x19024,x19025,x19022,x19026,x19027,x19028)) % 186.05/186.64 [1903]~E(x19031,x19032)+E(f692(x19033,x19034,x19035,x19036,x19031,x19037,x19038),f692(x19033,x19034,x19035,x19036,x19032,x19037,x19038)) % 186.05/186.64 [1904]~E(x19041,x19042)+E(f692(x19043,x19044,x19045,x19046,x19047,x19041,x19048),f692(x19043,x19044,x19045,x19046,x19047,x19042,x19048)) % 186.05/186.64 [1905]~E(x19051,x19052)+E(f692(x19053,x19054,x19055,x19056,x19057,x19058,x19051),f692(x19053,x19054,x19055,x19056,x19057,x19058,x19052)) % 186.05/186.64 [1906]~E(x19061,x19062)+E(f264(x19061),f264(x19062)) % 186.05/186.64 [1907]~E(x19071,x19072)+E(f354(x19071,x19073),f354(x19072,x19073)) % 186.05/186.64 [1908]~E(x19081,x19082)+E(f354(x19083,x19081),f354(x19083,x19082)) % 186.05/186.64 [1909]~E(x19091,x19092)+E(f669(x19091,x19093,x19094,x19095,x19096,x19097,x19098),f669(x19092,x19093,x19094,x19095,x19096,x19097,x19098)) % 186.05/186.64 [1910]~E(x19101,x19102)+E(f669(x19103,x19101,x19104,x19105,x19106,x19107,x19108),f669(x19103,x19102,x19104,x19105,x19106,x19107,x19108)) % 186.05/186.64 [1911]~E(x19111,x19112)+E(f669(x19113,x19114,x19111,x19115,x19116,x19117,x19118),f669(x19113,x19114,x19112,x19115,x19116,x19117,x19118)) % 186.05/186.64 [1912]~E(x19121,x19122)+E(f669(x19123,x19124,x19125,x19121,x19126,x19127,x19128),f669(x19123,x19124,x19125,x19122,x19126,x19127,x19128)) % 186.05/186.64 [1913]~E(x19131,x19132)+E(f669(x19133,x19134,x19135,x19136,x19131,x19137,x19138),f669(x19133,x19134,x19135,x19136,x19132,x19137,x19138)) % 186.05/186.64 [1914]~E(x19141,x19142)+E(f669(x19143,x19144,x19145,x19146,x19147,x19141,x19148),f669(x19143,x19144,x19145,x19146,x19147,x19142,x19148)) % 186.05/186.64 [1915]~E(x19151,x19152)+E(f669(x19153,x19154,x19155,x19156,x19157,x19158,x19151),f669(x19153,x19154,x19155,x19156,x19157,x19158,x19152)) % 186.05/186.64 [1916]~E(x19161,x19162)+E(f19(x19161,x19163,x19164,x19165),f19(x19162,x19163,x19164,x19165)) % 186.05/186.64 [1917]~E(x19171,x19172)+E(f19(x19173,x19171,x19174,x19175),f19(x19173,x19172,x19174,x19175)) % 186.05/186.64 [1918]~E(x19181,x19182)+E(f19(x19183,x19184,x19181,x19185),f19(x19183,x19184,x19182,x19185)) % 186.05/186.64 [1919]~E(x19191,x19192)+E(f19(x19193,x19194,x19195,x19191),f19(x19193,x19194,x19195,x19192)) % 186.05/186.64 [1920]~E(x19201,x19202)+E(f219(x19201,x19203,x19204,x19205,x19206),f219(x19202,x19203,x19204,x19205,x19206)) % 186.05/186.64 [1921]~E(x19211,x19212)+E(f219(x19213,x19211,x19214,x19215,x19216),f219(x19213,x19212,x19214,x19215,x19216)) % 186.05/186.64 [1922]~E(x19221,x19222)+E(f219(x19223,x19224,x19221,x19225,x19226),f219(x19223,x19224,x19222,x19225,x19226)) % 186.05/186.64 [1923]~E(x19231,x19232)+E(f219(x19233,x19234,x19235,x19231,x19236),f219(x19233,x19234,x19235,x19232,x19236)) % 186.05/186.64 [1924]~E(x19241,x19242)+E(f219(x19243,x19244,x19245,x19246,x19241),f219(x19243,x19244,x19245,x19246,x19242)) % 186.05/186.64 [1925]~E(x19251,x19252)+E(f745(x19251,x19253,x19254,x19255),f745(x19252,x19253,x19254,x19255)) % 186.05/186.64 [1926]~E(x19261,x19262)+E(f745(x19263,x19261,x19264,x19265),f745(x19263,x19262,x19264,x19265)) % 186.05/186.64 [1927]~E(x19271,x19272)+E(f745(x19273,x19274,x19271,x19275),f745(x19273,x19274,x19272,x19275)) % 186.05/186.64 [1928]~E(x19281,x19282)+E(f745(x19283,x19284,x19285,x19281),f745(x19283,x19284,x19285,x19282)) % 186.05/186.64 [1929]~E(x19291,x19292)+E(f731(x19291,x19293,x19294),f731(x19292,x19293,x19294)) % 186.05/186.64 [1930]~E(x19301,x19302)+E(f731(x19303,x19301,x19304),f731(x19303,x19302,x19304)) % 186.05/186.64 [1931]~E(x19311,x19312)+E(f731(x19313,x19314,x19311),f731(x19313,x19314,x19312)) % 186.05/186.64 [1932]~E(x19321,x19322)+E(f197(x19321),f197(x19322)) % 186.05/186.64 [1933]~E(x19331,x19332)+E(f759(x19331,x19333,x19334),f759(x19332,x19333,x19334)) % 186.05/186.64 [1934]~E(x19341,x19342)+E(f759(x19343,x19341,x19344),f759(x19343,x19342,x19344)) % 186.05/186.64 [1935]~E(x19351,x19352)+E(f759(x19353,x19354,x19351),f759(x19353,x19354,x19352)) % 186.05/186.64 [1936]~E(x19361,x19362)+E(f195(x19361),f195(x19362)) % 186.05/186.64 [1937]~E(x19371,x19372)+E(f672(x19371,x19373,x19374),f672(x19372,x19373,x19374)) % 186.05/186.64 [1938]~E(x19381,x19382)+E(f672(x19383,x19381,x19384),f672(x19383,x19382,x19384)) % 186.05/186.64 [1939]~E(x19391,x19392)+E(f672(x19393,x19394,x19391),f672(x19393,x19394,x19392)) % 186.05/186.64 [1940]~E(x19401,x19402)+E(f624(x19401,x19403,x19404,x19405),f624(x19402,x19403,x19404,x19405)) % 186.05/186.64 [1941]~E(x19411,x19412)+E(f624(x19413,x19411,x19414,x19415),f624(x19413,x19412,x19414,x19415)) % 186.05/186.64 [1942]~E(x19421,x19422)+E(f624(x19423,x19424,x19421,x19425),f624(x19423,x19424,x19422,x19425)) % 186.05/186.64 [1943]~E(x19431,x19432)+E(f624(x19433,x19434,x19435,x19431),f624(x19433,x19434,x19435,x19432)) % 186.05/186.64 [1944]~E(x19441,x19442)+E(f392(x19441,x19443,x19444,x19445,x19446),f392(x19442,x19443,x19444,x19445,x19446)) % 186.05/186.64 [1945]~E(x19451,x19452)+E(f392(x19453,x19451,x19454,x19455,x19456),f392(x19453,x19452,x19454,x19455,x19456)) % 186.05/186.64 [1946]~E(x19461,x19462)+E(f392(x19463,x19464,x19461,x19465,x19466),f392(x19463,x19464,x19462,x19465,x19466)) % 186.05/186.64 [1947]~E(x19471,x19472)+E(f392(x19473,x19474,x19475,x19471,x19476),f392(x19473,x19474,x19475,x19472,x19476)) % 186.05/186.64 [1948]~E(x19481,x19482)+E(f392(x19483,x19484,x19485,x19486,x19481),f392(x19483,x19484,x19485,x19486,x19482)) % 186.05/186.64 [1949]~E(x19491,x19492)+E(f449(x19491),f449(x19492)) % 186.05/186.64 [1950]~E(x19501,x19502)+E(f546(x19501,x19503,x19504,x19505,x19506),f546(x19502,x19503,x19504,x19505,x19506)) % 186.05/186.64 [1951]~E(x19511,x19512)+E(f546(x19513,x19511,x19514,x19515,x19516),f546(x19513,x19512,x19514,x19515,x19516)) % 186.05/186.64 [1952]~E(x19521,x19522)+E(f546(x19523,x19524,x19521,x19525,x19526),f546(x19523,x19524,x19522,x19525,x19526)) % 186.05/186.64 [1953]~E(x19531,x19532)+E(f546(x19533,x19534,x19535,x19531,x19536),f546(x19533,x19534,x19535,x19532,x19536)) % 186.05/186.64 [1954]~E(x19541,x19542)+E(f546(x19543,x19544,x19545,x19546,x19541),f546(x19543,x19544,x19545,x19546,x19542)) % 186.05/186.64 [1955]~E(x19551,x19552)+E(f753(x19551,x19553,x19554,x19555,x19556),f753(x19552,x19553,x19554,x19555,x19556)) % 186.05/186.64 [1956]~E(x19561,x19562)+E(f753(x19563,x19561,x19564,x19565,x19566),f753(x19563,x19562,x19564,x19565,x19566)) % 186.05/186.64 [1957]~E(x19571,x19572)+E(f753(x19573,x19574,x19571,x19575,x19576),f753(x19573,x19574,x19572,x19575,x19576)) % 186.05/186.64 [1958]~E(x19581,x19582)+E(f753(x19583,x19584,x19585,x19581,x19586),f753(x19583,x19584,x19585,x19582,x19586)) % 186.05/186.64 [1959]~E(x19591,x19592)+E(f753(x19593,x19594,x19595,x19596,x19591),f753(x19593,x19594,x19595,x19596,x19592)) % 186.05/186.64 [1960]~E(x19601,x19602)+E(f436(x19601,x19603,x19604,x19605),f436(x19602,x19603,x19604,x19605)) % 186.05/186.64 [1961]~E(x19611,x19612)+E(f436(x19613,x19611,x19614,x19615),f436(x19613,x19612,x19614,x19615)) % 186.05/186.64 [1962]~E(x19621,x19622)+E(f436(x19623,x19624,x19621,x19625),f436(x19623,x19624,x19622,x19625)) % 186.05/186.64 [1963]~E(x19631,x19632)+E(f436(x19633,x19634,x19635,x19631),f436(x19633,x19634,x19635,x19632)) % 186.05/186.64 [1964]~E(x19641,x19642)+E(f675(x19641,x19643,x19644),f675(x19642,x19643,x19644)) % 186.05/186.64 [1965]~E(x19651,x19652)+E(f675(x19653,x19651,x19654),f675(x19653,x19652,x19654)) % 186.05/186.64 [1966]~E(x19661,x19662)+E(f675(x19663,x19664,x19661),f675(x19663,x19664,x19662)) % 186.05/186.64 [1967]~E(x19671,x19672)+E(f741(x19671,x19673,x19674,x19675,x19676),f741(x19672,x19673,x19674,x19675,x19676)) % 186.05/186.64 [1968]~E(x19681,x19682)+E(f741(x19683,x19681,x19684,x19685,x19686),f741(x19683,x19682,x19684,x19685,x19686)) % 186.05/186.64 [1969]~E(x19691,x19692)+E(f741(x19693,x19694,x19691,x19695,x19696),f741(x19693,x19694,x19692,x19695,x19696)) % 186.05/186.64 [1970]~E(x19701,x19702)+E(f741(x19703,x19704,x19705,x19701,x19706),f741(x19703,x19704,x19705,x19702,x19706)) % 186.05/186.64 [1971]~E(x19711,x19712)+E(f741(x19713,x19714,x19715,x19716,x19711),f741(x19713,x19714,x19715,x19716,x19712)) % 186.05/186.64 [1972]~E(x19721,x19722)+E(f338(x19721),f338(x19722)) % 186.05/186.64 [1973]~E(x19731,x19732)+E(f509(x19731,x19733,x19734,x19735,x19736,x19737,x19738),f509(x19732,x19733,x19734,x19735,x19736,x19737,x19738)) % 186.05/186.64 [1974]~E(x19741,x19742)+E(f509(x19743,x19741,x19744,x19745,x19746,x19747,x19748),f509(x19743,x19742,x19744,x19745,x19746,x19747,x19748)) % 186.05/186.64 [1975]~E(x19751,x19752)+E(f509(x19753,x19754,x19751,x19755,x19756,x19757,x19758),f509(x19753,x19754,x19752,x19755,x19756,x19757,x19758)) % 186.05/186.64 [1976]~E(x19761,x19762)+E(f509(x19763,x19764,x19765,x19761,x19766,x19767,x19768),f509(x19763,x19764,x19765,x19762,x19766,x19767,x19768)) % 186.05/186.64 [1977]~E(x19771,x19772)+E(f509(x19773,x19774,x19775,x19776,x19771,x19777,x19778),f509(x19773,x19774,x19775,x19776,x19772,x19777,x19778)) % 186.05/186.64 [1978]~E(x19781,x19782)+E(f509(x19783,x19784,x19785,x19786,x19787,x19781,x19788),f509(x19783,x19784,x19785,x19786,x19787,x19782,x19788)) % 186.05/186.64 [1979]~E(x19791,x19792)+E(f509(x19793,x19794,x19795,x19796,x19797,x19798,x19791),f509(x19793,x19794,x19795,x19796,x19797,x19798,x19792)) % 186.05/186.64 [1980]~E(x19801,x19802)+E(f205(x19801,x19803,x19804,x19805),f205(x19802,x19803,x19804,x19805)) % 186.05/186.64 [1981]~E(x19811,x19812)+E(f205(x19813,x19811,x19814,x19815),f205(x19813,x19812,x19814,x19815)) % 186.05/186.64 [1982]~E(x19821,x19822)+E(f205(x19823,x19824,x19821,x19825),f205(x19823,x19824,x19822,x19825)) % 186.05/186.64 [1983]~E(x19831,x19832)+E(f205(x19833,x19834,x19835,x19831),f205(x19833,x19834,x19835,x19832)) % 186.05/186.64 [1984]~E(x19841,x19842)+E(f737(x19841,x19843),f737(x19842,x19843)) % 186.05/186.64 [1985]~E(x19851,x19852)+E(f737(x19853,x19851),f737(x19853,x19852)) % 186.05/186.64 [1986]~E(x19861,x19862)+E(f410(x19861,x19863,x19864,x19865),f410(x19862,x19863,x19864,x19865)) % 186.05/186.64 [1987]~E(x19871,x19872)+E(f410(x19873,x19871,x19874,x19875),f410(x19873,x19872,x19874,x19875)) % 186.05/186.64 [1988]~E(x19881,x19882)+E(f410(x19883,x19884,x19881,x19885),f410(x19883,x19884,x19882,x19885)) % 186.05/186.64 [1989]~E(x19891,x19892)+E(f410(x19893,x19894,x19895,x19891),f410(x19893,x19894,x19895,x19892)) % 186.05/186.64 [1990]~E(x19901,x19902)+E(f640(x19901,x19903,x19904),f640(x19902,x19903,x19904)) % 186.05/186.64 [1991]~E(x19911,x19912)+E(f640(x19913,x19911,x19914),f640(x19913,x19912,x19914)) % 186.05/186.64 [1992]~E(x19921,x19922)+E(f640(x19923,x19924,x19921),f640(x19923,x19924,x19922)) % 186.05/186.64 [1993]~E(x19931,x19932)+E(f626(x19931),f626(x19932)) % 186.05/186.64 [1994]~E(x19941,x19942)+E(f367(x19941,x19943,x19944,x19945,x19946),f367(x19942,x19943,x19944,x19945,x19946)) % 186.05/186.64 [1995]~E(x19951,x19952)+E(f367(x19953,x19951,x19954,x19955,x19956),f367(x19953,x19952,x19954,x19955,x19956)) % 186.05/186.64 [1996]~E(x19961,x19962)+E(f367(x19963,x19964,x19961,x19965,x19966),f367(x19963,x19964,x19962,x19965,x19966)) % 186.05/186.64 [1997]~E(x19971,x19972)+E(f367(x19973,x19974,x19975,x19971,x19976),f367(x19973,x19974,x19975,x19972,x19976)) % 186.05/186.64 [1998]~E(x19981,x19982)+E(f367(x19983,x19984,x19985,x19986,x19981),f367(x19983,x19984,x19985,x19986,x19982)) % 186.05/186.64 [1999]~E(x19991,x19992)+E(f432(x19991,x19993,x19994,x19995),f432(x19992,x19993,x19994,x19995)) % 186.05/186.64 [2000]~E(x20001,x20002)+E(f432(x20003,x20001,x20004,x20005),f432(x20003,x20002,x20004,x20005)) % 186.05/186.64 [2001]~E(x20011,x20012)+E(f432(x20013,x20014,x20011,x20015),f432(x20013,x20014,x20012,x20015)) % 186.05/186.64 [2002]~E(x20021,x20022)+E(f432(x20023,x20024,x20025,x20021),f432(x20023,x20024,x20025,x20022)) % 186.05/186.64 [2003]~E(x20031,x20032)+E(f218(x20031,x20033,x20034,x20035,x20036),f218(x20032,x20033,x20034,x20035,x20036)) % 186.05/186.64 [2004]~E(x20041,x20042)+E(f218(x20043,x20041,x20044,x20045,x20046),f218(x20043,x20042,x20044,x20045,x20046)) % 186.05/186.64 [2005]~E(x20051,x20052)+E(f218(x20053,x20054,x20051,x20055,x20056),f218(x20053,x20054,x20052,x20055,x20056)) % 186.05/186.64 [2006]~E(x20061,x20062)+E(f218(x20063,x20064,x20065,x20061,x20066),f218(x20063,x20064,x20065,x20062,x20066)) % 186.05/186.64 [2007]~E(x20071,x20072)+E(f218(x20073,x20074,x20075,x20076,x20071),f218(x20073,x20074,x20075,x20076,x20072)) % 186.05/186.64 [2008]~E(x20081,x20082)+E(f459(x20081,x20083,x20084,x20085),f459(x20082,x20083,x20084,x20085)) % 186.05/186.64 [2009]~E(x20091,x20092)+E(f459(x20093,x20091,x20094,x20095),f459(x20093,x20092,x20094,x20095)) % 186.05/186.64 [2010]~E(x20101,x20102)+E(f459(x20103,x20104,x20101,x20105),f459(x20103,x20104,x20102,x20105)) % 186.05/186.64 [2011]~E(x20111,x20112)+E(f459(x20113,x20114,x20115,x20111),f459(x20113,x20114,x20115,x20112)) % 186.05/186.64 [2012]~E(x20121,x20122)+E(f489(x20121,x20123,x20124,x20125,x20126),f489(x20122,x20123,x20124,x20125,x20126)) % 186.05/186.64 [2013]~E(x20131,x20132)+E(f489(x20133,x20131,x20134,x20135,x20136),f489(x20133,x20132,x20134,x20135,x20136)) % 186.05/186.64 [2014]~E(x20141,x20142)+E(f489(x20143,x20144,x20141,x20145,x20146),f489(x20143,x20144,x20142,x20145,x20146)) % 186.05/186.64 [2015]~E(x20151,x20152)+E(f489(x20153,x20154,x20155,x20151,x20156),f489(x20153,x20154,x20155,x20152,x20156)) % 186.05/186.64 [2016]~E(x20161,x20162)+E(f489(x20163,x20164,x20165,x20166,x20161),f489(x20163,x20164,x20165,x20166,x20162)) % 186.05/186.64 [2017]~E(x20171,x20172)+E(f464(x20171,x20173,x20174,x20175,x20176,x20177),f464(x20172,x20173,x20174,x20175,x20176,x20177)) % 186.05/186.64 [2018]~E(x20181,x20182)+E(f464(x20183,x20181,x20184,x20185,x20186,x20187),f464(x20183,x20182,x20184,x20185,x20186,x20187)) % 186.05/186.64 [2019]~E(x20191,x20192)+E(f464(x20193,x20194,x20191,x20195,x20196,x20197),f464(x20193,x20194,x20192,x20195,x20196,x20197)) % 186.05/186.64 [2020]~E(x20201,x20202)+E(f464(x20203,x20204,x20205,x20201,x20206,x20207),f464(x20203,x20204,x20205,x20202,x20206,x20207)) % 186.05/186.64 [2021]~E(x20211,x20212)+E(f464(x20213,x20214,x20215,x20216,x20211,x20217),f464(x20213,x20214,x20215,x20216,x20212,x20217)) % 186.05/186.64 [2022]~E(x20221,x20222)+E(f464(x20223,x20224,x20225,x20226,x20227,x20221),f464(x20223,x20224,x20225,x20226,x20227,x20222)) % 186.05/186.64 [2023]~E(x20231,x20232)+E(f291(x20231,x20233,x20234,x20235),f291(x20232,x20233,x20234,x20235)) % 186.05/186.64 [2024]~E(x20241,x20242)+E(f291(x20243,x20241,x20244,x20245),f291(x20243,x20242,x20244,x20245)) % 186.05/186.64 [2025]~E(x20251,x20252)+E(f291(x20253,x20254,x20251,x20255),f291(x20253,x20254,x20252,x20255)) % 186.05/186.64 [2026]~E(x20261,x20262)+E(f291(x20263,x20264,x20265,x20261),f291(x20263,x20264,x20265,x20262)) % 186.05/186.64 [2027]~E(x20271,x20272)+E(f635(x20271,x20273),f635(x20272,x20273)) % 186.05/186.64 [2028]~E(x20281,x20282)+E(f635(x20283,x20281),f635(x20283,x20282)) % 186.05/186.64 [2029]~E(x20291,x20292)+E(f443(x20291,x20293),f443(x20292,x20293)) % 186.05/186.64 [2030]~E(x20301,x20302)+E(f443(x20303,x20301),f443(x20303,x20302)) % 186.05/186.64 [2031]~E(x20311,x20312)+E(f705(x20311,x20313,x20314,x20315),f705(x20312,x20313,x20314,x20315)) % 186.05/186.64 [2032]~E(x20321,x20322)+E(f705(x20323,x20321,x20324,x20325),f705(x20323,x20322,x20324,x20325)) % 186.05/186.64 [2033]~E(x20331,x20332)+E(f705(x20333,x20334,x20331,x20335),f705(x20333,x20334,x20332,x20335)) % 186.05/186.64 [2034]~E(x20341,x20342)+E(f705(x20343,x20344,x20345,x20341),f705(x20343,x20344,x20345,x20342)) % 186.05/186.64 [2035]~E(x20351,x20352)+E(f423(x20351,x20353,x20354,x20355),f423(x20352,x20353,x20354,x20355)) % 186.05/186.64 [2036]~E(x20361,x20362)+E(f423(x20363,x20361,x20364,x20365),f423(x20363,x20362,x20364,x20365)) % 186.05/186.64 [2037]~E(x20371,x20372)+E(f423(x20373,x20374,x20371,x20375),f423(x20373,x20374,x20372,x20375)) % 186.05/186.64 [2038]~E(x20381,x20382)+E(f423(x20383,x20384,x20385,x20381),f423(x20383,x20384,x20385,x20382)) % 186.05/186.64 [2039]~E(x20391,x20392)+E(f262(x20391,x20393,x20394),f262(x20392,x20393,x20394)) % 186.05/186.64 [2040]~E(x20401,x20402)+E(f262(x20403,x20401,x20404),f262(x20403,x20402,x20404)) % 186.05/186.64 [2041]~E(x20411,x20412)+E(f262(x20413,x20414,x20411),f262(x20413,x20414,x20412)) % 186.05/186.64 [2042]~E(x20421,x20422)+E(f508(x20421,x20423,x20424),f508(x20422,x20423,x20424)) % 186.05/186.64 [2043]~E(x20431,x20432)+E(f508(x20433,x20431,x20434),f508(x20433,x20432,x20434)) % 186.05/186.64 [2044]~E(x20441,x20442)+E(f508(x20443,x20444,x20441),f508(x20443,x20444,x20442)) % 186.05/186.64 [2045]~E(x20451,x20452)+E(f434(x20451,x20453,x20454,x20455),f434(x20452,x20453,x20454,x20455)) % 186.05/186.64 [2046]~E(x20461,x20462)+E(f434(x20463,x20461,x20464,x20465),f434(x20463,x20462,x20464,x20465)) % 186.05/186.64 [2047]~E(x20471,x20472)+E(f434(x20473,x20474,x20471,x20475),f434(x20473,x20474,x20472,x20475)) % 186.05/186.64 [2048]~E(x20481,x20482)+E(f434(x20483,x20484,x20485,x20481),f434(x20483,x20484,x20485,x20482)) % 186.05/186.64 [2049]~E(x20491,x20492)+E(f309(x20491,x20493,x20494),f309(x20492,x20493,x20494)) % 186.05/186.64 [2050]~E(x20501,x20502)+E(f309(x20503,x20501,x20504),f309(x20503,x20502,x20504)) % 186.05/186.64 [2051]~E(x20511,x20512)+E(f309(x20513,x20514,x20511),f309(x20513,x20514,x20512)) % 186.05/186.64 [2052]~E(x20521,x20522)+E(f202(x20521,x20523,x20524,x20525,x20526,x20527,x20528),f202(x20522,x20523,x20524,x20525,x20526,x20527,x20528)) % 186.05/186.64 [2053]~E(x20531,x20532)+E(f202(x20533,x20531,x20534,x20535,x20536,x20537,x20538),f202(x20533,x20532,x20534,x20535,x20536,x20537,x20538)) % 186.05/186.64 [2054]~E(x20541,x20542)+E(f202(x20543,x20544,x20541,x20545,x20546,x20547,x20548),f202(x20543,x20544,x20542,x20545,x20546,x20547,x20548)) % 186.05/186.64 [2055]~E(x20551,x20552)+E(f202(x20553,x20554,x20555,x20551,x20556,x20557,x20558),f202(x20553,x20554,x20555,x20552,x20556,x20557,x20558)) % 186.05/186.64 [2056]~E(x20561,x20562)+E(f202(x20563,x20564,x20565,x20566,x20561,x20567,x20568),f202(x20563,x20564,x20565,x20566,x20562,x20567,x20568)) % 186.05/186.64 [2057]~E(x20571,x20572)+E(f202(x20573,x20574,x20575,x20576,x20577,x20571,x20578),f202(x20573,x20574,x20575,x20576,x20577,x20572,x20578)) % 186.05/186.64 [2058]~E(x20581,x20582)+E(f202(x20583,x20584,x20585,x20586,x20587,x20588,x20581),f202(x20583,x20584,x20585,x20586,x20587,x20588,x20582)) % 186.05/186.64 [2059]~E(x20591,x20592)+E(f161(x20591,x20593,x20594),f161(x20592,x20593,x20594)) % 186.05/186.64 [2060]~E(x20601,x20602)+E(f161(x20603,x20601,x20604),f161(x20603,x20602,x20604)) % 186.05/186.64 [2061]~E(x20611,x20612)+E(f161(x20613,x20614,x20611),f161(x20613,x20614,x20612)) % 186.05/186.64 [2062]~E(x20621,x20622)+E(f806(x20621,x20623,x20624),f806(x20622,x20623,x20624)) % 186.05/186.64 [2063]~E(x20631,x20632)+E(f806(x20633,x20631,x20634),f806(x20633,x20632,x20634)) % 186.05/186.64 [2064]~E(x20641,x20642)+E(f806(x20643,x20644,x20641),f806(x20643,x20644,x20642)) % 186.05/186.64 [2065]~E(x20651,x20652)+E(f677(x20651,x20653,x20654),f677(x20652,x20653,x20654)) % 186.05/186.64 [2066]~E(x20661,x20662)+E(f677(x20663,x20661,x20664),f677(x20663,x20662,x20664)) % 186.05/186.64 [2067]~E(x20671,x20672)+E(f677(x20673,x20674,x20671),f677(x20673,x20674,x20672)) % 186.05/186.64 [2068]~E(x20681,x20682)+E(f254(x20681,x20683,x20684,x20685,x20686),f254(x20682,x20683,x20684,x20685,x20686)) % 186.05/186.64 [2069]~E(x20691,x20692)+E(f254(x20693,x20691,x20694,x20695,x20696),f254(x20693,x20692,x20694,x20695,x20696)) % 186.05/186.64 [2070]~E(x20701,x20702)+E(f254(x20703,x20704,x20701,x20705,x20706),f254(x20703,x20704,x20702,x20705,x20706)) % 186.05/186.64 [2071]~E(x20711,x20712)+E(f254(x20713,x20714,x20715,x20711,x20716),f254(x20713,x20714,x20715,x20712,x20716)) % 186.05/186.64 [2072]~E(x20721,x20722)+E(f254(x20723,x20724,x20725,x20726,x20721),f254(x20723,x20724,x20725,x20726,x20722)) % 186.05/186.64 [2073]~E(x20731,x20732)+E(f799(x20731,x20733),f799(x20732,x20733)) % 186.05/186.64 [2074]~E(x20741,x20742)+E(f799(x20743,x20741),f799(x20743,x20742)) % 186.05/186.64 [2075]~E(x20751,x20752)+E(f529(x20751,x20753,x20754,x20755),f529(x20752,x20753,x20754,x20755)) % 186.05/186.64 [2076]~E(x20761,x20762)+E(f529(x20763,x20761,x20764,x20765),f529(x20763,x20762,x20764,x20765)) % 186.05/186.64 [2077]~E(x20771,x20772)+E(f529(x20773,x20774,x20771,x20775),f529(x20773,x20774,x20772,x20775)) % 186.05/186.64 [2078]~E(x20781,x20782)+E(f529(x20783,x20784,x20785,x20781),f529(x20783,x20784,x20785,x20782)) % 186.05/186.64 [2079]~E(x20791,x20792)+E(f792(x20791,x20793),f792(x20792,x20793)) % 186.05/186.64 [2080]~E(x20801,x20802)+E(f792(x20803,x20801),f792(x20803,x20802)) % 186.05/186.64 [2081]~E(x20811,x20812)+E(f668(x20811,x20813,x20814,x20815,x20816),f668(x20812,x20813,x20814,x20815,x20816)) % 186.05/186.64 [2082]~E(x20821,x20822)+E(f668(x20823,x20821,x20824,x20825,x20826),f668(x20823,x20822,x20824,x20825,x20826)) % 186.05/186.64 [2083]~E(x20831,x20832)+E(f668(x20833,x20834,x20831,x20835,x20836),f668(x20833,x20834,x20832,x20835,x20836)) % 186.05/186.64 [2084]~E(x20841,x20842)+E(f668(x20843,x20844,x20845,x20841,x20846),f668(x20843,x20844,x20845,x20842,x20846)) % 186.05/186.64 [2085]~E(x20851,x20852)+E(f668(x20853,x20854,x20855,x20856,x20851),f668(x20853,x20854,x20855,x20856,x20852)) % 186.05/186.64 [2086]~E(x20861,x20862)+E(f647(x20861,x20863,x20864),f647(x20862,x20863,x20864)) % 186.05/186.64 [2087]~E(x20871,x20872)+E(f647(x20873,x20871,x20874),f647(x20873,x20872,x20874)) % 186.05/186.64 [2088]~E(x20881,x20882)+E(f647(x20883,x20884,x20881),f647(x20883,x20884,x20882)) % 186.05/186.64 [2089]~E(x20891,x20892)+E(f548(x20891,x20893,x20894),f548(x20892,x20893,x20894)) % 186.05/186.64 [2090]~E(x20901,x20902)+E(f548(x20903,x20901,x20904),f548(x20903,x20902,x20904)) % 186.05/186.64 [2091]~E(x20911,x20912)+E(f548(x20913,x20914,x20911),f548(x20913,x20914,x20912)) % 186.05/186.64 [2092]~E(x20921,x20922)+E(f458(x20921,x20923,x20924,x20925),f458(x20922,x20923,x20924,x20925)) % 186.05/186.64 [2093]~E(x20931,x20932)+E(f458(x20933,x20931,x20934,x20935),f458(x20933,x20932,x20934,x20935)) % 186.05/186.64 [2094]~E(x20941,x20942)+E(f458(x20943,x20944,x20941,x20945),f458(x20943,x20944,x20942,x20945)) % 186.05/186.64 [2095]~E(x20951,x20952)+E(f458(x20953,x20954,x20955,x20951),f458(x20953,x20954,x20955,x20952)) % 186.05/186.64 [2096]~E(x20961,x20962)+E(f770(x20961,x20963),f770(x20962,x20963)) % 186.05/186.64 [2097]~E(x20971,x20972)+E(f770(x20973,x20971),f770(x20973,x20972)) % 186.05/186.64 [2098]~E(x20981,x20982)+E(f682(x20981,x20983),f682(x20982,x20983)) % 186.05/186.64 [2099]~E(x20991,x20992)+E(f682(x20993,x20991),f682(x20993,x20992)) % 186.05/186.64 [2100]~E(x21001,x21002)+E(f560(x21001,x21003,x21004,x21005),f560(x21002,x21003,x21004,x21005)) % 186.05/186.64 [2101]~E(x21011,x21012)+E(f560(x21013,x21011,x21014,x21015),f560(x21013,x21012,x21014,x21015)) % 186.05/186.64 [2102]~E(x21021,x21022)+E(f560(x21023,x21024,x21021,x21025),f560(x21023,x21024,x21022,x21025)) % 186.05/186.64 [2103]~E(x21031,x21032)+E(f560(x21033,x21034,x21035,x21031),f560(x21033,x21034,x21035,x21032)) % 186.05/186.64 [2104]~E(x21041,x21042)+E(f773(x21041),f773(x21042)) % 186.05/186.64 [2105]~E(x21051,x21052)+E(f339(x21051,x21053),f339(x21052,x21053)) % 186.05/186.64 [2106]~E(x21061,x21062)+E(f339(x21063,x21061),f339(x21063,x21062)) % 186.05/186.64 [2107]~E(x21071,x21072)+E(f362(x21071,x21073,x21074,x21075,x21076),f362(x21072,x21073,x21074,x21075,x21076)) % 186.05/186.64 [2108]~E(x21081,x21082)+E(f362(x21083,x21081,x21084,x21085,x21086),f362(x21083,x21082,x21084,x21085,x21086)) % 186.05/186.64 [2109]~E(x21091,x21092)+E(f362(x21093,x21094,x21091,x21095,x21096),f362(x21093,x21094,x21092,x21095,x21096)) % 186.05/186.64 [2110]~E(x21101,x21102)+E(f362(x21103,x21104,x21105,x21101,x21106),f362(x21103,x21104,x21105,x21102,x21106)) % 186.05/186.64 [2111]~E(x21111,x21112)+E(f362(x21113,x21114,x21115,x21116,x21111),f362(x21113,x21114,x21115,x21116,x21112)) % 186.05/186.64 [2112]~E(x21121,x21122)+E(f619(x21121,x21123),f619(x21122,x21123)) % 186.05/186.64 [2113]~E(x21131,x21132)+E(f619(x21133,x21131),f619(x21133,x21132)) % 186.05/186.64 [2114]~E(x21141,x21142)+E(f723(x21141,x21143),f723(x21142,x21143)) % 186.05/186.64 [2115]~E(x21151,x21152)+E(f723(x21153,x21151),f723(x21153,x21152)) % 186.05/186.64 [2116]~E(x21161,x21162)+E(f825(x21161,x21163,x21164),f825(x21162,x21163,x21164)) % 186.05/186.64 [2117]~E(x21171,x21172)+E(f825(x21173,x21171,x21174),f825(x21173,x21172,x21174)) % 186.05/186.64 [2118]~E(x21181,x21182)+E(f825(x21183,x21184,x21181),f825(x21183,x21184,x21182)) % 186.05/186.64 [2119]~E(x21191,x21192)+E(f577(x21191,x21193,x21194,x21195,x21196),f577(x21192,x21193,x21194,x21195,x21196)) % 186.05/186.64 [2120]~E(x21201,x21202)+E(f577(x21203,x21201,x21204,x21205,x21206),f577(x21203,x21202,x21204,x21205,x21206)) % 186.05/186.64 [2121]~E(x21211,x21212)+E(f577(x21213,x21214,x21211,x21215,x21216),f577(x21213,x21214,x21212,x21215,x21216)) % 186.05/186.64 [2122]~E(x21221,x21222)+E(f577(x21223,x21224,x21225,x21221,x21226),f577(x21223,x21224,x21225,x21222,x21226)) % 186.05/186.64 [2123]~E(x21231,x21232)+E(f577(x21233,x21234,x21235,x21236,x21231),f577(x21233,x21234,x21235,x21236,x21232)) % 186.05/186.64 [2124]~E(x21241,x21242)+E(f275(x21241,x21243,x21244,x21245),f275(x21242,x21243,x21244,x21245)) % 186.05/186.64 [2125]~E(x21251,x21252)+E(f275(x21253,x21251,x21254,x21255),f275(x21253,x21252,x21254,x21255)) % 186.05/186.64 [2126]~E(x21261,x21262)+E(f275(x21263,x21264,x21261,x21265),f275(x21263,x21264,x21262,x21265)) % 186.05/186.64 [2127]~E(x21271,x21272)+E(f275(x21273,x21274,x21275,x21271),f275(x21273,x21274,x21275,x21272)) % 186.05/186.64 [2128]~E(x21281,x21282)+E(f306(x21281,x21283),f306(x21282,x21283)) % 186.05/186.64 [2129]~E(x21291,x21292)+E(f306(x21293,x21291),f306(x21293,x21292)) % 186.05/186.64 [2130]~E(x21301,x21302)+E(f545(x21301,x21303,x21304,x21305,x21306),f545(x21302,x21303,x21304,x21305,x21306)) % 186.05/186.64 [2131]~E(x21311,x21312)+E(f545(x21313,x21311,x21314,x21315,x21316),f545(x21313,x21312,x21314,x21315,x21316)) % 186.05/186.64 [2132]~E(x21321,x21322)+E(f545(x21323,x21324,x21321,x21325,x21326),f545(x21323,x21324,x21322,x21325,x21326)) % 186.05/186.64 [2133]~E(x21331,x21332)+E(f545(x21333,x21334,x21335,x21331,x21336),f545(x21333,x21334,x21335,x21332,x21336)) % 186.05/186.64 [2134]~E(x21341,x21342)+E(f545(x21343,x21344,x21345,x21346,x21341),f545(x21343,x21344,x21345,x21346,x21342)) % 186.05/186.64 [2135]~E(x21351,x21352)+E(f119(x21351,x21353,x21354,x21355),f119(x21352,x21353,x21354,x21355)) % 186.05/186.64 [2136]~E(x21361,x21362)+E(f119(x21363,x21361,x21364,x21365),f119(x21363,x21362,x21364,x21365)) % 186.05/186.64 [2137]~E(x21371,x21372)+E(f119(x21373,x21374,x21371,x21375),f119(x21373,x21374,x21372,x21375)) % 186.05/186.64 [2138]~E(x21381,x21382)+E(f119(x21383,x21384,x21385,x21381),f119(x21383,x21384,x21385,x21382)) % 186.05/186.64 [2139]~E(x21391,x21392)+E(f583(x21391,x21393),f583(x21392,x21393)) % 186.05/186.64 [2140]~E(x21401,x21402)+E(f583(x21403,x21401),f583(x21403,x21402)) % 186.05/186.64 [2141]~E(x21411,x21412)+E(f599(x21411,x21413,x21414,x21415),f599(x21412,x21413,x21414,x21415)) % 186.05/186.64 [2142]~E(x21421,x21422)+E(f599(x21423,x21421,x21424,x21425),f599(x21423,x21422,x21424,x21425)) % 186.05/186.64 [2143]~E(x21431,x21432)+E(f599(x21433,x21434,x21431,x21435),f599(x21433,x21434,x21432,x21435)) % 186.05/186.64 [2144]~E(x21441,x21442)+E(f599(x21443,x21444,x21445,x21441),f599(x21443,x21444,x21445,x21442)) % 186.05/186.64 [2145]~E(x21451,x21452)+E(f376(x21451),f376(x21452)) % 186.05/186.64 [2146]~E(x21461,x21462)+E(f760(x21461),f760(x21462)) % 186.05/186.64 [2147]~E(x21471,x21472)+E(f687(x21471,x21473,x21474),f687(x21472,x21473,x21474)) % 186.05/186.64 [2148]~E(x21481,x21482)+E(f687(x21483,x21481,x21484),f687(x21483,x21482,x21484)) % 186.05/186.64 [2149]~E(x21491,x21492)+E(f687(x21493,x21494,x21491),f687(x21493,x21494,x21492)) % 186.05/186.64 [2150]~E(x21501,x21502)+E(f715(x21501,x21503,x21504,x21505,x21506),f715(x21502,x21503,x21504,x21505,x21506)) % 186.05/186.64 [2151]~E(x21511,x21512)+E(f715(x21513,x21511,x21514,x21515,x21516),f715(x21513,x21512,x21514,x21515,x21516)) % 186.05/186.64 [2152]~E(x21521,x21522)+E(f715(x21523,x21524,x21521,x21525,x21526),f715(x21523,x21524,x21522,x21525,x21526)) % 186.05/186.64 [2153]~E(x21531,x21532)+E(f715(x21533,x21534,x21535,x21531,x21536),f715(x21533,x21534,x21535,x21532,x21536)) % 186.05/186.64 [2154]~E(x21541,x21542)+E(f715(x21543,x21544,x21545,x21546,x21541),f715(x21543,x21544,x21545,x21546,x21542)) % 186.05/186.64 [2155]~E(x21551,x21552)+E(f336(x21551,x21553,x21554,x21555),f336(x21552,x21553,x21554,x21555)) % 186.05/186.64 [2156]~E(x21561,x21562)+E(f336(x21563,x21561,x21564,x21565),f336(x21563,x21562,x21564,x21565)) % 186.05/186.64 [2157]~E(x21571,x21572)+E(f336(x21573,x21574,x21571,x21575),f336(x21573,x21574,x21572,x21575)) % 186.05/186.64 [2158]~E(x21581,x21582)+E(f336(x21583,x21584,x21585,x21581),f336(x21583,x21584,x21585,x21582)) % 186.05/186.64 [2159]~E(x21591,x21592)+E(f480(x21591,x21593,x21594,x21595,x21596),f480(x21592,x21593,x21594,x21595,x21596)) % 186.05/186.64 [2160]~E(x21601,x21602)+E(f480(x21603,x21601,x21604,x21605,x21606),f480(x21603,x21602,x21604,x21605,x21606)) % 186.05/186.64 [2161]~E(x21611,x21612)+E(f480(x21613,x21614,x21611,x21615,x21616),f480(x21613,x21614,x21612,x21615,x21616)) % 186.05/186.64 [2162]~E(x21621,x21622)+E(f480(x21623,x21624,x21625,x21621,x21626),f480(x21623,x21624,x21625,x21622,x21626)) % 186.05/186.64 [2163]~E(x21631,x21632)+E(f480(x21633,x21634,x21635,x21636,x21631),f480(x21633,x21634,x21635,x21636,x21632)) % 186.05/186.64 [2164]~E(x21641,x21642)+E(f623(x21641,x21643,x21644,x21645),f623(x21642,x21643,x21644,x21645)) % 186.05/186.64 [2165]~E(x21651,x21652)+E(f623(x21653,x21651,x21654,x21655),f623(x21653,x21652,x21654,x21655)) % 186.05/186.64 [2166]~E(x21661,x21662)+E(f623(x21663,x21664,x21661,x21665),f623(x21663,x21664,x21662,x21665)) % 186.05/186.64 [2167]~E(x21671,x21672)+E(f623(x21673,x21674,x21675,x21671),f623(x21673,x21674,x21675,x21672)) % 186.05/186.64 [2168]~E(x21681,x21682)+E(f585(x21681,x21683,x21684,x21685),f585(x21682,x21683,x21684,x21685)) % 186.05/186.64 [2169]~E(x21691,x21692)+E(f585(x21693,x21691,x21694,x21695),f585(x21693,x21692,x21694,x21695)) % 186.05/186.64 [2170]~E(x21701,x21702)+E(f585(x21703,x21704,x21701,x21705),f585(x21703,x21704,x21702,x21705)) % 186.05/186.64 [2171]~E(x21711,x21712)+E(f585(x21713,x21714,x21715,x21711),f585(x21713,x21714,x21715,x21712)) % 186.05/186.64 [2172]~E(x21721,x21722)+E(f450(x21721,x21723,x21724),f450(x21722,x21723,x21724)) % 186.05/186.64 [2173]~E(x21731,x21732)+E(f450(x21733,x21731,x21734),f450(x21733,x21732,x21734)) % 186.05/186.64 [2174]~E(x21741,x21742)+E(f450(x21743,x21744,x21741),f450(x21743,x21744,x21742)) % 186.05/186.64 [2175]~E(x21751,x21752)+E(f686(x21751,x21753,x21754),f686(x21752,x21753,x21754)) % 186.05/186.64 [2176]~E(x21761,x21762)+E(f686(x21763,x21761,x21764),f686(x21763,x21762,x21764)) % 186.05/186.64 [2177]~E(x21771,x21772)+E(f686(x21773,x21774,x21771),f686(x21773,x21774,x21772)) % 186.05/186.64 [2178]~E(x21781,x21782)+E(f268(x21781,x21783,x21784,x21785),f268(x21782,x21783,x21784,x21785)) % 186.05/186.64 [2179]~E(x21791,x21792)+E(f268(x21793,x21791,x21794,x21795),f268(x21793,x21792,x21794,x21795)) % 186.05/186.64 [2180]~E(x21801,x21802)+E(f268(x21803,x21804,x21801,x21805),f268(x21803,x21804,x21802,x21805)) % 186.05/186.64 [2181]~E(x21811,x21812)+E(f268(x21813,x21814,x21815,x21811),f268(x21813,x21814,x21815,x21812)) % 186.05/186.64 [2182]~E(x21821,x21822)+E(f700(x21821,x21823,x21824,x21825,x21826),f700(x21822,x21823,x21824,x21825,x21826)) % 186.05/186.64 [2183]~E(x21831,x21832)+E(f700(x21833,x21831,x21834,x21835,x21836),f700(x21833,x21832,x21834,x21835,x21836)) % 186.05/186.64 [2184]~E(x21841,x21842)+E(f700(x21843,x21844,x21841,x21845,x21846),f700(x21843,x21844,x21842,x21845,x21846)) % 186.05/186.64 [2185]~E(x21851,x21852)+E(f700(x21853,x21854,x21855,x21851,x21856),f700(x21853,x21854,x21855,x21852,x21856)) % 186.05/186.64 [2186]~E(x21861,x21862)+E(f700(x21863,x21864,x21865,x21866,x21861),f700(x21863,x21864,x21865,x21866,x21862)) % 186.05/186.64 [2187]~E(x21871,x21872)+E(f496(x21871,x21873,x21874,x21875,x21876,x21877),f496(x21872,x21873,x21874,x21875,x21876,x21877)) % 186.05/186.64 [2188]~E(x21881,x21882)+E(f496(x21883,x21881,x21884,x21885,x21886,x21887),f496(x21883,x21882,x21884,x21885,x21886,x21887)) % 186.05/186.64 [2189]~E(x21891,x21892)+E(f496(x21893,x21894,x21891,x21895,x21896,x21897),f496(x21893,x21894,x21892,x21895,x21896,x21897)) % 186.05/186.64 [2190]~E(x21901,x21902)+E(f496(x21903,x21904,x21905,x21901,x21906,x21907),f496(x21903,x21904,x21905,x21902,x21906,x21907)) % 186.05/186.64 [2191]~E(x21911,x21912)+E(f496(x21913,x21914,x21915,x21916,x21911,x21917),f496(x21913,x21914,x21915,x21916,x21912,x21917)) % 186.05/186.64 [2192]~E(x21921,x21922)+E(f496(x21923,x21924,x21925,x21926,x21927,x21921),f496(x21923,x21924,x21925,x21926,x21927,x21922)) % 186.05/186.64 [2193]~E(x21931,x21932)+E(f273(x21931),f273(x21932)) % 186.05/186.64 [2194]~E(x21941,x21942)+E(f345(x21941,x21943,x21944),f345(x21942,x21943,x21944)) % 186.05/186.64 [2195]~E(x21951,x21952)+E(f345(x21953,x21951,x21954),f345(x21953,x21952,x21954)) % 186.05/186.64 [2196]~E(x21961,x21962)+E(f345(x21963,x21964,x21961),f345(x21963,x21964,x21962)) % 186.05/186.64 [2197]~E(x21971,x21972)+E(f554(x21971),f554(x21972)) % 186.05/186.64 [2198]~E(x21981,x21982)+E(f575(x21981,x21983),f575(x21982,x21983)) % 186.05/186.64 [2199]~E(x21991,x21992)+E(f575(x21993,x21991),f575(x21993,x21992)) % 186.05/186.64 [2200]~E(x22001,x22002)+E(f355(x22001,x22003,x22004,x22005),f355(x22002,x22003,x22004,x22005)) % 186.05/186.64 [2201]~E(x22011,x22012)+E(f355(x22013,x22011,x22014,x22015),f355(x22013,x22012,x22014,x22015)) % 186.05/186.64 [2202]~E(x22021,x22022)+E(f355(x22023,x22024,x22021,x22025),f355(x22023,x22024,x22022,x22025)) % 186.05/186.64 [2203]~E(x22031,x22032)+E(f355(x22033,x22034,x22035,x22031),f355(x22033,x22034,x22035,x22032)) % 186.05/186.64 [2204]~E(x22041,x22042)+E(f807(x22041,x22043,x22044),f807(x22042,x22043,x22044)) % 186.05/186.64 [2205]~E(x22051,x22052)+E(f807(x22053,x22051,x22054),f807(x22053,x22052,x22054)) % 186.05/186.64 [2206]~E(x22061,x22062)+E(f807(x22063,x22064,x22061),f807(x22063,x22064,x22062)) % 186.05/186.64 [2207]~E(x22071,x22072)+E(f688(x22071,x22073,x22074,x22075),f688(x22072,x22073,x22074,x22075)) % 186.05/186.64 [2208]~E(x22081,x22082)+E(f688(x22083,x22081,x22084,x22085),f688(x22083,x22082,x22084,x22085)) % 186.05/186.64 [2209]~E(x22091,x22092)+E(f688(x22093,x22094,x22091,x22095),f688(x22093,x22094,x22092,x22095)) % 186.05/186.64 [2210]~E(x22101,x22102)+E(f688(x22103,x22104,x22105,x22101),f688(x22103,x22104,x22105,x22102)) % 186.05/186.64 [2211]~E(x22111,x22112)+E(f490(x22111),f490(x22112)) % 186.05/186.64 [2212]~E(x22121,x22122)+E(f348(x22121,x22123,x22124,x22125),f348(x22122,x22123,x22124,x22125)) % 186.05/186.64 [2213]~E(x22131,x22132)+E(f348(x22133,x22131,x22134,x22135),f348(x22133,x22132,x22134,x22135)) % 186.05/186.64 [2214]~E(x22141,x22142)+E(f348(x22143,x22144,x22141,x22145),f348(x22143,x22144,x22142,x22145)) % 186.05/186.64 [2215]~E(x22151,x22152)+E(f348(x22153,x22154,x22155,x22151),f348(x22153,x22154,x22155,x22152)) % 186.05/186.64 [2216]~E(x22161,x22162)+E(f612(x22161,x22163,x22164),f612(x22162,x22163,x22164)) % 186.05/186.64 [2217]~E(x22171,x22172)+E(f612(x22173,x22171,x22174),f612(x22173,x22172,x22174)) % 186.05/186.64 [2218]~E(x22181,x22182)+E(f612(x22183,x22184,x22181),f612(x22183,x22184,x22182)) % 186.05/186.64 [2219]~E(x22191,x22192)+E(f716(x22191,x22193,x22194,x22195,x22196),f716(x22192,x22193,x22194,x22195,x22196)) % 186.05/186.64 [2220]~E(x22201,x22202)+E(f716(x22203,x22201,x22204,x22205,x22206),f716(x22203,x22202,x22204,x22205,x22206)) % 186.05/186.64 [2221]~E(x22211,x22212)+E(f716(x22213,x22214,x22211,x22215,x22216),f716(x22213,x22214,x22212,x22215,x22216)) % 186.05/186.64 [2222]~E(x22221,x22222)+E(f716(x22223,x22224,x22225,x22221,x22226),f716(x22223,x22224,x22225,x22222,x22226)) % 186.05/186.64 [2223]~E(x22231,x22232)+E(f716(x22233,x22234,x22235,x22236,x22231),f716(x22233,x22234,x22235,x22236,x22232)) % 186.05/186.64 [2224]~E(x22241,x22242)+E(f527(x22241,x22243,x22244,x22245),f527(x22242,x22243,x22244,x22245)) % 186.05/186.64 [2225]~E(x22251,x22252)+E(f527(x22253,x22251,x22254,x22255),f527(x22253,x22252,x22254,x22255)) % 186.05/186.64 [2226]~E(x22261,x22262)+E(f527(x22263,x22264,x22261,x22265),f527(x22263,x22264,x22262,x22265)) % 186.05/186.64 [2227]~E(x22271,x22272)+E(f527(x22273,x22274,x22275,x22271),f527(x22273,x22274,x22275,x22272)) % 186.05/186.64 [2228]~E(x22281,x22282)+E(f637(x22281,x22283,x22284,x22285,x22286,x22287,x22288,x22289),f637(x22282,x22283,x22284,x22285,x22286,x22287,x22288,x22289)) % 186.05/186.64 [2229]~E(x22291,x22292)+E(f637(x22293,x22291,x22294,x22295,x22296,x22297,x22298,x22299),f637(x22293,x22292,x22294,x22295,x22296,x22297,x22298,x22299)) % 186.05/186.64 [2230]~E(x22301,x22302)+E(f637(x22303,x22304,x22301,x22305,x22306,x22307,x22308,x22309),f637(x22303,x22304,x22302,x22305,x22306,x22307,x22308,x22309)) % 186.05/186.64 [2231]~E(x22311,x22312)+E(f637(x22313,x22314,x22315,x22311,x22316,x22317,x22318,x22319),f637(x22313,x22314,x22315,x22312,x22316,x22317,x22318,x22319)) % 186.05/186.64 [2232]~E(x22321,x22322)+E(f637(x22323,x22324,x22325,x22326,x22321,x22327,x22328,x22329),f637(x22323,x22324,x22325,x22326,x22322,x22327,x22328,x22329)) % 186.05/186.64 [2233]~E(x22331,x22332)+E(f637(x22333,x22334,x22335,x22336,x22337,x22331,x22338,x22339),f637(x22333,x22334,x22335,x22336,x22337,x22332,x22338,x22339)) % 186.05/186.64 [2234]~E(x22341,x22342)+E(f637(x22343,x22344,x22345,x22346,x22347,x22348,x22341,x22349),f637(x22343,x22344,x22345,x22346,x22347,x22348,x22342,x22349)) % 186.05/186.64 [2235]~E(x22351,x22352)+E(f637(x22353,x22354,x22355,x22356,x22357,x22358,x22359,x22351),f637(x22353,x22354,x22355,x22356,x22357,x22358,x22359,x22352)) % 186.05/186.64 [2236]~E(x22361,x22362)+E(f739(x22361,x22363,x22364,x22365),f739(x22362,x22363,x22364,x22365)) % 186.05/186.64 [2237]~E(x22371,x22372)+E(f739(x22373,x22371,x22374,x22375),f739(x22373,x22372,x22374,x22375)) % 186.05/186.64 [2238]~E(x22381,x22382)+E(f739(x22383,x22384,x22381,x22385),f739(x22383,x22384,x22382,x22385)) % 186.05/186.64 [2239]~E(x22391,x22392)+E(f739(x22393,x22394,x22395,x22391),f739(x22393,x22394,x22395,x22392)) % 186.05/186.64 [2240]~E(x22401,x22402)+E(f719(x22401,x22403,x22404,x22405,x22406),f719(x22402,x22403,x22404,x22405,x22406)) % 186.05/186.64 [2241]~E(x22411,x22412)+E(f719(x22413,x22411,x22414,x22415,x22416),f719(x22413,x22412,x22414,x22415,x22416)) % 186.05/186.64 [2242]~E(x22421,x22422)+E(f719(x22423,x22424,x22421,x22425,x22426),f719(x22423,x22424,x22422,x22425,x22426)) % 186.05/186.64 [2243]~E(x22431,x22432)+E(f719(x22433,x22434,x22435,x22431,x22436),f719(x22433,x22434,x22435,x22432,x22436)) % 186.05/186.64 [2244]~E(x22441,x22442)+E(f719(x22443,x22444,x22445,x22446,x22441),f719(x22443,x22444,x22445,x22446,x22442)) % 186.05/186.64 [2245]~E(x22451,x22452)+E(f549(x22451,x22453,x22454),f549(x22452,x22453,x22454)) % 186.05/186.64 [2246]~E(x22461,x22462)+E(f549(x22463,x22461,x22464),f549(x22463,x22462,x22464)) % 186.05/186.64 [2247]~E(x22471,x22472)+E(f549(x22473,x22474,x22471),f549(x22473,x22474,x22472)) % 186.05/186.64 [2248]~E(x22481,x22482)+E(f714(x22481,x22483,x22484),f714(x22482,x22483,x22484)) % 186.05/186.64 [2249]~E(x22491,x22492)+E(f714(x22493,x22491,x22494),f714(x22493,x22492,x22494)) % 186.05/186.64 [2250]~E(x22501,x22502)+E(f714(x22503,x22504,x22501),f714(x22503,x22504,x22502)) % 186.05/186.64 [2251]~E(x22511,x22512)+E(f829(x22511,x22513,x22514,x22515),f829(x22512,x22513,x22514,x22515)) % 186.05/186.64 [2252]~E(x22521,x22522)+E(f829(x22523,x22521,x22524,x22525),f829(x22523,x22522,x22524,x22525)) % 186.05/186.64 [2253]~E(x22531,x22532)+E(f829(x22533,x22534,x22531,x22535),f829(x22533,x22534,x22532,x22535)) % 186.05/186.64 [2254]~E(x22541,x22542)+E(f829(x22543,x22544,x22545,x22541),f829(x22543,x22544,x22545,x22542)) % 186.05/186.64 [2255]~E(x22551,x22552)+E(f337(x22551),f337(x22552)) % 186.05/186.64 [2256]~E(x22561,x22562)+E(f389(x22561,x22563,x22564,x22565,x22566),f389(x22562,x22563,x22564,x22565,x22566)) % 186.05/186.64 [2257]~E(x22571,x22572)+E(f389(x22573,x22571,x22574,x22575,x22576),f389(x22573,x22572,x22574,x22575,x22576)) % 186.05/186.64 [2258]~E(x22581,x22582)+E(f389(x22583,x22584,x22581,x22585,x22586),f389(x22583,x22584,x22582,x22585,x22586)) % 186.05/186.64 [2259]~E(x22591,x22592)+E(f389(x22593,x22594,x22595,x22591,x22596),f389(x22593,x22594,x22595,x22592,x22596)) % 186.05/186.64 [2260]~E(x22601,x22602)+E(f389(x22603,x22604,x22605,x22606,x22601),f389(x22603,x22604,x22605,x22606,x22602)) % 186.05/186.64 [2261]~E(x22611,x22612)+E(f122(x22611),f122(x22612)) % 186.05/186.64 [2262]~E(x22621,x22622)+E(f222(x22621,x22623,x22624),f222(x22622,x22623,x22624)) % 186.05/186.64 [2263]~E(x22631,x22632)+E(f222(x22633,x22631,x22634),f222(x22633,x22632,x22634)) % 186.05/186.64 [2264]~E(x22641,x22642)+E(f222(x22643,x22644,x22641),f222(x22643,x22644,x22642)) % 186.05/186.64 [2265]~E(x22651,x22652)+E(f629(x22651,x22653),f629(x22652,x22653)) % 186.05/186.64 [2266]~E(x22661,x22662)+E(f629(x22663,x22661),f629(x22663,x22662)) % 186.05/186.64 [2267]~E(x22671,x22672)+E(f190(x22671,x22673,x22674,x22675),f190(x22672,x22673,x22674,x22675)) % 186.05/186.64 [2268]~E(x22681,x22682)+E(f190(x22683,x22681,x22684,x22685),f190(x22683,x22682,x22684,x22685)) % 186.05/186.64 [2269]~E(x22691,x22692)+E(f190(x22693,x22694,x22691,x22695),f190(x22693,x22694,x22692,x22695)) % 186.05/186.64 [2270]~E(x22701,x22702)+E(f190(x22703,x22704,x22705,x22701),f190(x22703,x22704,x22705,x22702)) % 186.05/186.64 [2271]~E(x22711,x22712)+E(f694(x22711,x22713,x22714,x22715),f694(x22712,x22713,x22714,x22715)) % 186.05/186.64 [2272]~E(x22721,x22722)+E(f694(x22723,x22721,x22724,x22725),f694(x22723,x22722,x22724,x22725)) % 186.05/186.64 [2273]~E(x22731,x22732)+E(f694(x22733,x22734,x22731,x22735),f694(x22733,x22734,x22732,x22735)) % 186.05/186.64 [2274]~E(x22741,x22742)+E(f694(x22743,x22744,x22745,x22741),f694(x22743,x22744,x22745,x22742)) % 186.05/186.64 [2275]~E(x22751,x22752)+E(f691(x22751,x22753,x22754,x22755,x22756,x22757),f691(x22752,x22753,x22754,x22755,x22756,x22757)) % 186.05/186.64 [2276]~E(x22761,x22762)+E(f691(x22763,x22761,x22764,x22765,x22766,x22767),f691(x22763,x22762,x22764,x22765,x22766,x22767)) % 186.05/186.64 [2277]~E(x22771,x22772)+E(f691(x22773,x22774,x22771,x22775,x22776,x22777),f691(x22773,x22774,x22772,x22775,x22776,x22777)) % 186.05/186.64 [2278]~E(x22781,x22782)+E(f691(x22783,x22784,x22785,x22781,x22786,x22787),f691(x22783,x22784,x22785,x22782,x22786,x22787)) % 186.05/186.64 [2279]~E(x22791,x22792)+E(f691(x22793,x22794,x22795,x22796,x22791,x22797),f691(x22793,x22794,x22795,x22796,x22792,x22797)) % 186.05/186.64 [2280]~E(x22801,x22802)+E(f691(x22803,x22804,x22805,x22806,x22807,x22801),f691(x22803,x22804,x22805,x22806,x22807,x22802)) % 186.05/186.64 [2281]~E(x22811,x22812)+E(f778(x22811),f778(x22812)) % 186.05/186.64 [2282]~E(x22821,x22822)+E(f592(x22821,x22823),f592(x22822,x22823)) % 186.05/186.64 [2283]~E(x22831,x22832)+E(f592(x22833,x22831),f592(x22833,x22832)) % 186.05/186.64 [2284]~E(x22841,x22842)+E(f665(x22841,x22843,x22844,x22845,x22846),f665(x22842,x22843,x22844,x22845,x22846)) % 186.05/186.64 [2285]~E(x22851,x22852)+E(f665(x22853,x22851,x22854,x22855,x22856),f665(x22853,x22852,x22854,x22855,x22856)) % 186.05/186.64 [2286]~E(x22861,x22862)+E(f665(x22863,x22864,x22861,x22865,x22866),f665(x22863,x22864,x22862,x22865,x22866)) % 186.05/186.64 [2287]~E(x22871,x22872)+E(f665(x22873,x22874,x22875,x22871,x22876),f665(x22873,x22874,x22875,x22872,x22876)) % 186.05/186.64 [2288]~E(x22881,x22882)+E(f665(x22883,x22884,x22885,x22886,x22881),f665(x22883,x22884,x22885,x22886,x22882)) % 186.05/186.64 [2289]~E(x22891,x22892)+E(f742(x22891,x22893,x22894,x22895),f742(x22892,x22893,x22894,x22895)) % 186.05/186.64 [2290]~E(x22901,x22902)+E(f742(x22903,x22901,x22904,x22905),f742(x22903,x22902,x22904,x22905)) % 186.05/186.64 [2291]~E(x22911,x22912)+E(f742(x22913,x22914,x22911,x22915),f742(x22913,x22914,x22912,x22915)) % 186.05/186.64 [2292]~E(x22921,x22922)+E(f742(x22923,x22924,x22925,x22921),f742(x22923,x22924,x22925,x22922)) % 186.05/186.64 [2293]~E(x22931,x22932)+E(f552(x22931,x22933,x22934),f552(x22932,x22933,x22934)) % 186.05/186.64 [2294]~E(x22941,x22942)+E(f552(x22943,x22941,x22944),f552(x22943,x22942,x22944)) % 186.05/186.64 [2295]~E(x22951,x22952)+E(f552(x22953,x22954,x22951),f552(x22953,x22954,x22952)) % 186.05/186.64 [2296]~E(x22961,x22962)+E(f556(x22961,x22963,x22964,x22965,x22966,x22967),f556(x22962,x22963,x22964,x22965,x22966,x22967)) % 186.05/186.64 [2297]~E(x22971,x22972)+E(f556(x22973,x22971,x22974,x22975,x22976,x22977),f556(x22973,x22972,x22974,x22975,x22976,x22977)) % 186.05/186.64 [2298]~E(x22981,x22982)+E(f556(x22983,x22984,x22981,x22985,x22986,x22987),f556(x22983,x22984,x22982,x22985,x22986,x22987)) % 186.05/186.64 [2299]~E(x22991,x22992)+E(f556(x22993,x22994,x22995,x22991,x22996,x22997),f556(x22993,x22994,x22995,x22992,x22996,x22997)) % 186.05/186.64 [2300]~E(x23001,x23002)+E(f556(x23003,x23004,x23005,x23006,x23001,x23007),f556(x23003,x23004,x23005,x23006,x23002,x23007)) % 186.05/186.64 [2301]~E(x23011,x23012)+E(f556(x23013,x23014,x23015,x23016,x23017,x23011),f556(x23013,x23014,x23015,x23016,x23017,x23012)) % 186.05/186.64 [2302]~E(x23021,x23022)+E(f308(x23021,x23023,x23024),f308(x23022,x23023,x23024)) % 186.05/186.64 [2303]~E(x23031,x23032)+E(f308(x23033,x23031,x23034),f308(x23033,x23032,x23034)) % 186.05/186.64 [2304]~E(x23041,x23042)+E(f308(x23043,x23044,x23041),f308(x23043,x23044,x23042)) % 186.05/186.64 [2305]~E(x23051,x23052)+E(f136(x23051,x23053),f136(x23052,x23053)) % 186.05/186.64 [2306]~E(x23061,x23062)+E(f136(x23063,x23061),f136(x23063,x23062)) % 186.05/186.64 [2307]~E(x23071,x23072)+E(f484(x23071,x23073,x23074,x23075,x23076),f484(x23072,x23073,x23074,x23075,x23076)) % 186.05/186.64 [2308]~E(x23081,x23082)+E(f484(x23083,x23081,x23084,x23085,x23086),f484(x23083,x23082,x23084,x23085,x23086)) % 186.05/186.64 [2309]~E(x23091,x23092)+E(f484(x23093,x23094,x23091,x23095,x23096),f484(x23093,x23094,x23092,x23095,x23096)) % 186.05/186.64 [2310]~E(x23101,x23102)+E(f484(x23103,x23104,x23105,x23101,x23106),f484(x23103,x23104,x23105,x23102,x23106)) % 186.05/186.64 [2311]~E(x23111,x23112)+E(f484(x23113,x23114,x23115,x23116,x23111),f484(x23113,x23114,x23115,x23116,x23112)) % 186.05/186.64 [2312]~E(x23121,x23122)+E(f358(x23121,x23123,x23124,x23125),f358(x23122,x23123,x23124,x23125)) % 186.05/186.64 [2313]~E(x23131,x23132)+E(f358(x23133,x23131,x23134,x23135),f358(x23133,x23132,x23134,x23135)) % 186.05/186.64 [2314]~E(x23141,x23142)+E(f358(x23143,x23144,x23141,x23145),f358(x23143,x23144,x23142,x23145)) % 186.05/186.64 [2315]~E(x23151,x23152)+E(f358(x23153,x23154,x23155,x23151),f358(x23153,x23154,x23155,x23152)) % 186.05/186.64 [2316]~E(x23161,x23162)+E(f503(x23161,x23163),f503(x23162,x23163)) % 186.05/186.64 [2317]~E(x23171,x23172)+E(f503(x23173,x23171),f503(x23173,x23172)) % 186.05/186.64 [2318]~E(x23181,x23182)+E(f751(x23181,x23183,x23184),f751(x23182,x23183,x23184)) % 186.05/186.64 [2319]~E(x23191,x23192)+E(f751(x23193,x23191,x23194),f751(x23193,x23192,x23194)) % 186.05/186.64 [2320]~E(x23201,x23202)+E(f751(x23203,x23204,x23201),f751(x23203,x23204,x23202)) % 186.05/186.64 [2321]~E(x23211,x23212)+E(f813(x23211,x23213,x23214,x23215),f813(x23212,x23213,x23214,x23215)) % 186.05/186.64 [2322]~E(x23221,x23222)+E(f813(x23223,x23221,x23224,x23225),f813(x23223,x23222,x23224,x23225)) % 186.05/186.64 [2323]~E(x23231,x23232)+E(f813(x23233,x23234,x23231,x23235),f813(x23233,x23234,x23232,x23235)) % 186.05/186.64 [2324]~E(x23241,x23242)+E(f813(x23243,x23244,x23245,x23241),f813(x23243,x23244,x23245,x23242)) % 186.05/186.64 [2325]~E(x23251,x23252)+E(f428(x23251,x23253,x23254,x23255),f428(x23252,x23253,x23254,x23255)) % 186.05/186.64 [2326]~E(x23261,x23262)+E(f428(x23263,x23261,x23264,x23265),f428(x23263,x23262,x23264,x23265)) % 186.05/186.64 [2327]~E(x23271,x23272)+E(f428(x23273,x23274,x23271,x23275),f428(x23273,x23274,x23272,x23275)) % 186.05/186.64 [2328]~E(x23281,x23282)+E(f428(x23283,x23284,x23285,x23281),f428(x23283,x23284,x23285,x23282)) % 186.05/186.64 [2329]~E(x23291,x23292)+E(f620(x23291,x23293,x23294),f620(x23292,x23293,x23294)) % 186.05/186.64 [2330]~E(x23301,x23302)+E(f620(x23303,x23301,x23304),f620(x23303,x23302,x23304)) % 186.05/186.64 [2331]~E(x23311,x23312)+E(f620(x23313,x23314,x23311),f620(x23313,x23314,x23312)) % 186.05/186.64 [2332]~E(x23321,x23322)+E(f356(x23321,x23323,x23324,x23325),f356(x23322,x23323,x23324,x23325)) % 186.05/186.64 [2333]~E(x23331,x23332)+E(f356(x23333,x23331,x23334,x23335),f356(x23333,x23332,x23334,x23335)) % 186.05/186.64 [2334]~E(x23341,x23342)+E(f356(x23343,x23344,x23341,x23345),f356(x23343,x23344,x23342,x23345)) % 186.05/186.64 [2335]~E(x23351,x23352)+E(f356(x23353,x23354,x23355,x23351),f356(x23353,x23354,x23355,x23352)) % 186.05/186.64 [2336]~E(x23361,x23362)+E(f690(x23361,x23363,x23364,x23365),f690(x23362,x23363,x23364,x23365)) % 186.05/186.64 [2337]~E(x23371,x23372)+E(f690(x23373,x23371,x23374,x23375),f690(x23373,x23372,x23374,x23375)) % 186.05/186.64 [2338]~E(x23381,x23382)+E(f690(x23383,x23384,x23381,x23385),f690(x23383,x23384,x23382,x23385)) % 186.05/186.64 [2339]~E(x23391,x23392)+E(f690(x23393,x23394,x23395,x23391),f690(x23393,x23394,x23395,x23392)) % 186.05/186.64 [2340]~E(x23401,x23402)+E(f747(x23401,x23403,x23404),f747(x23402,x23403,x23404)) % 186.05/186.64 [2341]~E(x23411,x23412)+E(f747(x23413,x23411,x23414),f747(x23413,x23412,x23414)) % 186.05/186.64 [2342]~E(x23421,x23422)+E(f747(x23423,x23424,x23421),f747(x23423,x23424,x23422)) % 186.05/186.64 [2343]~E(x23431,x23432)+E(f377(x23431,x23433),f377(x23432,x23433)) % 186.05/186.64 [2344]~E(x23441,x23442)+E(f377(x23443,x23441),f377(x23443,x23442)) % 186.05/186.64 [2345]~E(x23451,x23452)+E(f613(x23451,x23453,x23454,x23455,x23456,x23457),f613(x23452,x23453,x23454,x23455,x23456,x23457)) % 186.05/186.64 [2346]~E(x23461,x23462)+E(f613(x23463,x23461,x23464,x23465,x23466,x23467),f613(x23463,x23462,x23464,x23465,x23466,x23467)) % 186.05/186.64 [2347]~E(x23471,x23472)+E(f613(x23473,x23474,x23471,x23475,x23476,x23477),f613(x23473,x23474,x23472,x23475,x23476,x23477)) % 186.05/186.64 [2348]~E(x23481,x23482)+E(f613(x23483,x23484,x23485,x23481,x23486,x23487),f613(x23483,x23484,x23485,x23482,x23486,x23487)) % 186.05/186.64 [2349]~E(x23491,x23492)+E(f613(x23493,x23494,x23495,x23496,x23491,x23497),f613(x23493,x23494,x23495,x23496,x23492,x23497)) % 186.05/186.64 [2350]~E(x23501,x23502)+E(f613(x23503,x23504,x23505,x23506,x23507,x23501),f613(x23503,x23504,x23505,x23506,x23507,x23502)) % 186.05/186.64 [2351]~E(x23511,x23512)+E(f235(x23511,x23513),f235(x23512,x23513)) % 186.05/186.64 [2352]~E(x23521,x23522)+E(f235(x23523,x23521),f235(x23523,x23522)) % 186.05/186.64 [2353]~E(x23531,x23532)+E(f494(x23531,x23533,x23534,x23535),f494(x23532,x23533,x23534,x23535)) % 186.05/186.64 [2354]~E(x23541,x23542)+E(f494(x23543,x23541,x23544,x23545),f494(x23543,x23542,x23544,x23545)) % 186.05/186.64 [2355]~E(x23551,x23552)+E(f494(x23553,x23554,x23551,x23555),f494(x23553,x23554,x23552,x23555)) % 186.05/186.64 [2356]~E(x23561,x23562)+E(f494(x23563,x23564,x23565,x23561),f494(x23563,x23564,x23565,x23562)) % 186.05/186.64 [2357]~E(x23571,x23572)+E(f603(x23571,x23573),f603(x23572,x23573)) % 186.05/186.64 [2358]~E(x23581,x23582)+E(f603(x23583,x23581),f603(x23583,x23582)) % 186.05/186.64 [2359]~E(x23591,x23592)+E(f543(x23591,x23593,x23594,x23595,x23596,x23597),f543(x23592,x23593,x23594,x23595,x23596,x23597)) % 186.05/186.64 [2360]~E(x23601,x23602)+E(f543(x23603,x23601,x23604,x23605,x23606,x23607),f543(x23603,x23602,x23604,x23605,x23606,x23607)) % 186.05/186.64 [2361]~E(x23611,x23612)+E(f543(x23613,x23614,x23611,x23615,x23616,x23617),f543(x23613,x23614,x23612,x23615,x23616,x23617)) % 186.05/186.64 [2362]~E(x23621,x23622)+E(f543(x23623,x23624,x23625,x23621,x23626,x23627),f543(x23623,x23624,x23625,x23622,x23626,x23627)) % 186.05/186.64 [2363]~E(x23631,x23632)+E(f543(x23633,x23634,x23635,x23636,x23631,x23637),f543(x23633,x23634,x23635,x23636,x23632,x23637)) % 186.05/186.64 [2364]~E(x23641,x23642)+E(f543(x23643,x23644,x23645,x23646,x23647,x23641),f543(x23643,x23644,x23645,x23646,x23647,x23642)) % 186.05/186.64 [2365]~E(x23651,x23652)+E(f812(x23651,x23653,x23654),f812(x23652,x23653,x23654)) % 186.05/186.64 [2366]~E(x23661,x23662)+E(f812(x23663,x23661,x23664),f812(x23663,x23662,x23664)) % 186.05/186.64 [2367]~E(x23671,x23672)+E(f812(x23673,x23674,x23671),f812(x23673,x23674,x23672)) % 186.05/186.64 [2368]~E(x23681,x23682)+E(f580(x23681,x23683),f580(x23682,x23683)) % 186.05/186.64 [2369]~E(x23691,x23692)+E(f580(x23693,x23691),f580(x23693,x23692)) % 186.05/186.64 [2370]~E(x23701,x23702)+E(f750(x23701,x23703,x23704),f750(x23702,x23703,x23704)) % 186.05/186.64 [2371]~E(x23711,x23712)+E(f750(x23713,x23711,x23714),f750(x23713,x23712,x23714)) % 186.05/186.64 [2372]~E(x23721,x23722)+E(f750(x23723,x23724,x23721),f750(x23723,x23724,x23722)) % 186.05/186.64 [2373]~E(x23731,x23732)+E(f648(x23731,x23733,x23734,x23735,x23736),f648(x23732,x23733,x23734,x23735,x23736)) % 186.05/186.64 [2374]~E(x23741,x23742)+E(f648(x23743,x23741,x23744,x23745,x23746),f648(x23743,x23742,x23744,x23745,x23746)) % 186.05/186.64 [2375]~E(x23751,x23752)+E(f648(x23753,x23754,x23751,x23755,x23756),f648(x23753,x23754,x23752,x23755,x23756)) % 186.05/186.64 [2376]~E(x23761,x23762)+E(f648(x23763,x23764,x23765,x23761,x23766),f648(x23763,x23764,x23765,x23762,x23766)) % 186.05/186.64 [2377]~E(x23771,x23772)+E(f648(x23773,x23774,x23775,x23776,x23771),f648(x23773,x23774,x23775,x23776,x23772)) % 186.05/186.64 [2378]~E(x23781,x23782)+E(f616(x23781,x23783,x23784,x23785,x23786,x23787),f616(x23782,x23783,x23784,x23785,x23786,x23787)) % 186.05/186.64 [2379]~E(x23791,x23792)+E(f616(x23793,x23791,x23794,x23795,x23796,x23797),f616(x23793,x23792,x23794,x23795,x23796,x23797)) % 186.05/186.64 [2380]~E(x23801,x23802)+E(f616(x23803,x23804,x23801,x23805,x23806,x23807),f616(x23803,x23804,x23802,x23805,x23806,x23807)) % 186.05/186.64 [2381]~E(x23811,x23812)+E(f616(x23813,x23814,x23815,x23811,x23816,x23817),f616(x23813,x23814,x23815,x23812,x23816,x23817)) % 186.05/186.64 [2382]~E(x23821,x23822)+E(f616(x23823,x23824,x23825,x23826,x23821,x23827),f616(x23823,x23824,x23825,x23826,x23822,x23827)) % 186.05/186.64 [2383]~E(x23831,x23832)+E(f616(x23833,x23834,x23835,x23836,x23837,x23831),f616(x23833,x23834,x23835,x23836,x23837,x23832)) % 186.05/186.64 [2384]~E(x23841,x23842)+E(f388(x23841,x23843,x23844,x23845,x23846),f388(x23842,x23843,x23844,x23845,x23846)) % 186.05/186.64 [2385]~E(x23851,x23852)+E(f388(x23853,x23851,x23854,x23855,x23856),f388(x23853,x23852,x23854,x23855,x23856)) % 186.05/186.64 [2386]~E(x23861,x23862)+E(f388(x23863,x23864,x23861,x23865,x23866),f388(x23863,x23864,x23862,x23865,x23866)) % 186.05/186.64 [2387]~E(x23871,x23872)+E(f388(x23873,x23874,x23875,x23871,x23876),f388(x23873,x23874,x23875,x23872,x23876)) % 186.05/186.64 [2388]~E(x23881,x23882)+E(f388(x23883,x23884,x23885,x23886,x23881),f388(x23883,x23884,x23885,x23886,x23882)) % 186.05/186.64 [2389]~E(x23891,x23892)+E(f511(x23891,x23893,x23894,x23895,x23896),f511(x23892,x23893,x23894,x23895,x23896)) % 186.05/186.64 [2390]~E(x23901,x23902)+E(f511(x23903,x23901,x23904,x23905,x23906),f511(x23903,x23902,x23904,x23905,x23906)) % 186.05/186.64 [2391]~E(x23911,x23912)+E(f511(x23913,x23914,x23911,x23915,x23916),f511(x23913,x23914,x23912,x23915,x23916)) % 186.05/186.64 [2392]~E(x23921,x23922)+E(f511(x23923,x23924,x23925,x23921,x23926),f511(x23923,x23924,x23925,x23922,x23926)) % 186.05/186.64 [2393]~E(x23931,x23932)+E(f511(x23933,x23934,x23935,x23936,x23931),f511(x23933,x23934,x23935,x23936,x23932)) % 186.05/186.64 [2394]~E(x23941,x23942)+E(f557(x23941),f557(x23942)) % 186.05/186.64 [2395]~E(x23951,x23952)+E(f582(x23951,x23953),f582(x23952,x23953)) % 186.05/186.64 [2396]~E(x23961,x23962)+E(f582(x23963,x23961),f582(x23963,x23962)) % 186.05/186.64 [2397]~E(x23971,x23972)+E(f657(x23971,x23973,x23974,x23975,x23976),f657(x23972,x23973,x23974,x23975,x23976)) % 186.05/186.64 [2398]~E(x23981,x23982)+E(f657(x23983,x23981,x23984,x23985,x23986),f657(x23983,x23982,x23984,x23985,x23986)) % 186.05/186.64 [2399]~E(x23991,x23992)+E(f657(x23993,x23994,x23991,x23995,x23996),f657(x23993,x23994,x23992,x23995,x23996)) % 186.05/186.64 [2400]~E(x24001,x24002)+E(f657(x24003,x24004,x24005,x24001,x24006),f657(x24003,x24004,x24005,x24002,x24006)) % 186.05/186.64 [2401]~E(x24011,x24012)+E(f657(x24013,x24014,x24015,x24016,x24011),f657(x24013,x24014,x24015,x24016,x24012)) % 186.05/186.64 [2402]~E(x24021,x24022)+E(f479(x24021,x24023,x24024,x24025,x24026),f479(x24022,x24023,x24024,x24025,x24026)) % 186.05/186.64 [2403]~E(x24031,x24032)+E(f479(x24033,x24031,x24034,x24035,x24036),f479(x24033,x24032,x24034,x24035,x24036)) % 186.05/186.64 [2404]~E(x24041,x24042)+E(f479(x24043,x24044,x24041,x24045,x24046),f479(x24043,x24044,x24042,x24045,x24046)) % 186.05/186.64 [2405]~E(x24051,x24052)+E(f479(x24053,x24054,x24055,x24051,x24056),f479(x24053,x24054,x24055,x24052,x24056)) % 186.05/186.64 [2406]~E(x24061,x24062)+E(f479(x24063,x24064,x24065,x24066,x24061),f479(x24063,x24064,x24065,x24066,x24062)) % 186.05/186.64 [2407]~E(x24071,x24072)+E(f118(x24071,x24073,x24074,x24075),f118(x24072,x24073,x24074,x24075)) % 186.05/186.64 [2408]~E(x24081,x24082)+E(f118(x24083,x24081,x24084,x24085),f118(x24083,x24082,x24084,x24085)) % 186.05/186.64 [2409]~E(x24091,x24092)+E(f118(x24093,x24094,x24091,x24095),f118(x24093,x24094,x24092,x24095)) % 186.05/186.64 [2410]~E(x24101,x24102)+E(f118(x24103,x24104,x24105,x24101),f118(x24103,x24104,x24105,x24102)) % 186.05/186.64 [2411]~E(x24111,x24112)+E(f764(x24111,x24113,x24114),f764(x24112,x24113,x24114)) % 186.05/186.64 [2412]~E(x24121,x24122)+E(f764(x24123,x24121,x24124),f764(x24123,x24122,x24124)) % 186.05/186.64 [2413]~E(x24131,x24132)+E(f764(x24133,x24134,x24131),f764(x24133,x24134,x24132)) % 186.05/186.64 [2414]~E(x24141,x24142)+E(f547(x24141,x24143,x24144),f547(x24142,x24143,x24144)) % 186.05/186.64 [2415]~E(x24151,x24152)+E(f547(x24153,x24151,x24154),f547(x24153,x24152,x24154)) % 186.05/186.64 [2416]~E(x24161,x24162)+E(f547(x24163,x24164,x24161),f547(x24163,x24164,x24162)) % 186.05/186.64 [2417]~E(x24171,x24172)+E(f608(x24171,x24173),f608(x24172,x24173)) % 186.05/186.64 [2418]~E(x24181,x24182)+E(f608(x24183,x24181),f608(x24183,x24182)) % 186.05/186.64 [2419]~E(x24191,x24192)+E(f588(x24191,x24193,x24194,x24195),f588(x24192,x24193,x24194,x24195)) % 186.05/186.64 [2420]~E(x24201,x24202)+E(f588(x24203,x24201,x24204,x24205),f588(x24203,x24202,x24204,x24205)) % 186.05/186.64 [2421]~E(x24211,x24212)+E(f588(x24213,x24214,x24211,x24215),f588(x24213,x24214,x24212,x24215)) % 186.05/186.64 [2422]~E(x24221,x24222)+E(f588(x24223,x24224,x24225,x24221),f588(x24223,x24224,x24225,x24222)) % 186.05/186.64 [2423]~E(x24231,x24232)+E(f452(x24231,x24233),f452(x24232,x24233)) % 186.05/186.64 [2424]~E(x24241,x24242)+E(f452(x24243,x24241),f452(x24243,x24242)) % 186.05/186.64 [2425]~E(x24251,x24252)+E(f266(x24251,x24253),f266(x24252,x24253)) % 186.05/186.64 [2426]~E(x24261,x24262)+E(f266(x24263,x24261),f266(x24263,x24262)) % 186.05/186.64 [2427]~E(x24271,x24272)+E(f632(x24271,x24273,x24274,x24275,x24276,x24277),f632(x24272,x24273,x24274,x24275,x24276,x24277)) % 186.05/186.64 [2428]~E(x24281,x24282)+E(f632(x24283,x24281,x24284,x24285,x24286,x24287),f632(x24283,x24282,x24284,x24285,x24286,x24287)) % 186.05/186.64 [2429]~E(x24291,x24292)+E(f632(x24293,x24294,x24291,x24295,x24296,x24297),f632(x24293,x24294,x24292,x24295,x24296,x24297)) % 186.05/186.64 [2430]~E(x24301,x24302)+E(f632(x24303,x24304,x24305,x24301,x24306,x24307),f632(x24303,x24304,x24305,x24302,x24306,x24307)) % 186.05/186.64 [2431]~E(x24311,x24312)+E(f632(x24313,x24314,x24315,x24316,x24311,x24317),f632(x24313,x24314,x24315,x24316,x24312,x24317)) % 186.05/186.64 [2432]~E(x24321,x24322)+E(f632(x24323,x24324,x24325,x24326,x24327,x24321),f632(x24323,x24324,x24325,x24326,x24327,x24322)) % 186.05/186.64 [2433]~E(x24331,x24332)+E(f523(x24331,x24333,x24334,x24335),f523(x24332,x24333,x24334,x24335)) % 186.05/186.64 [2434]~E(x24341,x24342)+E(f523(x24343,x24341,x24344,x24345),f523(x24343,x24342,x24344,x24345)) % 186.05/186.64 [2435]~E(x24351,x24352)+E(f523(x24353,x24354,x24351,x24355),f523(x24353,x24354,x24352,x24355)) % 186.05/186.64 [2436]~E(x24361,x24362)+E(f523(x24363,x24364,x24365,x24361),f523(x24363,x24364,x24365,x24362)) % 186.05/186.64 [2437]~E(x24371,x24372)+E(f698(x24371,x24373,x24374),f698(x24372,x24373,x24374)) % 186.05/186.64 [2438]~E(x24381,x24382)+E(f698(x24383,x24381,x24384),f698(x24383,x24382,x24384)) % 186.05/186.64 [2439]~E(x24391,x24392)+E(f698(x24393,x24394,x24391),f698(x24393,x24394,x24392)) % 186.05/186.64 [2440]~E(x24401,x24402)+E(f831(x24401,x24403,x24404),f831(x24402,x24403,x24404)) % 186.05/186.64 [2441]~E(x24411,x24412)+E(f831(x24413,x24411,x24414),f831(x24413,x24412,x24414)) % 186.05/186.64 [2442]~E(x24421,x24422)+E(f831(x24423,x24424,x24421),f831(x24423,x24424,x24422)) % 186.05/186.64 [2443]~E(x24431,x24432)+E(f201(x24431,x24433,x24434,x24435),f201(x24432,x24433,x24434,x24435)) % 186.05/186.64 [2444]~E(x24441,x24442)+E(f201(x24443,x24441,x24444,x24445),f201(x24443,x24442,x24444,x24445)) % 186.05/186.64 [2445]~E(x24451,x24452)+E(f201(x24453,x24454,x24451,x24455),f201(x24453,x24454,x24452,x24455)) % 186.05/186.64 [2446]~E(x24461,x24462)+E(f201(x24463,x24464,x24465,x24461),f201(x24463,x24464,x24465,x24462)) % 186.05/186.64 [2447]~E(x24471,x24472)+E(f312(x24471,x24473,x24474),f312(x24472,x24473,x24474)) % 186.05/186.64 [2448]~E(x24481,x24482)+E(f312(x24483,x24481,x24484),f312(x24483,x24482,x24484)) % 186.05/186.64 [2449]~E(x24491,x24492)+E(f312(x24493,x24494,x24491),f312(x24493,x24494,x24492)) % 186.05/186.64 [2450]~E(x24501,x24502)+E(f796(x24501,x24503,x24504),f796(x24502,x24503,x24504)) % 186.05/186.64 [2451]~E(x24511,x24512)+E(f796(x24513,x24511,x24514),f796(x24513,x24512,x24514)) % 186.05/186.64 [2452]~E(x24521,x24522)+E(f796(x24523,x24524,x24521),f796(x24523,x24524,x24522)) % 186.05/186.64 [2453]~E(x24531,x24532)+E(f357(x24531,x24533,x24534,x24535),f357(x24532,x24533,x24534,x24535)) % 186.05/186.64 [2454]~E(x24541,x24542)+E(f357(x24543,x24541,x24544,x24545),f357(x24543,x24542,x24544,x24545)) % 186.05/186.64 [2455]~E(x24551,x24552)+E(f357(x24553,x24554,x24551,x24555),f357(x24553,x24554,x24552,x24555)) % 186.05/186.64 [2456]~E(x24561,x24562)+E(f357(x24563,x24564,x24565,x24561),f357(x24563,x24564,x24565,x24562)) % 186.05/186.64 [2457]~E(x24571,x24572)+E(f401(x24571),f401(x24572)) % 186.05/186.64 [2458]~E(x24581,x24582)+E(f584(x24581,x24583),f584(x24582,x24583)) % 186.05/186.64 [2459]~E(x24591,x24592)+E(f584(x24593,x24591),f584(x24593,x24592)) % 186.05/186.64 [2460]~E(x24601,x24602)+E(f359(x24601,x24603,x24604,x24605,x24606),f359(x24602,x24603,x24604,x24605,x24606)) % 186.05/186.64 [2461]~E(x24611,x24612)+E(f359(x24613,x24611,x24614,x24615,x24616),f359(x24613,x24612,x24614,x24615,x24616)) % 186.05/186.64 [2462]~E(x24621,x24622)+E(f359(x24623,x24624,x24621,x24625,x24626),f359(x24623,x24624,x24622,x24625,x24626)) % 186.05/186.64 [2463]~E(x24631,x24632)+E(f359(x24633,x24634,x24635,x24631,x24636),f359(x24633,x24634,x24635,x24632,x24636)) % 186.05/186.64 [2464]~E(x24641,x24642)+E(f359(x24643,x24644,x24645,x24646,x24641),f359(x24643,x24644,x24645,x24646,x24642)) % 186.05/186.64 [2465]~E(x24651,x24652)+E(f407(x24651,x24653,x24654),f407(x24652,x24653,x24654)) % 186.05/186.64 [2466]~E(x24661,x24662)+E(f407(x24663,x24661,x24664),f407(x24663,x24662,x24664)) % 186.05/186.64 [2467]~E(x24671,x24672)+E(f407(x24673,x24674,x24671),f407(x24673,x24674,x24672)) % 186.05/186.64 [2468]~E(x24681,x24682)+E(f618(x24681),f618(x24682)) % 186.05/186.64 [2469]~E(x24691,x24692)+E(f467(x24691,x24693,x24694),f467(x24692,x24693,x24694)) % 186.05/186.64 [2470]~E(x24701,x24702)+E(f467(x24703,x24701,x24704),f467(x24703,x24702,x24704)) % 186.05/186.64 [2471]~E(x24711,x24712)+E(f467(x24713,x24714,x24711),f467(x24713,x24714,x24712)) % 186.05/186.64 [2472]~E(x24721,x24722)+E(f285(x24721,x24723),f285(x24722,x24723)) % 186.05/186.64 [2473]~E(x24731,x24732)+E(f285(x24733,x24731),f285(x24733,x24732)) % 186.05/186.64 [2474]~E(x24741,x24742)+E(f95(x24741,x24743,x24744),f95(x24742,x24743,x24744)) % 186.05/186.64 [2475]~E(x24751,x24752)+E(f95(x24753,x24751,x24754),f95(x24753,x24752,x24754)) % 186.05/186.64 [2476]~E(x24761,x24762)+E(f95(x24763,x24764,x24761),f95(x24763,x24764,x24762)) % 186.05/186.64 [2477]~E(x24771,x24772)+E(f271(x24771,x24773,x24774,x24775),f271(x24772,x24773,x24774,x24775)) % 186.05/186.64 [2478]~E(x24781,x24782)+E(f271(x24783,x24781,x24784,x24785),f271(x24783,x24782,x24784,x24785)) % 186.05/186.64 [2479]~E(x24791,x24792)+E(f271(x24793,x24794,x24791,x24795),f271(x24793,x24794,x24792,x24795)) % 186.05/186.64 [2480]~E(x24801,x24802)+E(f271(x24803,x24804,x24805,x24801),f271(x24803,x24804,x24805,x24802)) % 186.05/186.64 [2481]~E(x24811,x24812)+E(f471(x24811),f471(x24812)) % 186.05/186.64 [2482]~E(x24821,x24822)+E(f756(x24821,x24823,x24824),f756(x24822,x24823,x24824)) % 186.05/186.64 [2483]~E(x24831,x24832)+E(f756(x24833,x24831,x24834),f756(x24833,x24832,x24834)) % 186.05/186.64 [2484]~E(x24841,x24842)+E(f756(x24843,x24844,x24841),f756(x24843,x24844,x24842)) % 186.05/186.64 [2485]~E(x24851,x24852)+E(f315(x24851,x24853,x24854),f315(x24852,x24853,x24854)) % 186.05/186.64 [2486]~E(x24861,x24862)+E(f315(x24863,x24861,x24864),f315(x24863,x24862,x24864)) % 186.05/186.64 [2487]~E(x24871,x24872)+E(f315(x24873,x24874,x24871),f315(x24873,x24874,x24872)) % 186.05/186.64 [2488]~E(x24881,x24882)+E(f316(x24881,x24883,x24884,x24885),f316(x24882,x24883,x24884,x24885)) % 186.05/186.64 [2489]~E(x24891,x24892)+E(f316(x24893,x24891,x24894,x24895),f316(x24893,x24892,x24894,x24895)) % 186.05/186.64 [2490]~E(x24901,x24902)+E(f316(x24903,x24904,x24901,x24905),f316(x24903,x24904,x24902,x24905)) % 186.05/186.64 [2491]~E(x24911,x24912)+E(f316(x24913,x24914,x24915,x24911),f316(x24913,x24914,x24915,x24912)) % 186.05/186.64 [2492]~E(x24921,x24922)+E(f217(x24921,x24923,x24924),f217(x24922,x24923,x24924)) % 186.05/186.64 [2493]~E(x24931,x24932)+E(f217(x24933,x24931,x24934),f217(x24933,x24932,x24934)) % 186.05/186.64 [2494]~E(x24941,x24942)+E(f217(x24943,x24944,x24941),f217(x24943,x24944,x24942)) % 186.05/186.64 [2495]~E(x24951,x24952)+E(f343(x24951,x24953),f343(x24952,x24953)) % 186.05/186.64 [2496]~E(x24961,x24962)+E(f343(x24963,x24961),f343(x24963,x24962)) % 186.05/186.64 [2497]~E(x24971,x24972)+E(f653(x24971,x24973,x24974,x24975),f653(x24972,x24973,x24974,x24975)) % 186.05/186.64 [2498]~E(x24981,x24982)+E(f653(x24983,x24981,x24984,x24985),f653(x24983,x24982,x24984,x24985)) % 186.05/186.64 [2499]~E(x24991,x24992)+E(f653(x24993,x24994,x24991,x24995),f653(x24993,x24994,x24992,x24995)) % 186.05/186.64 [2500]~E(x25001,x25002)+E(f653(x25003,x25004,x25005,x25001),f653(x25003,x25004,x25005,x25002)) % 186.05/186.64 [2501]~E(x25011,x25012)+E(f274(x25011,x25013,x25014,x25015),f274(x25012,x25013,x25014,x25015)) % 186.05/186.64 [2502]~E(x25021,x25022)+E(f274(x25023,x25021,x25024,x25025),f274(x25023,x25022,x25024,x25025)) % 186.05/186.64 [2503]~E(x25031,x25032)+E(f274(x25033,x25034,x25031,x25035),f274(x25033,x25034,x25032,x25035)) % 186.05/186.64 [2504]~E(x25041,x25042)+E(f274(x25043,x25044,x25045,x25041),f274(x25043,x25044,x25045,x25042)) % 186.05/186.64 [2505]~E(x25051,x25052)+E(f695(x25051,x25053,x25054),f695(x25052,x25053,x25054)) % 186.05/186.64 [2506]~E(x25061,x25062)+E(f695(x25063,x25061,x25064),f695(x25063,x25062,x25064)) % 186.05/186.64 [2507]~E(x25071,x25072)+E(f695(x25073,x25074,x25071),f695(x25073,x25074,x25072)) % 186.05/186.64 [2508]~E(x25081,x25082)+E(f510(x25081,x25083,x25084,x25085,x25086),f510(x25082,x25083,x25084,x25085,x25086)) % 186.05/186.64 [2509]~E(x25091,x25092)+E(f510(x25093,x25091,x25094,x25095,x25096),f510(x25093,x25092,x25094,x25095,x25096)) % 186.05/186.64 [2510]~E(x25101,x25102)+E(f510(x25103,x25104,x25101,x25105,x25106),f510(x25103,x25104,x25102,x25105,x25106)) % 186.05/186.64 [2511]~E(x25111,x25112)+E(f510(x25113,x25114,x25115,x25111,x25116),f510(x25113,x25114,x25115,x25112,x25116)) % 186.05/186.64 [2512]~E(x25121,x25122)+E(f510(x25123,x25124,x25125,x25126,x25121),f510(x25123,x25124,x25125,x25126,x25122)) % 186.05/186.64 [2513]~E(x25131,x25132)+E(f402(x25131,x25133),f402(x25132,x25133)) % 186.05/186.64 [2514]~E(x25141,x25142)+E(f402(x25143,x25141),f402(x25143,x25142)) % 186.05/186.64 [2515]~E(x25151,x25152)+E(f96(x25151,x25153,x25154,x25155),f96(x25152,x25153,x25154,x25155)) % 186.05/186.64 [2516]~E(x25161,x25162)+E(f96(x25163,x25161,x25164,x25165),f96(x25163,x25162,x25164,x25165)) % 186.05/186.64 [2517]~E(x25171,x25172)+E(f96(x25173,x25174,x25171,x25175),f96(x25173,x25174,x25172,x25175)) % 186.05/186.64 [2518]~E(x25181,x25182)+E(f96(x25183,x25184,x25185,x25181),f96(x25183,x25184,x25185,x25182)) % 186.05/186.64 [2519]~E(x25191,x25192)+E(f811(x25191,x25193,x25194),f811(x25192,x25193,x25194)) % 186.05/186.64 [2520]~E(x25201,x25202)+E(f811(x25203,x25201,x25204),f811(x25203,x25202,x25204)) % 186.05/186.64 [2521]~E(x25211,x25212)+E(f811(x25213,x25214,x25211),f811(x25213,x25214,x25212)) % 186.05/186.64 [2522]~E(x25221,x25222)+E(f571(x25221),f571(x25222)) % 186.05/186.64 [2523]~E(x25231,x25232)+E(f791(x25231,x25233),f791(x25232,x25233)) % 186.05/186.64 [2524]~E(x25241,x25242)+E(f791(x25243,x25241),f791(x25243,x25242)) % 186.05/186.64 [2525]~E(x25251,x25252)+E(f473(x25251,x25253),f473(x25252,x25253)) % 186.05/186.64 [2526]~E(x25261,x25262)+E(f473(x25263,x25261),f473(x25263,x25262)) % 186.05/186.64 [2527]~E(x25271,x25272)+E(f597(x25271,x25273,x25274,x25275),f597(x25272,x25273,x25274,x25275)) % 186.05/186.64 [2528]~E(x25281,x25282)+E(f597(x25283,x25281,x25284,x25285),f597(x25283,x25282,x25284,x25285)) % 186.05/186.64 [2529]~E(x25291,x25292)+E(f597(x25293,x25294,x25291,x25295),f597(x25293,x25294,x25292,x25295)) % 186.05/186.64 [2530]~E(x25301,x25302)+E(f597(x25303,x25304,x25305,x25301),f597(x25303,x25304,x25305,x25302)) % 186.05/186.64 [2531]~E(x25311,x25312)+E(f199(x25311),f199(x25312)) % 186.05/186.64 [2532]~E(x25321,x25322)+E(f491(x25321,x25323),f491(x25322,x25323)) % 186.05/186.64 [2533]~E(x25331,x25332)+E(f491(x25333,x25331),f491(x25333,x25332)) % 186.05/186.64 [2534]~E(x25341,x25342)+E(f129(x25341),f129(x25342)) % 186.05/186.64 [2535]~E(x25351,x25352)+E(f596(x25351,x25353),f596(x25352,x25353)) % 186.05/186.64 [2536]~E(x25361,x25362)+E(f596(x25363,x25361),f596(x25363,x25362)) % 186.05/186.64 [2537]~E(x25371,x25372)+E(f589(x25371,x25373),f589(x25372,x25373)) % 186.05/186.64 [2538]~E(x25381,x25382)+E(f589(x25383,x25381),f589(x25383,x25382)) % 186.05/186.64 [2539]~E(x25391,x25392)+E(f573(x25391,x25393,x25394,x25395,x25396,x25397,x25398,x25399),f573(x25392,x25393,x25394,x25395,x25396,x25397,x25398,x25399)) % 186.05/186.64 [2540]~E(x25401,x25402)+E(f573(x25403,x25401,x25404,x25405,x25406,x25407,x25408,x25409),f573(x25403,x25402,x25404,x25405,x25406,x25407,x25408,x25409)) % 186.05/186.64 [2541]~E(x25411,x25412)+E(f573(x25413,x25414,x25411,x25415,x25416,x25417,x25418,x25419),f573(x25413,x25414,x25412,x25415,x25416,x25417,x25418,x25419)) % 186.05/186.64 [2542]~E(x25421,x25422)+E(f573(x25423,x25424,x25425,x25421,x25426,x25427,x25428,x25429),f573(x25423,x25424,x25425,x25422,x25426,x25427,x25428,x25429)) % 186.05/186.64 [2543]~E(x25431,x25432)+E(f573(x25433,x25434,x25435,x25436,x25431,x25437,x25438,x25439),f573(x25433,x25434,x25435,x25436,x25432,x25437,x25438,x25439)) % 186.05/186.64 [2544]~E(x25441,x25442)+E(f573(x25443,x25444,x25445,x25446,x25447,x25441,x25448,x25449),f573(x25443,x25444,x25445,x25446,x25447,x25442,x25448,x25449)) % 186.05/186.64 [2545]~E(x25451,x25452)+E(f573(x25453,x25454,x25455,x25456,x25457,x25458,x25451,x25459),f573(x25453,x25454,x25455,x25456,x25457,x25458,x25452,x25459)) % 186.05/186.64 [2546]~E(x25461,x25462)+E(f573(x25463,x25464,x25465,x25466,x25467,x25468,x25469,x25461),f573(x25463,x25464,x25465,x25466,x25467,x25468,x25469,x25462)) % 186.05/186.64 [2547]~E(x25471,x25472)+E(f403(x25471,x25473),f403(x25472,x25473)) % 186.05/186.64 [2548]~E(x25481,x25482)+E(f403(x25483,x25481),f403(x25483,x25482)) % 186.05/186.64 [2549]~P1(x25491)+P1(x25492)+~E(x25491,x25492) % 186.05/186.64 [2550]~P2(x25501)+P2(x25502)+~E(x25501,x25502) % 186.05/186.64 [2551]~P100(x25511)+P100(x25512)+~E(x25511,x25512) % 186.05/186.64 [2552]~P9(x25521)+P9(x25522)+~E(x25521,x25522) % 186.05/186.64 [2553]~P3(x25531)+P3(x25532)+~E(x25531,x25532) % 186.05/186.64 [2554]~P102(x25541)+P102(x25542)+~E(x25541,x25542) % 186.05/186.64 [2555]~P7(x25551)+P7(x25552)+~E(x25551,x25552) % 186.05/186.64 [2556]~P4(x25561)+P4(x25562)+~E(x25561,x25562) % 186.05/186.64 [2557]P50(x25572,x25573,x25574,x25575)+~E(x25571,x25572)+~P50(x25571,x25573,x25574,x25575) % 186.05/186.64 [2558]P50(x25583,x25582,x25584,x25585)+~E(x25581,x25582)+~P50(x25583,x25581,x25584,x25585) % 186.05/186.64 [2559]P50(x25593,x25594,x25592,x25595)+~E(x25591,x25592)+~P50(x25593,x25594,x25591,x25595) % 186.05/186.64 [2560]P50(x25603,x25604,x25605,x25602)+~E(x25601,x25602)+~P50(x25603,x25604,x25605,x25601) % 186.05/186.64 [2561]~P93(x25611)+P93(x25612)+~E(x25611,x25612) % 186.05/186.64 [2562]~P5(x25621)+P5(x25622)+~E(x25621,x25622) % 186.05/186.64 [2563]P28(x25632,x25633,x25634)+~E(x25631,x25632)+~P28(x25631,x25633,x25634) % 186.05/186.64 [2564]P28(x25643,x25642,x25644)+~E(x25641,x25642)+~P28(x25643,x25641,x25644) % 186.05/186.64 [2565]P28(x25653,x25654,x25652)+~E(x25651,x25652)+~P28(x25653,x25654,x25651) % 186.05/186.64 [2566]~P137(x25661)+P137(x25662)+~E(x25661,x25662) % 186.05/186.64 [2567]~P66(x25671)+P66(x25672)+~E(x25671,x25672) % 186.05/186.64 [2568]~P78(x25681)+P78(x25682)+~E(x25681,x25682) % 186.05/186.64 [2569]~P111(x25691)+P111(x25692)+~E(x25691,x25692) % 186.05/186.64 [2570]~P67(x25701)+P67(x25702)+~E(x25701,x25702) % 186.05/186.64 [2571]P39(x25712,x25713,x25714,x25715)+~E(x25711,x25712)+~P39(x25711,x25713,x25714,x25715) % 186.05/186.64 [2572]P39(x25723,x25722,x25724,x25725)+~E(x25721,x25722)+~P39(x25723,x25721,x25724,x25725) % 186.05/186.64 [2573]P39(x25733,x25734,x25732,x25735)+~E(x25731,x25732)+~P39(x25733,x25734,x25731,x25735) % 186.05/186.64 [2574]P39(x25743,x25744,x25745,x25742)+~E(x25741,x25742)+~P39(x25743,x25744,x25745,x25741) % 186.05/186.64 [2575]~P110(x25751)+P110(x25752)+~E(x25751,x25752) % 186.05/186.64 [2576]~P68(x25761)+P68(x25762)+~E(x25761,x25762) % 186.05/186.64 [2577]~P73(x25771)+P73(x25772)+~E(x25771,x25772) % 186.05/186.64 [2578]~P62(x25781)+P62(x25782)+~E(x25781,x25782) % 186.05/186.64 [2579]~P119(x25791)+P119(x25792)+~E(x25791,x25792) % 186.05/186.64 [2580]~P91(x25801)+P91(x25802)+~E(x25801,x25802) % 186.05/186.64 [2581]~P74(x25811)+P74(x25812)+~E(x25811,x25812) % 186.05/186.64 [2582]~P85(x25821)+P85(x25822)+~E(x25821,x25822) % 186.05/186.64 [2583]P140(x25832,x25833,x25834)+~E(x25831,x25832)+~P140(x25831,x25833,x25834) % 186.05/186.64 [2584]P140(x25843,x25842,x25844)+~E(x25841,x25842)+~P140(x25843,x25841,x25844) % 186.05/186.64 [2585]P140(x25853,x25854,x25852)+~E(x25851,x25852)+~P140(x25853,x25854,x25851) % 186.05/186.64 [2586]~P133(x25861)+P133(x25862)+~E(x25861,x25862) % 186.05/186.64 [2587]P18(x25872,x25873)+~E(x25871,x25872)+~P18(x25871,x25873) % 186.05/186.64 [2588]P18(x25883,x25882)+~E(x25881,x25882)+~P18(x25883,x25881) % 186.05/186.64 [2589]~P99(x25891)+P99(x25892)+~E(x25891,x25892) % 186.05/186.64 [2590]~P63(x25901)+P63(x25902)+~E(x25901,x25902) % 186.05/186.64 [2591]~P80(x25911)+P80(x25912)+~E(x25911,x25912) % 186.05/186.64 [2592]~P38(x25921)+P38(x25922)+~E(x25921,x25922) % 186.05/186.64 [2593]~P117(x25931)+P117(x25932)+~E(x25931,x25932) % 186.05/186.64 [2594]P141(x25942,x25943,x25944)+~E(x25941,x25942)+~P141(x25941,x25943,x25944) % 186.05/186.64 [2595]P141(x25953,x25952,x25954)+~E(x25951,x25952)+~P141(x25953,x25951,x25954) % 186.05/186.64 [2596]P141(x25963,x25964,x25962)+~E(x25961,x25962)+~P141(x25963,x25964,x25961) % 186.05/186.64 [2597]~P81(x25971)+P81(x25972)+~E(x25971,x25972) % 186.05/186.64 [2598]~P132(x25981)+P132(x25982)+~E(x25981,x25982) % 186.05/186.64 [2599]P29(x25992,x25993,x25994,x25995)+~E(x25991,x25992)+~P29(x25991,x25993,x25994,x25995) % 186.05/186.64 [2600]P29(x26003,x26002,x26004,x26005)+~E(x26001,x26002)+~P29(x26003,x26001,x26004,x26005) % 186.05/186.64 [2601]P29(x26013,x26014,x26012,x26015)+~E(x26011,x26012)+~P29(x26013,x26014,x26011,x26015) % 186.05/186.64 [2602]P29(x26023,x26024,x26025,x26022)+~E(x26021,x26022)+~P29(x26023,x26024,x26025,x26021) % 186.05/186.64 [2603]~P89(x26031)+P89(x26032)+~E(x26031,x26032) % 186.05/186.64 [2604]~P88(x26041)+P88(x26042)+~E(x26041,x26042) % 186.05/186.64 [2605]P55(x26052,x26053,x26054,x26055,x26056)+~E(x26051,x26052)+~P55(x26051,x26053,x26054,x26055,x26056) % 186.05/186.64 [2606]P55(x26063,x26062,x26064,x26065,x26066)+~E(x26061,x26062)+~P55(x26063,x26061,x26064,x26065,x26066) % 186.05/186.64 [2607]P55(x26073,x26074,x26072,x26075,x26076)+~E(x26071,x26072)+~P55(x26073,x26074,x26071,x26075,x26076) % 186.05/186.64 [2608]P55(x26083,x26084,x26085,x26082,x26086)+~E(x26081,x26082)+~P55(x26083,x26084,x26085,x26081,x26086) % 186.05/186.64 [2609]P55(x26093,x26094,x26095,x26096,x26092)+~E(x26091,x26092)+~P55(x26093,x26094,x26095,x26096,x26091) % 186.05/186.64 [2610]~P86(x26101)+P86(x26102)+~E(x26101,x26102) % 186.05/186.64 [2611]~P103(x26111)+P103(x26112)+~E(x26111,x26112) % 186.05/186.64 [2612]P36(x26122,x26123)+~E(x26121,x26122)+~P36(x26121,x26123) % 186.05/186.64 [2613]P36(x26133,x26132)+~E(x26131,x26132)+~P36(x26133,x26131) % 186.05/186.64 [2614]~P61(x26141)+P61(x26142)+~E(x26141,x26142) % 186.05/186.64 [2615]~P77(x26151)+P77(x26152)+~E(x26151,x26152) % 186.05/186.64 [2616]P22(x26162,x26163,x26164)+~E(x26161,x26162)+~P22(x26161,x26163,x26164) % 186.05/186.64 [2617]P22(x26173,x26172,x26174)+~E(x26171,x26172)+~P22(x26173,x26171,x26174) % 186.05/186.64 [2618]P22(x26183,x26184,x26182)+~E(x26181,x26182)+~P22(x26183,x26184,x26181) % 186.05/186.64 [2619]P23(x26192,x26193,x26194,x26195)+~E(x26191,x26192)+~P23(x26191,x26193,x26194,x26195) % 186.05/186.64 [2620]P23(x26203,x26202,x26204,x26205)+~E(x26201,x26202)+~P23(x26203,x26201,x26204,x26205) % 186.05/186.64 [2621]P23(x26213,x26214,x26212,x26215)+~E(x26211,x26212)+~P23(x26213,x26214,x26211,x26215) % 186.05/186.64 [2622]P23(x26223,x26224,x26225,x26222)+~E(x26221,x26222)+~P23(x26223,x26224,x26225,x26221) % 186.05/186.64 [2623]~P90(x26231)+P90(x26232)+~E(x26231,x26232) % 186.05/186.64 [2624]~P79(x26241)+P79(x26242)+~E(x26241,x26242) % 186.05/186.64 [2625]P53(x26252,x26253,x26254)+~E(x26251,x26252)+~P53(x26251,x26253,x26254) % 186.05/186.64 [2626]P53(x26263,x26262,x26264)+~E(x26261,x26262)+~P53(x26263,x26261,x26264) % 186.05/186.64 [2627]P53(x26273,x26274,x26272)+~E(x26271,x26272)+~P53(x26273,x26274,x26271) % 186.05/186.64 [2628]~P60(x26281)+P60(x26282)+~E(x26281,x26282) % 186.05/186.64 [2629]~P75(x26291)+P75(x26292)+~E(x26291,x26292) % 186.05/186.64 [2630]P47(x26302,x26303,x26304)+~E(x26301,x26302)+~P47(x26301,x26303,x26304) % 186.05/186.64 [2631]P47(x26313,x26312,x26314)+~E(x26311,x26312)+~P47(x26313,x26311,x26314) % 186.05/186.64 [2632]P47(x26323,x26324,x26322)+~E(x26321,x26322)+~P47(x26323,x26324,x26321) % 186.05/186.64 [2633]P56(x26332,x26333)+~E(x26331,x26332)+~P56(x26331,x26333) % 186.05/186.64 [2634]P56(x26343,x26342)+~E(x26341,x26342)+~P56(x26343,x26341) % 186.05/186.64 [2635]P12(x26352,x26353,x26354)+~E(x26351,x26352)+~P12(x26351,x26353,x26354) % 186.05/186.64 [2636]P12(x26363,x26362,x26364)+~E(x26361,x26362)+~P12(x26363,x26361,x26364) % 186.05/186.64 [2637]P12(x26373,x26374,x26372)+~E(x26371,x26372)+~P12(x26373,x26374,x26371) % 186.05/186.64 [2638]~P65(x26381)+P65(x26382)+~E(x26381,x26382) % 186.05/186.64 [2639]~P129(x26391)+P129(x26392)+~E(x26391,x26392) % 186.05/186.64 [2640]P20(x26402,x26403,x26404)+~E(x26401,x26402)+~P20(x26401,x26403,x26404) % 186.05/186.64 [2641]P20(x26413,x26412,x26414)+~E(x26411,x26412)+~P20(x26413,x26411,x26414) % 186.05/186.64 [2642]P20(x26423,x26424,x26422)+~E(x26421,x26422)+~P20(x26423,x26424,x26421) % 186.05/186.64 [2643]~P92(x26431)+P92(x26432)+~E(x26431,x26432) % 186.05/186.64 [2644]~P120(x26441)+P120(x26442)+~E(x26441,x26442) % 186.05/186.64 [2645]~P121(x26451)+P121(x26452)+~E(x26451,x26452) % 186.05/186.64 [2646]~P64(x26461)+P64(x26462)+~E(x26461,x26462) % 186.05/186.64 [2647]~P112(x26471)+P112(x26472)+~E(x26471,x26472) % 186.05/186.64 [2648]P32(x26482,x26483,x26484)+~E(x26481,x26482)+~P32(x26481,x26483,x26484) % 186.05/186.64 [2649]P32(x26493,x26492,x26494)+~E(x26491,x26492)+~P32(x26493,x26491,x26494) % 186.05/186.64 [2650]P32(x26503,x26504,x26502)+~E(x26501,x26502)+~P32(x26503,x26504,x26501) % 186.05/186.64 [2651]~P69(x26511)+P69(x26512)+~E(x26511,x26512) % 186.05/186.64 [2652]~P70(x26521)+P70(x26522)+~E(x26521,x26522) % 186.05/186.64 [2653]~P105(x26531)+P105(x26532)+~E(x26531,x26532) % 186.05/186.64 [2654]P27(x26542,x26543,x26544,x26545,x26546,x26547)+~E(x26541,x26542)+~P27(x26541,x26543,x26544,x26545,x26546,x26547) % 186.05/186.64 [2655]P27(x26553,x26552,x26554,x26555,x26556,x26557)+~E(x26551,x26552)+~P27(x26553,x26551,x26554,x26555,x26556,x26557) % 186.05/186.64 [2656]P27(x26563,x26564,x26562,x26565,x26566,x26567)+~E(x26561,x26562)+~P27(x26563,x26564,x26561,x26565,x26566,x26567) % 186.05/186.64 [2657]P27(x26573,x26574,x26575,x26572,x26576,x26577)+~E(x26571,x26572)+~P27(x26573,x26574,x26575,x26571,x26576,x26577) % 186.05/186.64 [2658]P27(x26583,x26584,x26585,x26586,x26582,x26587)+~E(x26581,x26582)+~P27(x26583,x26584,x26585,x26586,x26581,x26587) % 186.05/186.64 [2659]P27(x26593,x26594,x26595,x26596,x26597,x26592)+~E(x26591,x26592)+~P27(x26593,x26594,x26595,x26596,x26597,x26591) % 186.05/186.64 [2660]~P59(x26601)+P59(x26602)+~E(x26601,x26602) % 186.05/186.64 [2661]P57(x26612,x26613,x26614,x26615)+~E(x26611,x26612)+~P57(x26611,x26613,x26614,x26615) % 186.05/186.64 [2662]P57(x26623,x26622,x26624,x26625)+~E(x26621,x26622)+~P57(x26623,x26621,x26624,x26625) % 186.05/186.64 [2663]P57(x26633,x26634,x26632,x26635)+~E(x26631,x26632)+~P57(x26633,x26634,x26631,x26635) % 186.05/186.64 [2664]P57(x26643,x26644,x26645,x26642)+~E(x26641,x26642)+~P57(x26643,x26644,x26645,x26641) % 186.05/186.64 [2665]P26(x26652,x26653,x26654,x26655,x26656,x26657)+~E(x26651,x26652)+~P26(x26651,x26653,x26654,x26655,x26656,x26657) % 186.05/186.64 [2666]P26(x26663,x26662,x26664,x26665,x26666,x26667)+~E(x26661,x26662)+~P26(x26663,x26661,x26664,x26665,x26666,x26667) % 186.05/186.64 [2667]P26(x26673,x26674,x26672,x26675,x26676,x26677)+~E(x26671,x26672)+~P26(x26673,x26674,x26671,x26675,x26676,x26677) % 186.05/186.64 [2668]P26(x26683,x26684,x26685,x26682,x26686,x26687)+~E(x26681,x26682)+~P26(x26683,x26684,x26685,x26681,x26686,x26687) % 186.05/186.64 [2669]P26(x26693,x26694,x26695,x26696,x26692,x26697)+~E(x26691,x26692)+~P26(x26693,x26694,x26695,x26696,x26691,x26697) % 186.05/186.64 [2670]P26(x26703,x26704,x26705,x26706,x26707,x26702)+~E(x26701,x26702)+~P26(x26703,x26704,x26705,x26706,x26707,x26701) % 186.05/186.64 [2671]~P76(x26711)+P76(x26712)+~E(x26711,x26712) % 186.05/186.64 [2672]~P98(x26721)+P98(x26722)+~E(x26721,x26722) % 186.05/186.64 [2673]~P136(x26731)+P136(x26732)+~E(x26731,x26732) % 186.05/186.64 [2674]~P87(x26741)+P87(x26742)+~E(x26741,x26742) % 186.05/186.64 [2675]~P10(x26751)+P10(x26752)+~E(x26751,x26752) % 186.05/186.64 [2676]~P104(x26761)+P104(x26762)+~E(x26761,x26762) % 186.05/186.64 [2677]P58(x26772,x26773)+~E(x26771,x26772)+~P58(x26771,x26773) % 186.05/186.64 [2678]P58(x26783,x26782)+~E(x26781,x26782)+~P58(x26783,x26781) % 186.05/186.64 [2679]~P6(x26791)+P6(x26792)+~E(x26791,x26792) % 186.05/186.64 [2680]~P122(x26801)+P122(x26802)+~E(x26801,x26802) % 186.05/186.64 [2681]P31(x26812,x26813,x26814)+~E(x26811,x26812)+~P31(x26811,x26813,x26814) % 186.05/186.64 [2682]P31(x26823,x26822,x26824)+~E(x26821,x26822)+~P31(x26823,x26821,x26824) % 186.05/186.64 [2683]P31(x26833,x26834,x26832)+~E(x26831,x26832)+~P31(x26833,x26834,x26831) % 186.05/186.64 [2684]P33(x26842,x26843)+~E(x26841,x26842)+~P33(x26841,x26843) % 186.05/186.64 [2685]P33(x26853,x26852)+~E(x26851,x26852)+~P33(x26853,x26851) % 186.05/186.64 [2686]~P134(x26861)+P134(x26862)+~E(x26861,x26862) % 186.05/186.64 [2687]~P127(x26871)+P127(x26872)+~E(x26871,x26872) % 186.05/186.64 [2688]P42(x26882,x26883)+~E(x26881,x26882)+~P42(x26881,x26883) % 186.05/186.64 [2689]P42(x26893,x26892)+~E(x26891,x26892)+~P42(x26893,x26891) % 186.05/186.64 [2690]P25(x26902,x26903,x26904,x26905,x26906)+~E(x26901,x26902)+~P25(x26901,x26903,x26904,x26905,x26906) % 186.05/186.64 [2691]P25(x26913,x26912,x26914,x26915,x26916)+~E(x26911,x26912)+~P25(x26913,x26911,x26914,x26915,x26916) % 186.05/186.64 [2692]P25(x26923,x26924,x26922,x26925,x26926)+~E(x26921,x26922)+~P25(x26923,x26924,x26921,x26925,x26926) % 186.05/186.64 [2693]P25(x26933,x26934,x26935,x26932,x26936)+~E(x26931,x26932)+~P25(x26933,x26934,x26935,x26931,x26936) % 186.05/186.64 [2694]P25(x26943,x26944,x26945,x26946,x26942)+~E(x26941,x26942)+~P25(x26943,x26944,x26945,x26946,x26941) % 186.05/186.64 [2695]~P138(x26951)+P138(x26952)+~E(x26951,x26952) % 186.05/186.64 [2696]P45(x26962,x26963,x26964)+~E(x26961,x26962)+~P45(x26961,x26963,x26964) % 186.05/186.64 [2697]P45(x26973,x26972,x26974)+~E(x26971,x26972)+~P45(x26973,x26971,x26974) % 186.05/186.64 [2698]P45(x26983,x26984,x26982)+~E(x26981,x26982)+~P45(x26983,x26984,x26981) % 186.05/186.64 [2699]P37(x26992,x26993)+~E(x26991,x26992)+~P37(x26991,x26993) % 186.05/186.64 [2700]P37(x27003,x27002)+~E(x27001,x27002)+~P37(x27003,x27001) % 186.05/186.64 [2701]~P109(x27011)+P109(x27012)+~E(x27011,x27012) % 186.05/186.64 [2702]P52(x27022,x27023,x27024,x27025)+~E(x27021,x27022)+~P52(x27021,x27023,x27024,x27025) % 186.05/186.64 [2703]P52(x27033,x27032,x27034,x27035)+~E(x27031,x27032)+~P52(x27033,x27031,x27034,x27035) % 186.05/186.64 [2704]P52(x27043,x27044,x27042,x27045)+~E(x27041,x27042)+~P52(x27043,x27044,x27041,x27045) % 186.05/186.64 [2705]P52(x27053,x27054,x27055,x27052)+~E(x27051,x27052)+~P52(x27053,x27054,x27055,x27051) % 186.05/186.64 [2706]~P123(x27061)+P123(x27062)+~E(x27061,x27062) % 186.05/186.64 [2707]~P135(x27071)+P135(x27072)+~E(x27071,x27072) % 186.05/186.64 [2708]~P43(x27081)+P43(x27082)+~E(x27081,x27082) % 186.05/186.64 [2709]~P139(x27091)+P139(x27092)+~E(x27091,x27092) % 186.05/186.64 [2710]~P118(x27101)+P118(x27102)+~E(x27101,x27102) % 186.05/186.64 [2711]~P94(x27111)+P94(x27112)+~E(x27111,x27112) % 186.05/186.64 [2712]~P113(x27121)+P113(x27122)+~E(x27121,x27122) % 186.05/186.64 [2713]P51(x27132,x27133,x27134,x27135,x27136,x27137,x27138)+~E(x27131,x27132)+~P51(x27131,x27133,x27134,x27135,x27136,x27137,x27138) % 186.05/186.64 [2714]P51(x27143,x27142,x27144,x27145,x27146,x27147,x27148)+~E(x27141,x27142)+~P51(x27143,x27141,x27144,x27145,x27146,x27147,x27148) % 186.05/186.64 [2715]P51(x27153,x27154,x27152,x27155,x27156,x27157,x27158)+~E(x27151,x27152)+~P51(x27153,x27154,x27151,x27155,x27156,x27157,x27158) % 186.05/186.64 [2716]P51(x27163,x27164,x27165,x27162,x27166,x27167,x27168)+~E(x27161,x27162)+~P51(x27163,x27164,x27165,x27161,x27166,x27167,x27168) % 186.05/186.64 [2717]P51(x27173,x27174,x27175,x27176,x27172,x27177,x27178)+~E(x27171,x27172)+~P51(x27173,x27174,x27175,x27176,x27171,x27177,x27178) % 186.05/186.64 [2718]P51(x27183,x27184,x27185,x27186,x27187,x27182,x27188)+~E(x27181,x27182)+~P51(x27183,x27184,x27185,x27186,x27187,x27181,x27188) % 186.05/186.64 [2719]P51(x27193,x27194,x27195,x27196,x27197,x27198,x27192)+~E(x27191,x27192)+~P51(x27193,x27194,x27195,x27196,x27197,x27198,x27191) % 186.05/186.64 [2720]~P82(x27201)+P82(x27202)+~E(x27201,x27202) % 186.05/186.64 [2721]~P115(x27211)+P115(x27212)+~E(x27211,x27212) % 186.05/186.64 [2722]P14(x27222,x27223,x27224)+~E(x27221,x27222)+~P14(x27221,x27223,x27224) % 186.05/186.64 [2723]P14(x27233,x27232,x27234)+~E(x27231,x27232)+~P14(x27233,x27231,x27234) % 186.05/186.64 [2724]P14(x27243,x27244,x27242)+~E(x27241,x27242)+~P14(x27243,x27244,x27241) % 186.05/186.64 [2725]~P130(x27251)+P130(x27252)+~E(x27251,x27252) % 186.05/186.64 [2726]P34(x27262,x27263,x27264,x27265)+~E(x27261,x27262)+~P34(x27261,x27263,x27264,x27265) % 186.05/186.64 [2727]P34(x27273,x27272,x27274,x27275)+~E(x27271,x27272)+~P34(x27273,x27271,x27274,x27275) % 186.05/186.64 [2728]P34(x27283,x27284,x27282,x27285)+~E(x27281,x27282)+~P34(x27283,x27284,x27281,x27285) % 186.05/186.64 [2729]P34(x27293,x27294,x27295,x27292)+~E(x27291,x27292)+~P34(x27293,x27294,x27295,x27291) % 186.05/186.64 [2730]~P124(x27301)+P124(x27302)+~E(x27301,x27302) % 186.05/186.64 [2731]P19(x27312,x27313,x27314)+~E(x27311,x27312)+~P19(x27311,x27313,x27314) % 186.05/186.64 [2732]P19(x27323,x27322,x27324)+~E(x27321,x27322)+~P19(x27323,x27321,x27324) % 186.05/186.64 [2733]P19(x27333,x27334,x27332)+~E(x27331,x27332)+~P19(x27333,x27334,x27331) % 186.05/186.64 [2734]~P128(x27341)+P128(x27342)+~E(x27341,x27342) % 186.05/186.64 [2735]~P131(x27351)+P131(x27352)+~E(x27351,x27352) % 186.05/186.64 [2736]P46(x27362,x27363,x27364)+~E(x27361,x27362)+~P46(x27361,x27363,x27364) % 186.05/186.64 [2737]P46(x27373,x27372,x27374)+~E(x27371,x27372)+~P46(x27373,x27371,x27374) % 186.05/186.64 [2738]P46(x27383,x27384,x27382)+~E(x27381,x27382)+~P46(x27383,x27384,x27381) % 186.05/186.64 [2739]P17(x27392,x27393,x27394,x27395,x27396,x27397)+~E(x27391,x27392)+~P17(x27391,x27393,x27394,x27395,x27396,x27397) % 186.05/186.64 [2740]P17(x27403,x27402,x27404,x27405,x27406,x27407)+~E(x27401,x27402)+~P17(x27403,x27401,x27404,x27405,x27406,x27407) % 186.05/186.64 [2741]P17(x27413,x27414,x27412,x27415,x27416,x27417)+~E(x27411,x27412)+~P17(x27413,x27414,x27411,x27415,x27416,x27417) % 186.05/186.64 [2742]P17(x27423,x27424,x27425,x27422,x27426,x27427)+~E(x27421,x27422)+~P17(x27423,x27424,x27425,x27421,x27426,x27427) % 186.05/186.64 [2743]P17(x27433,x27434,x27435,x27436,x27432,x27437)+~E(x27431,x27432)+~P17(x27433,x27434,x27435,x27436,x27431,x27437) % 186.05/186.64 [2744]P17(x27443,x27444,x27445,x27446,x27447,x27442)+~E(x27441,x27442)+~P17(x27443,x27444,x27445,x27446,x27447,x27441) % 186.05/186.64 [2745]P41(x27452,x27453,x27454,x27455,x27456,x27457)+~E(x27451,x27452)+~P41(x27451,x27453,x27454,x27455,x27456,x27457) % 186.05/186.64 [2746]P41(x27463,x27462,x27464,x27465,x27466,x27467)+~E(x27461,x27462)+~P41(x27463,x27461,x27464,x27465,x27466,x27467) % 186.05/186.64 [2747]P41(x27473,x27474,x27472,x27475,x27476,x27477)+~E(x27471,x27472)+~P41(x27473,x27474,x27471,x27475,x27476,x27477) % 186.05/186.64 [2748]P41(x27483,x27484,x27485,x27482,x27486,x27487)+~E(x27481,x27482)+~P41(x27483,x27484,x27485,x27481,x27486,x27487) % 186.05/186.64 [2749]P41(x27493,x27494,x27495,x27496,x27492,x27497)+~E(x27491,x27492)+~P41(x27493,x27494,x27495,x27496,x27491,x27497) % 186.05/186.64 [2750]P41(x27503,x27504,x27505,x27506,x27507,x27502)+~E(x27501,x27502)+~P41(x27503,x27504,x27505,x27506,x27507,x27501) % 186.05/186.64 [2751]P24(x27512,x27513,x27514,x27515)+~E(x27511,x27512)+~P24(x27511,x27513,x27514,x27515) % 186.05/186.64 [2752]P24(x27523,x27522,x27524,x27525)+~E(x27521,x27522)+~P24(x27523,x27521,x27524,x27525) % 186.05/186.64 [2753]P24(x27533,x27534,x27532,x27535)+~E(x27531,x27532)+~P24(x27533,x27534,x27531,x27535) % 186.05/186.64 [2754]P24(x27543,x27544,x27545,x27542)+~E(x27541,x27542)+~P24(x27543,x27544,x27545,x27541) % 186.05/186.64 [2755]~P13(x27551)+P13(x27552)+~E(x27551,x27552) % 186.05/186.64 [2756]P142(x27562,x27563)+~E(x27561,x27562)+~P142(x27561,x27563) % 186.05/186.64 [2757]P142(x27573,x27572)+~E(x27571,x27572)+~P142(x27573,x27571) % 186.05/186.64 [2758]~P114(x27581)+P114(x27582)+~E(x27581,x27582) % 186.05/186.64 [2759]P30(x27592,x27593)+~E(x27591,x27592)+~P30(x27591,x27593) % 186.05/186.64 [2760]P30(x27603,x27602)+~E(x27601,x27602)+~P30(x27603,x27601) % 186.05/186.64 [2761]~P125(x27611)+P125(x27612)+~E(x27611,x27612) % 186.05/186.64 [2762]~P8(x27621)+P8(x27622)+~E(x27621,x27622) % 186.05/186.64 [2763]P16(x27632,x27633,x27634,x27635)+~E(x27631,x27632)+~P16(x27631,x27633,x27634,x27635) % 186.05/186.64 [2764]P16(x27643,x27642,x27644,x27645)+~E(x27641,x27642)+~P16(x27643,x27641,x27644,x27645) % 186.05/186.64 [2765]P16(x27653,x27654,x27652,x27655)+~E(x27651,x27652)+~P16(x27653,x27654,x27651,x27655) % 186.05/186.64 [2766]P16(x27663,x27664,x27665,x27662)+~E(x27661,x27662)+~P16(x27663,x27664,x27665,x27661) % 186.05/186.64 [2767]P11(x27672,x27673)+~E(x27671,x27672)+~P11(x27671,x27673) % 186.05/186.64 [2768]P11(x27683,x27682)+~E(x27681,x27682)+~P11(x27683,x27681) % 186.05/186.64 [2769]~P108(x27691)+P108(x27692)+~E(x27691,x27692) % 186.05/186.64 [2770]~P126(x27701)+P126(x27702)+~E(x27701,x27702) % 186.05/186.64 [2771]~P84(x27711)+P84(x27712)+~E(x27711,x27712) % 186.05/186.64 [2772]~P95(x27721)+P95(x27722)+~E(x27721,x27722) % 186.05/186.64 [2773]P21(x27732,x27733,x27734)+~E(x27731,x27732)+~P21(x27731,x27733,x27734) % 186.05/186.64 [2774]P21(x27743,x27742,x27744)+~E(x27741,x27742)+~P21(x27743,x27741,x27744) % 186.05/186.64 [2775]P21(x27753,x27754,x27752)+~E(x27751,x27752)+~P21(x27753,x27754,x27751) % 186.05/186.64 [2776]~P101(x27761)+P101(x27762)+~E(x27761,x27762) % 186.05/186.64 [2777]P54(x27772,x27773,x27774)+~E(x27771,x27772)+~P54(x27771,x27773,x27774) % 186.05/186.64 [2778]P54(x27783,x27782,x27784)+~E(x27781,x27782)+~P54(x27783,x27781,x27784) % 186.05/186.64 [2779]P54(x27793,x27794,x27792)+~E(x27791,x27792)+~P54(x27793,x27794,x27791) % 186.05/186.64 [2780]~P97(x27801)+P97(x27802)+~E(x27801,x27802) % 186.05/186.64 [2781]P15(x27812,x27813,x27814,x27815,x27816)+~E(x27811,x27812)+~P15(x27811,x27813,x27814,x27815,x27816) % 186.05/186.64 [2782]P15(x27823,x27822,x27824,x27825,x27826)+~E(x27821,x27822)+~P15(x27823,x27821,x27824,x27825,x27826) % 186.05/186.64 [2783]P15(x27833,x27834,x27832,x27835,x27836)+~E(x27831,x27832)+~P15(x27833,x27834,x27831,x27835,x27836) % 186.05/186.64 [2784]P15(x27843,x27844,x27845,x27842,x27846)+~E(x27841,x27842)+~P15(x27843,x27844,x27845,x27841,x27846) % 186.05/186.64 [2785]P15(x27853,x27854,x27855,x27856,x27852)+~E(x27851,x27852)+~P15(x27853,x27854,x27855,x27856,x27851) % 186.05/186.64 [2786]~P71(x27861)+P71(x27862)+~E(x27861,x27862) % 186.05/186.64 [2787]~P72(x27871)+P72(x27872)+~E(x27871,x27872) % 186.05/186.64 [2788]~P96(x27881)+P96(x27882)+~E(x27881,x27882) % 186.05/186.64 [2789]~P106(x27891)+P106(x27892)+~E(x27891,x27892) % 186.05/186.64 [2790]~P83(x27901)+P83(x27902)+~E(x27901,x27902) % 186.05/186.64 [2791]~P107(x27911)+P107(x27912)+~E(x27911,x27912) % 186.05/186.64 [2792]P49(x27922,x27923)+~E(x27921,x27922)+~P49(x27921,x27923) % 186.05/186.64 [2793]P49(x27933,x27932)+~E(x27931,x27932)+~P49(x27933,x27931) % 186.05/186.64 [2794]P40(x27942,x27943,x27944,x27945)+~E(x27941,x27942)+~P40(x27941,x27943,x27944,x27945) % 186.05/186.64 [2795]P40(x27953,x27952,x27954,x27955)+~E(x27951,x27952)+~P40(x27953,x27951,x27954,x27955) % 186.05/186.64 [2796]P40(x27963,x27964,x27962,x27965)+~E(x27961,x27962)+~P40(x27963,x27964,x27961,x27965) % 186.05/186.64 [2797]P40(x27973,x27974,x27975,x27972)+~E(x27971,x27972)+~P40(x27973,x27974,x27975,x27971) % 186.05/186.64 [2798]~P35(x27981)+P35(x27982)+~E(x27981,x27982) % 186.05/186.64 [2799]P48(x27992,x27993)+~E(x27991,x27992)+~P48(x27991,x27993) % 186.05/186.64 [2800]P48(x28003,x28002)+~E(x28001,x28002)+~P48(x28003,x28001) % 186.05/186.64 [2801]P44(x28012,x28013)+~E(x28011,x28012)+~P44(x28011,x28013) % 186.05/186.64 [2802]P44(x28023,x28022)+~E(x28021,x28022)+~P44(x28023,x28021) % 186.05/186.64 [2803]~P116(x28031)+P116(x28032)+~E(x28031,x28032) % 186.05/186.64 % 186.05/186.64 %------------------------------------------- % 186.15/186.67 cnf(10037,plain, % 186.15/186.67 (E(f37(x100371,x100372,x100373,x100374,x100375,x100376,x100377,x100378,x100379,a25),x100372)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10040,plain, % 186.15/186.67 (E(f37(x100401,x100402,x100403,x100404,x100405,x100406,x100407,x100408,x100409,a25),x100402)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10043,plain, % 186.15/186.67 (~E(f775(a114,x100431),x100431)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10046,plain, % 186.15/186.67 (E(f37(x100461,x100462,x100463,x100464,x100465,x100466,x100467,x100468,x100469,a25),x100462)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10053,plain, % 186.15/186.67 (~E(f775(a114,x100531),x100531)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10064,plain, % 186.15/186.67 (~E(f775(a114,x100641),x100641)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10067,plain, % 186.15/186.67 (~P1(f775(f64(x100671,x100672,f180(f857(x100671,a844))),x100673))), % 186.15/186.67 inference(rename_variables,[],[4474])). % 186.15/186.67 cnf(10070,plain, % 186.15/186.67 (~P1(f775(f64(x100701,x100702,f180(f857(x100701,a844))),x100703))), % 186.15/186.67 inference(rename_variables,[],[4474])). % 186.15/186.67 cnf(10073,plain, % 186.15/186.67 (~E(f775(a114,x100731),x100731)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10076,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x100761),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10079,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x100791),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10096,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x100961)),x100961))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(10099,plain, % 186.15/186.67 (~E(f775(f775(f140(x100991),x100992),x100993),x100993)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(10105,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x101051),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10108,plain, % 186.15/186.67 (E(f37(x101081,x101082,x101083,x101084,x101085,x101086,x101087,x101088,x101089,a25),x101082)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10111,plain, % 186.15/186.67 (E(f37(x101111,x101112,x101113,x101114,x101115,x101116,x101117,x101118,x101119,a25),x101112)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10118,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x101181),x101182)),x101182))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(10121,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x101211),x101212)),x101212))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(10128,plain, % 186.15/186.67 (~E(x101281,f775(a114,x101281))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,4363,10043,10053,10064,3026,3084,3049,3033,4397,3252,4451,10076,10079,4448,4391,4460,4005,4458,3160,4443,4474,10067,4477,4475,10118,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069])). % 186.15/186.67 cnf(10142,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x101421),x101421))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10145,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f52(a850,x101451,x101452)),x101451))), % 186.15/186.67 inference(rename_variables,[],[3635])). % 186.15/186.67 cnf(10164,plain, % 186.15/186.67 (E(f775(f42(a850),f775(f257(a850),x101641)),x101641)), % 186.15/186.67 inference(rename_variables,[],[3081])). % 186.15/186.67 cnf(10172,plain, % 186.15/186.67 (~E(f775(a114,x101721),x101721)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10175,plain, % 186.15/186.67 (~E(f775(a114,x101751),x101751)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10178,plain, % 186.15/186.67 (~E(f775(a114,x101781),x101781)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10183,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x101831),f775(a114,x101831)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10186,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x101861),f775(a114,x101861)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10188,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x101881),f775(a114,x101881)))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,4363,10043,10053,10064,10073,10172,10175,3026,3084,3049,3033,3117,4397,3081,4479,3100,3252,10183,4451,10076,10079,3768,3186,4448,4391,4447,10142,3278,3699,3635,4460,10096,4005,4458,4439,3160,4443,4474,10067,4477,4475,10118,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211])). % 186.15/186.67 cnf(10195,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x101951),x101951))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(10202,plain, % 186.15/186.67 (E(f37(x102021,x102022,x102023,x102024,x102025,x102026,x102027,x102028,x102029,a25),x102022)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10205,plain, % 186.15/186.67 (E(f37(x102051,x102052,x102053,x102054,x102055,x102056,x102057,x102058,x102059,a25),x102052)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10230,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x102301),x102301))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10235,plain, % 186.15/186.67 (~E(f775(f775(f775(f74(x102351,f854(x102352)),x102353),x102354),f775(f227(x102352),x102355)),f775(f18(f854(x102352),x102351),f183(x102352)))), % 186.15/186.67 inference(rename_variables,[],[4471])). % 186.15/186.67 cnf(10239,plain, % 186.15/186.67 (E(f775(f775(f82(a850),x102391),f681(x102391,x102391)),x102391)), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,4363,10043,10053,10064,10073,10172,10175,3026,3084,3049,3033,3117,4471,4397,3081,3960,4479,3100,3252,10183,10186,4451,10076,10079,3615,3768,3211,3213,3186,4448,4391,3910,3182,3183,4447,10142,3278,3699,3635,10145,4460,10096,4005,4458,4439,3160,4443,4474,10067,4477,3658,4475,10118,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340])). % 186.15/186.67 cnf(10264,plain, % 186.15/186.67 (~E(f775(f775(f140(x102641),x102642),x102643),x102643)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(10267,plain, % 186.15/186.67 (~E(f775(a27,x102671),f35(x102672,x102673))), % 186.15/186.67 inference(rename_variables,[],[4381])). % 186.15/186.67 cnf(10280,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x102801),x102801))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(10283,plain, % 186.15/186.67 (~E(f775(a114,x102831),x102831)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10290,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x102901),x102901))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(10299,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x102991),f775(a114,x102991)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10304,plain, % 186.15/186.67 (E(f775(f775(f125(x103041),f115(x103041)),x103042),x103042)), % 186.15/186.67 inference(rename_variables,[],[3137])). % 186.15/186.67 cnf(10322,plain, % 186.15/186.67 (~P1(f775(f64(x103221,x103222,f180(f857(x103221,a844))),x103223))), % 186.15/186.67 inference(rename_variables,[],[4474])). % 186.15/186.67 cnf(10341,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x103411),x103411))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10362,plain, % 186.15/186.67 (~E(f775(a27,x103621),f35(x103622,x103623))), % 186.15/186.67 inference(rename_variables,[],[4381])). % 186.15/186.67 cnf(10371,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x103711),x103711))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10376,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x103761),f775(a114,x103761)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10389,plain, % 186.15/186.67 (~E(f775(a114,x103891),x103891)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10414,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x104141),x104141))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(10417,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x104171),f775(a114,f775(f775(f82(a850),x104172),x104171))))), % 186.15/186.67 inference(rename_variables,[],[3628])). % 186.15/186.67 cnf(10420,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x104201),f775(f775(f83(a850),x104201),x104201)))), % 186.15/186.67 inference(rename_variables,[],[3452])). % 186.15/186.67 cnf(10423,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x104231),f775(f775(f83(a850),x104231),x104231)))), % 186.15/186.67 inference(rename_variables,[],[3452])). % 186.15/186.67 cnf(10428,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x104281),f775(a114,x104281)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10431,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x104311),f775(a114,x104311)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10434,plain, % 186.15/186.67 (P1(f775(f775(f334(x104341),x104342),f239(f857(x104341,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(10447,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x104471),x104472)),x104472))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(10450,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x104501),x104502)),x104502))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(10453,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x104531)),x104531))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(10456,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x104561)),x104561))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(10459,plain, % 186.15/186.67 (P1(f775(f239(f857(x104591,a844)),x104592))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(10462,plain, % 186.15/186.67 (E(f775(f42(a850),f775(f257(a850),x104621)),x104621)), % 186.15/186.67 inference(rename_variables,[],[3081])). % 186.15/186.67 cnf(10465,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x104651),f775(a114,x104651)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10472,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x104721),x104721))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(10477,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x104771),x104771))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(10486,plain, % 186.15/186.67 (E(f37(x104861,x104862,x104863,x104864,x104865,x104866,x104867,x104868,x104869,a25),x104862)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10489,plain, % 186.15/186.67 (P1(f775(f239(f857(x104891,a844)),x104892))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(10491,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(f775(f83(a850),f775(a114,x104911)),f775(a114,x104911))),x104911))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,4363,10043,10053,10064,10073,10172,10175,10178,10283,4381,10267,3026,3084,3049,3033,3117,3137,10304,4471,4397,10099,3081,10164,3960,4479,3100,3541,3487,3252,10183,10186,10299,10376,10428,10431,3630,4451,10076,10079,10105,4467,3615,3391,3768,3211,3213,3186,4448,4391,3910,3182,10195,10290,10414,3183,3184,10280,4447,10142,10230,10341,3339,3246,10459,3278,3699,3635,10145,4460,10096,10453,4005,4458,4439,4442,3160,3161,4443,4474,10067,10070,3452,10420,10423,4477,3658,4475,10118,10121,10447,3628,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201])). % 186.15/186.67 cnf(10492,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x104921),f775(f775(f83(a850),x104921),x104921)))), % 186.15/186.67 inference(rename_variables,[],[3452])). % 186.15/186.67 cnf(10496,plain, % 186.15/186.67 (E(f775(f142(x104961),f37(x104962,f775(f775(f125(x104961),f775(f142(x104961),x104963)),f775(f775(f140(x104961),x104964),f115(x104961))),x104965,x104966,x104967,x104968,x104969,x1049610,x1049611,a25)),f775(f775(f140(x104961),x104964),x104963))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,4381,10267,3026,3084,3049,3033,3117,3137,10304,4471,4397,10099,3081,10164,3960,4479,3100,3541,3487,3252,10183,10186,10299,10376,10428,10431,3630,4451,10076,10079,10105,4467,3615,3391,3768,3211,3213,3186,4448,4391,3910,3182,10195,10290,10414,3183,3184,10280,4447,10142,10230,10341,3339,3246,10459,3278,3699,3635,10145,4460,10096,10453,4005,4458,4439,4442,3160,3161,4443,4474,10067,10070,3452,10420,10423,4477,3658,4475,10118,10121,10447,3628,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244])). % 186.15/186.67 cnf(10497,plain, % 186.15/186.67 (E(f37(x104971,x104972,x104973,x104974,x104975,x104976,x104977,x104978,x104979,a25),x104972)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(10509,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,f775(a114,f775(f775(f82(a850),x105091),x105092)))),f775(a114,x105092)))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,4381,10267,3026,3084,3049,3033,3117,3137,10304,4471,4397,10099,3081,10164,3960,4479,3100,3541,3487,3252,10183,10186,10299,10376,10428,10431,10465,3630,4451,10076,10079,10105,4467,3615,3391,3768,3211,3213,3186,4448,4391,3910,3182,10195,10290,10414,3183,3184,10280,4447,10142,10230,10341,3339,3246,10459,3278,3699,3635,10145,4460,10096,10453,4005,4458,4439,4442,3160,3161,4441,4443,4474,10067,10070,3452,10420,10423,4477,3658,4475,10118,10121,10447,3628,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253])). % 186.15/186.67 cnf(10532,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x105321),x105321))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10543,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x105431,f857(x105432,a844))),x105433),x105434))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(10554,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x105541),f775(a114,x105541)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10557,plain, % 186.15/186.67 (~E(f775(a114,x105571),x105571)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10559,plain, % 186.15/186.67 (P1(f775(f775(f233(a1),f775(f775(f3(a1),x105591),f80(a1))),x105591))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,4381,10267,3026,3084,3049,3033,3117,3137,10304,4471,4397,10099,3081,10164,3960,3814,4479,3100,3541,3487,3252,10183,10186,10299,10376,10428,10431,10465,3630,4451,10076,10079,10105,4467,3615,3391,3768,3211,3213,3186,4448,4391,3910,3182,10195,10290,10414,3183,10532,3184,10280,10477,4447,10142,10230,10341,3339,4463,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,4005,4458,4439,4442,3160,3161,4441,4443,4474,10067,10070,3452,10420,10423,4477,4478,3658,4475,10118,10121,10447,3628,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526])). % 186.15/186.67 cnf(10560,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x105601),x105601))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(10565,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x105651),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10580,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x105801),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10583,plain, % 186.15/186.67 (~P1(f775(f775(f233(f857(x105831,a844)),x105832),f180(f857(x105831,a844))))), % 186.15/186.67 inference(rename_variables,[],[4472])). % 186.15/186.67 cnf(10586,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x105861),x105861))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10589,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x105891),x105891))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10604,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x106041),x106041))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10613,plain, % 186.15/186.67 (~P1(f775(f775(f334(x106131),x106132),f180(f857(x106131,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10622,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x106221),x106221))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10625,plain, % 186.15/186.67 (~P1(f775(f775(f334(x106251),x106252),f180(f857(x106251,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10628,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),x106281),x106281))), % 186.15/186.67 inference(rename_variables,[],[3185])). % 186.15/186.67 cnf(10631,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x106311,a844)),f775(f303(x106312,x106311,x106313),f775(f305(x106312,x106311,x106313),x106314))),x106314))), % 186.15/186.67 inference(rename_variables,[],[4065])). % 186.15/186.67 cnf(10638,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x106381,a844)),f775(f158(x106381),f775(f126(x106381,x106382),x106383))),f775(f158(x106381),x106383)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(10641,plain, % 186.15/186.67 (E(f775(f303(x106411,x106411,f7(x106411)),x106412),x106412)), % 186.15/186.67 inference(rename_variables,[],[3242])). % 186.15/186.67 cnf(10646,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x106461))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(10649,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x106491),x106491))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10652,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x106521),x106521))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10659,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x106591),x106591))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10670,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x106701),f775(a114,f775(f775(f82(a850),x106702),x106701))))), % 186.15/186.67 inference(rename_variables,[],[3628])). % 186.15/186.67 cnf(10673,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x106731),f775(f775(f83(a850),x106731),x106731)))), % 186.15/186.67 inference(rename_variables,[],[3452])). % 186.15/186.67 cnf(10683,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x106831),x106831))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10686,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x106861),x106861))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(10689,plain, % 186.15/186.67 (~E(f775(a114,x106891),x106891)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10694,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),x106941),x106941))), % 186.15/186.67 inference(rename_variables,[],[3185])). % 186.15/186.67 cnf(10697,plain, % 186.15/186.67 (P1(f775(f775(f334(x106971),x106972),f239(f857(x106971,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(10702,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x107021),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(10713,plain, % 186.15/186.67 (~E(f775(a114,x107131),f2(a850))), % 186.15/186.67 inference(rename_variables,[],[4375])). % 186.15/186.67 cnf(10720,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x107201))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(10727,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x107271),x107271))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10734,plain, % 186.15/186.67 (~P1(f775(f775(f334(x107341),x107342),f180(f857(x107341,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10741,plain, % 186.15/186.67 (P1(f775(f775(f334(f851(x107411)),x107412),f149(x107411,f239(f857(x107411,a844)))))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,4381,10267,4375,3026,3084,3049,3033,3242,3117,3137,10304,4471,4397,10099,3081,10164,3960,3814,4479,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,3630,4451,10076,10079,10105,10565,10580,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3542,3910,4472,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,4463,10613,10625,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,3205,10646,4005,4458,3707,4439,4442,3160,3161,4441,4443,4474,10067,10070,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724])). % 186.15/186.67 cnf(10742,plain, % 186.15/186.67 (P1(f775(f775(f334(x107421),x107422),f239(f857(x107421,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(10745,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x107451),f851(x107451))),f775(f775(f241(f851(x107451),f851(x107451)),x107452),f115(x107451))),f135(x107451,x107453)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(10751,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(x107511,x107511)),x107512),f260(x107511,f180(f857(x107511,a844)))))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,4381,10267,4375,3026,3084,3049,3033,3242,3117,3137,10304,4471,4397,10099,3081,10164,3960,3814,4479,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,3630,4451,10076,10079,10105,10565,10580,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3542,3910,4472,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,4463,10613,10625,10734,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,3205,10646,4005,4458,3707,4439,4442,3160,3161,4441,4443,4474,10067,10070,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861])). % 186.15/186.67 cnf(10752,plain, % 186.15/186.67 (~P1(f775(f775(f334(x107521),x107522),f180(f857(x107521,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10754,plain, % 186.15/186.67 (~P1(f775(f775(f334(x107541),x107542),f775(f305(x107541,x107543,x107544),f180(f857(x107543,a844)))))), % 186.15/186.67 inference(scs_inference,[],[4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,4381,10267,4375,3026,3084,3049,3033,3242,3117,3137,10304,4471,4397,10099,3081,10164,3960,3814,4479,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,3630,4451,10076,10079,10105,10565,10580,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3542,3910,4472,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,4463,10613,10625,10734,10752,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,3205,10646,4005,4458,3707,4439,4442,3160,3161,4441,4443,4474,10067,10070,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893])). % 186.15/186.67 cnf(10755,plain, % 186.15/186.67 (~P1(f775(f775(f334(x107551),x107552),f180(f857(x107551,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10758,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x107581,a844)),x107582),f775(f775(f302(x107581),x107583),x107582)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(10761,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x107611),x107611))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(10764,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x107641,a844)),x107642),f775(f775(f302(x107641),x107643),x107642)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(10775,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x107751,a844)),x107752),f775(f775(f302(x107751),x107753),x107752)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(10780,plain, % 186.15/186.67 (~P1(f775(f64(x107801,x107802,f180(f857(x107801,a844))),x107803))), % 186.15/186.67 inference(rename_variables,[],[4474])). % 186.15/186.67 cnf(10793,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x107931),f775(a114,x107931)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(10803,plain, % 186.15/186.67 (~E(f775(f313(x108031,x108032),x108033),f775(f304(x108032,x108031),x108034))), % 186.15/186.67 inference(rename_variables,[],[4436])). % 186.15/186.67 cnf(10806,plain, % 186.15/186.67 (~P1(f775(f775(f334(x108061),x108062),f180(f857(x108061,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10809,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x108091,x108091)),f775(f775(f241(x108091,x108091),x108092),x108092)),f300(x108091,x108093)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(10812,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x108121,a844)),f775(f158(x108121),f151(x108121,x108122,x108123))),f775(f158(x108121),x108123)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(10815,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x108151,a844)),x108152),f239(f857(x108151,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(10822,plain, % 186.15/186.67 (~E(f775(a114,x108221),x108221)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(10838,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x108381,a844)),f180(f857(x108381,a844))),x108382))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(10849,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x108491),f851(x108491))),f775(f775(f241(f851(x108491),f851(x108491)),x108492),f115(x108491))),f137(x108491,x108493)))), % 186.15/186.67 inference(rename_variables,[],[4480])). % 186.15/186.67 cnf(10867,plain, % 186.15/186.67 (P29(x108671,x108671,f7(x108671),x108672)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(10872,plain, % 186.15/186.67 (~E(f775(f303(x108721,f857(x108721,a844),x108722),x108723),f775(f301(x108721),x108723))), % 186.15/186.67 inference(rename_variables,[],[4461])). % 186.15/186.67 cnf(10877,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x108771,a844)),x108772),f239(f857(x108771,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(10884,plain, % 186.15/186.67 (P36(x108841,f775(f775(f280(a850,x108841),a237),x108842))), % 186.15/186.67 inference(rename_variables,[],[3288])). % 186.15/186.67 cnf(10891,plain, % 186.15/186.67 (~P1(f775(f775(f334(x108911),x108912),f180(f857(x108911,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10894,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x108941)),x108941))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(10901,plain, % 186.15/186.67 (~P1(f775(f775(f334(x109011),x109012),f180(f857(x109011,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10909,plain, % 186.15/186.67 (~P1(f775(f775(f334(a850),f775(a114,f775(f132(a850,a850,f82(a850),f2(a850)),x109091))),f775(f158(a850),x109091)))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,4381,10267,10362,4375,3638,3026,4436,3084,3049,3033,3242,3117,3137,10304,4471,3813,4397,10099,4461,3288,3081,10164,3960,3814,10809,4479,10745,4480,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3872,3542,3910,3559,10815,4472,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,10742,4463,10613,10625,10734,10752,10755,10806,10891,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,10894,3205,10646,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,4474,10067,10070,10322,3785,3623,10758,10764,3627,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744])). % 186.15/186.67 cnf(10910,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x109101)),x109101))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(10913,plain, % 186.15/186.67 (~P1(f775(f775(f334(x109131),x109132),f180(f857(x109131,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10921,plain, % 186.15/186.67 (E(f775(x109211,f703(f775(x109211,x109212),f775(f227(x109213),x109212),x109211,x109214,x109213)),f775(x109211,x109212))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,4381,10267,10362,4375,3638,3026,4436,3084,3049,3033,3242,3117,3137,10304,3287,4471,3813,4397,10099,4461,3288,3081,10164,3960,3814,10809,4479,10745,4480,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3872,3542,3910,3559,10815,4472,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,10742,4463,10613,10625,10734,10752,10755,10806,10891,10901,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,10894,3205,10646,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,4474,10067,10070,10322,3785,3623,10758,10764,3627,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806])). % 186.15/186.67 cnf(10928,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x109281,x109281)),f775(f775(f241(x109281,x109281),x109282),x109282)),f300(x109281,x109283)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(10935,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x109351),f851(x109351))),f775(f775(f241(f851(x109351),f851(x109351)),x109352),f115(x109351))),f135(x109351,x109353)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(10938,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x109381),f851(x109381))),f775(f775(f241(f851(x109381),f851(x109381)),x109382),f115(x109381))),f137(x109381,x109383)))), % 186.15/186.67 inference(rename_variables,[],[4480])). % 186.15/186.67 cnf(10941,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x109411),f851(x109411))),f775(f775(f241(f851(x109411),f851(x109411)),x109412),f115(x109411))),f146(x109411,x109413)))), % 186.15/186.67 inference(rename_variables,[],[4481])). % 186.15/186.67 cnf(10946,plain, % 186.15/186.67 (~P1(f775(f775(f233(f857(x109461,a844)),x109462),f180(f857(x109461,a844))))), % 186.15/186.67 inference(rename_variables,[],[4472])). % 186.15/186.67 cnf(10949,plain, % 186.15/186.67 (~P1(f775(f775(f334(x109491),x109492),f180(f857(x109491,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10959,plain, % 186.15/186.67 (~P39(f36(x109591,f36(x109592,f36(f36(f775(a27,x109593),x109594),x109595))),x109596,f2(a850),x109597)), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,4381,10267,10362,4375,3638,3026,4436,3084,3049,3033,3242,3117,3137,10304,3287,4471,3813,4397,10099,4461,3288,3081,10164,3960,3814,10809,4479,10745,10935,4480,10849,4481,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3872,3542,3910,3559,10815,4472,10583,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,3339,10434,10697,10742,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,10894,3205,10646,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,4474,10067,10070,10322,3785,3623,10758,10764,3627,3452,10420,10423,10492,10673,4477,4478,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986])). % 186.15/186.67 cnf(10962,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x109621,a844)),x109622),f239(f857(x109621,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(10965,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x109651,f857(x109652,a844))),x109653),x109654))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(10972,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x109721),x109721))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(10977,plain, % 186.15/186.67 (~P1(f775(f775(f334(x109771),x109772),f180(f857(x109771,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10980,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x109801,a844)),x109802),x109802))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(10983,plain, % 186.15/186.67 (E(f319(x109831,x109832,x109833,f775(f775(f10(f858(x109831,x109833),x109832,x109831),x109834),f304(x109831,x109833)),f775(f775(f10(f858(x109831,x109833),x109832,x109833),x109834),f313(x109833,x109831))),x109834)), % 186.15/186.67 inference(rename_variables,[],[4045])). % 186.15/186.67 cnf(10989,plain, % 186.15/186.67 (~P1(f775(f775(f334(x109891),x109892),f180(f857(x109891,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(10992,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x109921,a844)),f180(f857(x109921,a844))),x109922))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(10995,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x109951,x109951)),f775(f775(f241(x109951,x109951),x109952),x109952)),f300(x109951,x109953)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(11002,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x110021),f851(x110021))),f775(f775(f241(f851(x110021),f851(x110021)),x110022),f115(x110021))),f146(x110021,x110023)))), % 186.15/186.67 inference(rename_variables,[],[4481])). % 186.15/186.67 cnf(11005,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x110051),f851(x110051))),f775(f775(f241(f851(x110051),f851(x110051)),f115(x110051)),x110052)),f135(x110051,x110053)))), % 186.15/186.67 inference(rename_variables,[],[4482])). % 186.15/186.67 cnf(11010,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f857(x110101,a844),f857(x110101,a844))),f775(f775(f241(f857(x110101,a844),f857(x110101,a844)),x110102),f180(f857(x110101,a844)))),f299(x110101)))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,4381,10267,10362,4375,3638,3026,4436,3084,3049,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,4461,3288,3081,10164,3960,3814,10809,10928,4479,10745,10935,4480,10849,4481,10941,4482,4483,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,4467,3615,3391,3768,3211,3213,3186,4448,4391,3921,3824,10638,3872,3542,3910,3559,10815,10877,4472,10583,10946,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,3185,10628,4447,10142,10230,10341,10371,10604,10652,10659,3339,10434,10697,10742,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,10894,3205,10646,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,4474,10067,10070,10322,3785,3623,10758,10764,3481,3627,10838,3452,10420,10423,10492,10673,4477,4478,10543,4065,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287])). % 186.15/186.67 cnf(11013,plain, % 186.15/186.67 (P1(f775(f775(f334(x110131),x110132),f239(f857(x110131,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(11018,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x110181,a844)),f180(f857(x110181,a844))),x110182))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(11021,plain, % 186.15/186.67 (~P1(f775(f775(f334(x110211),x110212),f180(f857(x110211,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11024,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x110241,a844)),x110242),f239(f857(x110241,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(11029,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x110291,a844)),f180(f857(x110291,a844))),x110292))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(11049,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x110491),f851(x110491))),f775(f775(f241(f851(x110491),f851(x110491)),x110492),f115(x110491))),f135(x110491,x110493)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(11052,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x110521),f851(x110521))),f775(f775(f241(f851(x110521),f851(x110521)),x110522),f115(x110521))),f137(x110521,x110523)))), % 186.15/186.67 inference(rename_variables,[],[4480])). % 186.15/186.67 cnf(11055,plain, % 186.15/186.67 (~E(f775(f775(f140(x110551),x110552),x110553),x110553)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(11058,plain, % 186.15/186.67 (~E(f775(a114,x110581),x110581)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11061,plain, % 186.15/186.67 (~P1(f775(f775(f334(x110611),x110612),f180(f857(x110611,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11066,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(f851(x110661),f851(x110661))),f775(f775(f241(f851(x110661),f851(x110661)),x110662),x110662)),f147(x110661,f300(x110661,x110663))))), % 186.15/186.67 inference(rename_variables,[],[3954])). % 186.15/186.67 cnf(11069,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x110691),f851(x110691))),f775(f775(f241(f851(x110691),f851(x110691)),x110692),f115(x110691))),f135(x110691,x110693)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(11077,plain, % 186.15/186.67 (~P1(f775(f775(f334(x110771),x110772),f180(f857(x110771,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11080,plain, % 186.15/186.67 (~P1(f775(f775(f334(x110801),x110802),f180(f857(x110801,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11083,plain, % 186.15/186.67 (~P1(f775(f775(f334(x110831),x110832),f180(f857(x110831,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11086,plain, % 186.15/186.67 (P1(f775(f775(f334(x110861),x110862),f239(f857(x110861,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(11097,plain, % 186.15/186.67 (~E(f775(f313(x110971,x110972),x110973),f775(f304(x110972,x110971),x110974))), % 186.15/186.67 inference(rename_variables,[],[4436])). % 186.15/186.67 cnf(11100,plain, % 186.15/186.67 (~E(f775(f313(x111001,x111002),x111003),f775(f304(x111002,x111001),x111004))), % 186.15/186.67 inference(rename_variables,[],[4436])). % 186.15/186.67 cnf(11105,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x111051),f851(x111051))),f775(f775(f241(f851(x111051),f851(x111051)),x111052),f115(x111051))),f135(x111051,x111053)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(11108,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x111081),f851(x111081))),f775(f775(f241(f851(x111081),f851(x111081)),x111082),f115(x111081))),f137(x111081,x111083)))), % 186.15/186.67 inference(rename_variables,[],[4480])). % 186.15/186.67 cnf(11111,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x111111),f851(x111111))),f775(f775(f241(f851(x111111),f851(x111111)),x111112),f115(x111111))),f135(x111111,x111113)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(11114,plain, % 186.15/186.67 (~P1(f775(f775(f334(x111141),x111142),f180(f857(x111141,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11117,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x111171,f857(x111172,a844))),x111173),x111174))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(11120,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x111201),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11122,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x111221,x111222)),f775(f775(f241(x111221,x111222),f775(x111223,x111224)),f775(x111225,x111224))),f775(f303(f856(x111226,x111226),f856(x111221,x111222),f252(x111226,x111221,x111226,x111222,x111223,x111225)),f300(x111226,x111227))))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,4381,10267,10362,4375,3638,3026,4436,10803,11097,3084,3049,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,4461,3288,3081,10164,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,4467,3615,3391,3768,3211,3213,3186,4448,4391,3954,11066,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,3185,10628,10694,4447,10142,10230,10341,10371,10604,10652,10659,3339,10434,10697,10742,11013,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,3246,10459,3278,3699,3635,10145,4460,10096,10453,10456,10894,3205,10646,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,4474,10067,10070,10322,3785,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,4478,10543,10965,4065,3965,3658,4475,10118,10121,10447,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885])). % 186.15/186.67 cnf(11125,plain, % 186.15/186.67 (~P1(f775(f775(f334(x111251),x111252),f180(f857(x111251,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11128,plain, % 186.15/186.67 (~P1(f775(f775(f334(x111281),x111282),f180(f857(x111281,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11131,plain, % 186.15/186.67 (P1(f775(f775(f334(x111311),f775(x111312,x111313)),f775(f303(x111314,x111311,x111312),f239(f857(x111314,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(11138,plain, % 186.15/186.67 (E(f37(x111381,x111382,x111383,x111384,x111385,x111386,x111387,x111388,x111389,a25),x111382)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11141,plain, % 186.15/186.67 (~E(f775(a114,x111411),x111411)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11148,plain, % 186.15/186.67 (~E(f775(a114,x111481),x111481)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11153,plain, % 186.15/186.67 (E(f37(x111531,x111532,x111533,x111534,x111535,x111536,x111537,x111538,x111539,a25),x111532)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11154,plain, % 186.15/186.67 (E(f38(x111541,x111542,x111543,x111544,x111545,x111546,x111547,x111548,x111549,a25),x111542)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(11157,plain, % 186.15/186.67 (E(f37(x111571,x111572,x111573,x111574,x111575,x111576,x111577,x111578,x111579,a25),x111572)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11158,plain, % 186.15/186.67 (E(f38(x111581,x111582,x111583,x111584,x111585,x111586,x111587,x111588,x111589,a25),x111582)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(11164,plain, % 186.15/186.67 (~E(f775(a114,x111641),x111641)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11169,plain, % 186.15/186.67 (~E(f775(f775(f82(a1),x111691),x111691),a99)), % 186.15/186.67 inference(rename_variables,[],[4394])). % 186.15/186.67 cnf(11178,plain, % 186.15/186.67 (E(f775(f775(f3(a850),f2(a850)),x111781),f2(a850))), % 186.15/186.67 inference(rename_variables,[],[3103])). % 186.15/186.67 cnf(11181,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x111811),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11186,plain, % 186.15/186.67 (E(f775(f775(f82(a1),f775(f775(f83(a1),x111861),f775(f775(f43(a1),x111862),x111861))),f52(a1,x111862,x111861)),x111862)), % 186.15/186.67 inference(rename_variables,[],[3731])). % 186.15/186.67 cnf(11198,plain, % 186.15/186.67 (E(f37(x111981,x111982,x111983,x111984,x111985,x111986,x111987,x111988,x111989,a25),x111982)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11201,plain, % 186.15/186.67 (E(f37(x112011,x112012,x112013,x112014,x112015,x112016,x112017,x112018,x112019,a25),x112012)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11204,plain, % 186.15/186.67 (E(f37(x112041,x112042,x112043,x112044,x112045,x112046,x112047,x112048,x112049,a25),x112042)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11207,plain, % 186.15/186.67 (E(f37(x112071,x112072,x112073,x112074,x112075,x112076,x112077,x112078,x112079,a25),x112072)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11212,plain, % 186.15/186.67 (~E(f775(a114,x112121),x112121)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11215,plain, % 186.15/186.67 (~E(f775(a114,x112151),x112151)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11219,plain, % 186.15/186.67 (E(f37(x112191,x112192,x112193,x112194,x112195,x112196,x112197,x112198,x112199,a25),x112192)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11242,plain, % 186.15/186.67 (P1(f775(f775(f334(x112421),x112422),f239(f857(x112421,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(11250,plain, % 186.15/186.67 (E(f37(x112501,x112502,x112503,x112504,x112505,x112506,x112507,x112508,x112509,a25),x112502)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11255,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x112551),x112551))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11262,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x112621),x112621))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11263,plain, % 186.15/186.67 (E(f37(x112631,x112632,x112633,x112634,x112635,x112636,x112637,x112638,x112639,a25),x112632)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11276,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x112761),x112762)),x112762))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(11279,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x112791)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(11290,plain, % 186.15/186.67 (E(f37(x112901,x112902,x112903,x112904,x112905,x112906,x112907,x112908,x112909,a25),x112902)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11293,plain, % 186.15/186.67 (E(f37(x112931,x112932,x112933,x112934,x112935,x112936,x112937,x112938,x112939,a25),x112932)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11304,plain, % 186.15/186.67 (E(f37(x113041,x113042,x113043,x113044,x113045,x113046,x113047,x113048,x113049,a25),x113042)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11309,plain, % 186.15/186.67 (E(f37(x113091,x113092,x113093,x113094,x113095,x113096,x113097,x113098,x113099,a25),x113092)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11312,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x113121)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(11315,plain, % 186.15/186.67 (E(f37(x113151,x113152,x113153,x113154,x113155,x113156,x113157,x113158,x113159,a25),x113152)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11318,plain, % 186.15/186.67 (~E(f775(a114,x113181),x113181)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11321,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x113211),x113211))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11330,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x113301),x113301))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11353,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x113531)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(11366,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x113661),x113661))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11369,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x113691)),x113691))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11370,plain, % 186.15/186.67 (~E(f775(a114,x113701),x113701)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11380,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x113801),x113802)),x113801))), % 186.15/186.67 inference(rename_variables,[],[4476])). % 186.15/186.67 cnf(11383,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x113831)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(11386,plain, % 186.15/186.67 (~E(f775(a114,x113861),x113861)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11399,plain, % 186.15/186.67 (P1(f775(f775(f334(x113991),x113992),f775(f775(f302(x113991),x113992),x113993)))), % 186.15/186.67 inference(rename_variables,[],[3496])). % 186.15/186.67 cnf(11400,plain, % 186.15/186.67 (~P1(f775(f775(f232(a1),f2(a1)),f775(f81(a1),f775(f102(a1),f775(a114,x114001)))))), % 186.15/186.67 inference(rename_variables,[],[4477])). % 186.15/186.67 cnf(11403,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),f775(f775(f3(a850),x114031),x114032)),f775(a114,x114031)))), % 186.15/186.67 inference(rename_variables,[],[3630])). % 186.15/186.67 cnf(11406,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f52(a850,x114061,x114062)),x114061))), % 186.15/186.67 inference(rename_variables,[],[3635])). % 186.15/186.67 cnf(11412,plain, % 186.15/186.67 (E(f775(f775(f125(x114121),x114122),f115(x114121)),x114122)), % 186.15/186.67 inference(rename_variables,[],[3118])). % 186.15/186.67 cnf(11415,plain, % 186.15/186.67 (E(f37(x114151,x114152,x114153,x114154,x114155,x114156,x114157,x114158,x114159,a25),x114152)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11418,plain, % 186.15/186.67 (E(f37(x114181,x114182,x114183,x114184,x114185,x114186,x114187,x114188,x114189,a25),x114182)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11422,plain, % 186.15/186.67 (E(f37(x114221,x114222,x114223,x114224,x114225,x114226,x114227,x114228,x114229,a25),x114222)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11425,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x114251)),x114251))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11426,plain, % 186.15/186.67 (E(f37(x114261,x114262,x114263,x114264,x114265,x114266,x114267,x114268,x114269,a25),x114262)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11435,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x114351),x114351))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11436,plain, % 186.15/186.67 (E(f37(x114361,x114362,x114363,x114364,x114365,x114366,x114367,x114368,x114369,a25),x114362)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11439,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f52(a850,x114391,x114392)),x114391))), % 186.15/186.67 inference(rename_variables,[],[3635])). % 186.15/186.67 cnf(11440,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x114401))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(11442,plain, % 186.15/186.67 (~P1(f775(f775(f232(a1),f80(a1)),f2(a1)))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2833,2841,2848,2851,2853,2855,2857,2859,2860,2872,2873,2883,2931,2942,2947,2958,2960,2961,2975,2977,4359,3118,11412,3638,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,4451,10076,10079,10105,10565,10580,10702,11120,11181,4467,11279,11312,11353,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,10472,11255,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,10686,11321,3185,10628,10694,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,3339,10434,10697,10742,11013,11086,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,3246,10459,3283,3278,3699,3635,10145,11406,4460,10096,10453,10456,10894,10910,11369,3205,10646,10720,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,3785,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,4478,10543,10965,4065,3965,3658,4475,10118,10121,10447,10450,4476,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673])). % 186.15/186.67 cnf(11457,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x114571),x114571))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11460,plain, % 186.15/186.67 (E(f37(x114601,x114602,x114603,x114604,x114605,x114606,x114607,x114608,x114609,a25),x114602)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11463,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x114631),x114631))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11466,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x114661),x114661))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11469,plain, % 186.15/186.67 (P1(f775(f775(f334(x114691),f775(x114692,x114693)),f775(f303(x114694,x114691,x114692),f239(f857(x114694,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(11470,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x114701),x114702)),x114702))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(11473,plain, % 186.15/186.67 (P1(f775(f775(f334(x114731),f775(x114732,x114733)),f775(f303(x114734,x114731,x114732),f239(f857(x114734,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(11474,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x114741)),x114741))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11479,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x114791),x114792)),x114791))), % 186.15/186.67 inference(rename_variables,[],[4476])). % 186.15/186.67 cnf(11482,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x114821),x114821))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11485,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x114851),x114851))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11492,plain, % 186.15/186.67 (P1(f775(f775(f334(x114921),x114922),f239(f857(x114921,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(11493,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x114931)),x114931))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11496,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x114961),x114961))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11509,plain, % 186.15/186.67 (~P1(f775(f775(f334(x115091),x115092),f180(f857(x115091,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11512,plain, % 186.15/186.67 (E(f775(f775(f18(x115121,x115122),x115123),x115124),x115123)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(11515,plain, % 186.15/186.67 (E(f775(f775(f18(x115151,x115152),x115153),x115154),x115153)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(11526,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f775(f775(f43(a850),x115261),x115262)),x115261))), % 186.15/186.67 inference(rename_variables,[],[3602])). % 186.15/186.67 cnf(11527,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),f2(a850)),f775(a114,x115271)))), % 186.15/186.67 inference(rename_variables,[],[3266])). % 186.15/186.67 cnf(11529,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),f775(f775(f43(a850),x115291),f37(x115292,f2(a850),x115293,x115294,x115295,x115296,x115297,x115298,x115299,a25))),f2(a850)))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2833,2841,2848,2851,2853,2855,2857,2859,2860,2872,2873,2883,2931,2942,2947,2958,2960,2961,2975,2977,4359,3118,11412,3638,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,11403,3266,4451,10076,10079,10105,10565,10580,10702,11120,11181,4467,11279,11312,11353,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,10686,11321,3185,10628,10694,3260,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,3246,10459,3283,3278,3699,3635,10145,11406,4460,10096,10453,10456,10894,10910,11369,11425,11474,3205,10646,10720,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,3785,11131,11469,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929])). % 186.15/186.67 cnf(11530,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x115301),x115301))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11531,plain, % 186.15/186.67 (E(f37(x115311,x115312,x115313,x115314,x115315,x115316,x115317,x115318,x115319,a25),x115312)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11534,plain, % 186.15/186.67 (P1(f775(f775(f334(x115341),f775(x115342,x115343)),f775(f303(x115344,x115341,x115342),f239(f857(x115344,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(11537,plain, % 186.15/186.67 (P1(f775(f63(x115371),f169(x115371,x115372,f166(x115371,x115372,x115373))))), % 186.15/186.67 inference(rename_variables,[],[3728])). % 186.15/186.67 cnf(11540,plain, % 186.15/186.67 (P1(f775(f63(x115401),f169(x115401,x115402,f166(x115401,x115402,x115403))))), % 186.15/186.67 inference(rename_variables,[],[3728])). % 186.15/186.67 cnf(11543,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f775(f81(a1),f775(f102(a1),x115431))),f775(f102(a1),x115432)))), % 186.15/186.67 inference(rename_variables,[],[3659])). % 186.15/186.67 cnf(11546,plain, % 186.15/186.67 (~P1(f775(f775(f334(x115461),x115462),f180(f857(x115461,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11560,plain, % 186.15/186.67 (~P1(f775(f775(f334(a850),x115601),f775(f257(a850),f2(a850))))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2833,2841,2848,2851,2853,2855,2857,2859,2860,2862,2872,2873,2883,2931,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3638,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,3630,11403,3266,4451,10076,10079,10105,10565,10580,10702,11120,11181,4467,11279,11312,11353,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,10686,11321,3185,10628,10694,3260,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,3246,10459,3283,3278,3699,3635,10145,11406,4460,10096,10453,10456,10894,10910,11369,11425,11474,3205,10646,10720,3659,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,3934,3785,11131,11469,11473,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018])). % 186.15/186.67 cnf(11567,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x115671),x115671))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11568,plain, % 186.15/186.67 (E(f37(x115681,x115682,x115683,x115684,x115685,x115686,x115687,x115688,x115689,a25),x115682)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(11571,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x115711),f775(a114,x115711)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11574,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x115741),x115741))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11585,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x115851),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11588,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x115881),x115881))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11593,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x115931),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11602,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x116021))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(11603,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x116031)),x116031))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11606,plain, % 186.15/186.67 (~P1(f775(f64(x116061,x116062,f180(f857(x116061,a844))),x116063))), % 186.15/186.67 inference(rename_variables,[],[4474])). % 186.15/186.67 cnf(11617,plain, % 186.15/186.67 (~P1(f775(f775(f279(a850),f775(a114,f775(f775(f82(a850),f775(a114,f2(a850))),x116171))),f775(a114,f2(a850))))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2872,2873,2883,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3638,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,3630,11403,3266,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,4467,11279,11312,11353,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,10686,11321,11366,11574,3185,10628,10694,3260,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,3205,10646,10720,11440,3659,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279])). % 186.15/186.67 cnf(11619,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x116191),f775(a114,x116191)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11629,plain, % 186.15/186.67 (P1(f775(f775(f233(a1),f775(f81(a1),f80(a1))),f2(a1)))), % 186.15/186.67 inference(scs_inference,[],[3424,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3638,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,4045,10983,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,3630,11403,3266,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,3921,3824,10638,3872,3542,3910,3559,10815,10877,10962,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,3183,10532,10586,10589,10622,10649,10683,10727,3184,10280,10477,10560,10686,11321,11366,11574,3185,10628,10694,3260,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,3205,10646,10720,11440,3659,4005,4458,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334])). % 186.15/186.67 cnf(11634,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x116341),x116341))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11637,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x116371),x116371))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11640,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x116401),x116401))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11643,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x116431),x116431))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11646,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x116461)),x116461))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11649,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x116491)),x116491))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11652,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x116521)),x116521))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11655,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x116551)),x116551))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(11673,plain, % 186.15/186.67 (E(f775(f181(f851(x116731)),f775(f141(x116731),x116732)),f775(f181(f851(x116731)),x116732))), % 186.15/186.67 inference(rename_variables,[],[3196])). % 186.15/186.67 cnf(11676,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x116761),x116761))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11682,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x116821),x116821))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11693,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x116931),x116931))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11696,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(f856(f851(x116961),f851(x116961)),a844)),f147(x116961,x116962)),f300(f851(x116961),f146(x116961,x116962))))), % 186.15/186.67 inference(rename_variables,[],[3877])). % 186.15/186.67 cnf(11703,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x117031),f775(a114,x117031)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11706,plain, % 186.15/186.67 (P1(f775(f775(f334(f857(x117061,a844)),x117062),f775(f301(x117061),x117062)))), % 186.15/186.67 inference(rename_variables,[],[3542])). % 186.15/186.67 cnf(11707,plain, % 186.15/186.67 (~E(f775(a114,x117071),x117071)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11714,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x117141),x117141))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11719,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x117191),x117191))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11728,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x117281,a844)),x117282),f775(f775(f302(x117281),x117283),x117282)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(11731,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x117311),x117311))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11732,plain, % 186.15/186.67 (~E(f775(a114,x117321),x117321)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11745,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x117451),x117451))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11746,plain, % 186.15/186.67 (~E(f775(a114,x117461),x117461)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11749,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x117491),x117491))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11752,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x117521),x117521))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11755,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x117551),x117551))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11758,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x117581),x117581))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11761,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x117611),x117611))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11764,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x117641),x117641))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11767,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x117671),x117671))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11770,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x117701),x117701))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11771,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x117711),f775(a114,x117711)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11780,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x117801),x117801))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11781,plain, % 186.15/186.67 (~E(f775(a114,x117811),x117811)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11786,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x117861),x117861))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11801,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x118011),x118011))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(11806,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x118061))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(11825,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118251),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11828,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118281),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11831,plain, % 186.15/186.67 (~P1(f775(f775(f334(x118311),x118312),f180(f857(x118311,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11834,plain, % 186.15/186.67 (~P1(f775(f775(f334(x118341),x118342),f180(f857(x118341,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11837,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118371),x118371))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11840,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118401),x118401))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11843,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118431),x118431))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11846,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x118461),x118461))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11849,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x118491),f775(a114,x118491)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11856,plain, % 186.15/186.67 (P1(f775(f775(f334(f857(x118561,a844)),x118562),f775(f301(x118561),x118562)))), % 186.15/186.67 inference(rename_variables,[],[3542])). % 186.15/186.67 cnf(11861,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x118611,a844)),f775(f158(x118611),f775(f126(x118611,x118612),x118613))),f775(f158(x118611),x118613)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(11868,plain, % 186.15/186.67 (~P1(f775(f775(f334(x118681),x118682),f180(f857(x118681,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11877,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x118771,a844)),x118772),f239(f857(x118771,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(11878,plain, % 186.15/186.67 (~E(f775(a114,x118781),x118781)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11881,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x118811,a844)),f775(f158(x118811),f775(f126(x118811,x118812),x118813))),f775(f158(x118811),x118813)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(11887,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x118871),f775(a114,x118871)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11896,plain, % 186.15/186.67 (E(f775(f181(f851(x118961)),f775(f141(x118961),x118962)),f775(f181(f851(x118961)),x118962))), % 186.15/186.67 inference(rename_variables,[],[3196])). % 186.15/186.67 cnf(11899,plain, % 186.15/186.67 (P39(a25,x118991,x118992,x118991)), % 186.15/186.67 inference(rename_variables,[],[3400])). % 186.15/186.67 cnf(11912,plain, % 186.15/186.67 (P1(f775(f63(x119121),f180(f857(x119121,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(11913,plain, % 186.15/186.67 (~P1(f775(f775(f334(x119131),x119132),f180(f857(x119131,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11916,plain, % 186.15/186.67 (P39(a25,x119161,x119162,x119161)), % 186.15/186.67 inference(rename_variables,[],[3400])). % 186.15/186.67 cnf(11921,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x119211),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(11922,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x119221),x119221))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(11929,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x119291,a844)),f775(f158(x119291),f151(x119291,x119292,x119293))),f775(f158(x119291),x119293)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(11934,plain, % 186.15/186.67 (P29(x119341,x119341,f7(x119341),x119342)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(11939,plain, % 186.15/186.67 (P1(f775(f775(f334(f857(x119391,a844)),x119392),f775(f301(x119391),x119392)))), % 186.15/186.67 inference(rename_variables,[],[3542])). % 186.15/186.67 cnf(11946,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x119461),x119461))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(11949,plain, % 186.15/186.67 (~P1(f775(f775(f334(x119491),x119492),f180(f857(x119491,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(11952,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x119521,a844)),x119522),f775(f775(f302(x119521),x119523),x119522)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(11953,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x119531,a844)),x119532),f239(f857(x119531,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(11960,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x119601),f775(a114,x119601)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11963,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x119631),f775(a114,x119631)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(11966,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x119661),x119661))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11969,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x119691),x119691))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11972,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x119721),x119721))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11975,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x119751),x119751))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(11978,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),x119781),x119781))), % 186.15/186.67 inference(rename_variables,[],[3185])). % 186.15/186.67 cnf(11981,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),x119811),x119811))), % 186.15/186.67 inference(rename_variables,[],[3185])). % 186.15/186.67 cnf(11985,plain, % 186.15/186.67 (~P1(f775(f775(f232(a1),f775(f775(f3(a1),a85),a99)),f2(a1)))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,3484,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2832,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3127,3235,3638,3947,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3196,11673,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,11540,3224,3921,3877,3824,10638,11861,3872,10812,3542,11706,11856,3910,3559,10815,10877,10962,11024,11877,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,10775,11728,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580])). % 186.15/186.67 cnf(11988,plain, % 186.15/186.67 (P1(f775(f775(f334(f857(x119881,a844)),x119882),f775(f301(x119881),x119882)))), % 186.15/186.67 inference(rename_variables,[],[3542])). % 186.15/186.67 cnf(11992,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f775(f82(a1),a85),a85)),f2(a1)))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,3484,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2832,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3127,3235,3638,3947,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3196,11673,3242,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,11540,3224,3921,3877,3824,10638,11861,3872,10812,3542,11706,11856,11939,3910,3559,10815,10877,10962,11024,11877,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,3339,10434,10697,10742,11013,11086,11242,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,10775,11728,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616])). % 186.15/186.67 cnf(11997,plain, % 186.15/186.67 (~E(f775(a114,x119971),x119971)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(11998,plain, % 186.15/186.67 (E(f775(f303(x119981,x119981,f7(x119981)),x119982),x119982)), % 186.15/186.67 inference(rename_variables,[],[3242])). % 186.15/186.67 cnf(12001,plain, % 186.15/186.67 (P34(x120011,x120012,f115(x120011),f115(x120011))), % 186.15/186.67 inference(rename_variables,[],[3432])). % 186.15/186.67 cnf(12004,plain, % 186.15/186.67 (~E(f775(a114,x120041),x120041)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12007,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120071,a844)),f775(f158(x120071),f151(x120071,x120072,x120073))),f775(f158(x120071),x120073)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(12008,plain, % 186.15/186.67 (P1(f775(f63(x120081),f775(f158(x120081),x120082)))), % 186.15/186.67 inference(rename_variables,[],[3224])). % 186.15/186.67 cnf(12019,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x120191),x120191))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12022,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x120221),x120221))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12031,plain, % 186.15/186.67 (E(f775(f181(f851(x120311)),f775(f141(x120311),x120312)),f775(f181(f851(x120311)),x120312))), % 186.15/186.67 inference(rename_variables,[],[3196])). % 186.15/186.67 cnf(12034,plain, % 186.15/186.67 (P18(a850,f775(f142(a850),f775(f775(f143(f851(x120341),a850),f181(f851(x120341))),f164(x120341,x120342))))), % 186.15/186.67 inference(rename_variables,[],[3741])). % 186.15/186.67 cnf(12037,plain, % 186.15/186.67 (P29(x120371,x120371,f7(x120371),x120372)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12040,plain, % 186.15/186.67 (P1(f775(f775(f334(f851(x120401)),f115(x120401)),f149(x120401,x120402)))), % 186.15/186.67 inference(rename_variables,[],[3381])). % 186.15/186.67 cnf(12043,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x120431,f857(x120432,a844))),x120433),x120434))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(12045,plain, % 186.15/186.67 (P1(f775(f775(f233(f857(x120451,a844)),f775(a114,f239(f857(x120451,a844)))),f775(f775(f302(x120451),x120452),f239(f857(x120451,a844)))))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,11934,3432,3484,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2832,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3127,3235,3638,3947,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3063,3196,11673,11896,3242,10641,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3741,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,11540,3224,3921,3877,3824,10638,11861,3872,10812,11929,3542,11706,11856,11939,11988,3910,3559,10815,10877,10962,11024,11877,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,3339,10434,10697,10742,11013,11086,11242,11492,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,10775,11728,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,11117,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616,7617,7623,7642,7651,7662,7667,7673,7674,7680,7690,7691,7693,7722,7749,7779,7816,7817,7864,7871,7872])). % 186.15/186.67 cnf(12048,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x120481),x120481))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12049,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x120491))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12051,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f2(a1)),f795(x120511,f180(f857(x120512,f857(x120513,a844))),f80(a1))))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,11934,3432,3484,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,4338,11154,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2832,2833,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3127,3235,3638,3947,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3063,3196,11673,11896,3242,10641,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,3541,4240,4241,4394,3487,3693,3741,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,11540,3224,3921,3877,3824,10638,11861,3872,10812,11929,3542,11706,11856,11939,11988,3910,3559,10815,10877,10962,11024,11877,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,3339,10434,10697,10742,11013,11086,11242,11492,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,11806,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,10775,11728,3481,3627,10838,10992,11018,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,11117,12043,4065,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616,7617,7623,7642,7651,7662,7667,7673,7674,7680,7690,7691,7693,7722,7749,7779,7816,7817,7864,7871,7872,7894,7895])). % 186.15/186.67 cnf(12052,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x120521,f857(x120522,a844))),x120523),x120524))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(12055,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(f856(f851(x120551),f851(x120551)),a844)),f147(x120551,x120552)),f300(f851(x120551),f146(x120551,x120552))))), % 186.15/186.67 inference(rename_variables,[],[3877])). % 186.15/186.67 cnf(12061,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120611,a844)),f180(f857(x120611,a844))),x120612))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(12064,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120641,a844)),f775(f303(x120642,x120641,x120643),f775(f305(x120642,x120641,x120643),x120644))),x120644))), % 186.15/186.67 inference(rename_variables,[],[4065])). % 186.15/186.67 cnf(12067,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120671,a844)),f775(f158(x120671),f151(x120671,x120672,x120673))),f775(f158(x120671),x120673)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(12068,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120681,a844)),f775(f158(x120681),f775(f126(x120681,x120682),x120683))),f775(f158(x120681),x120683)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(12073,plain, % 186.15/186.67 (P29(x120731,f854(x120731),f227(x120731),x120732)), % 186.15/186.67 inference(rename_variables,[],[3433])). % 186.15/186.67 cnf(12078,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120781,a844)),f775(f303(x120782,x120781,x120783),f775(f305(x120782,x120781,x120783),x120784))),x120784))), % 186.15/186.67 inference(rename_variables,[],[4065])). % 186.15/186.67 cnf(12081,plain, % 186.15/186.67 (P1(f775(f63(f854(x120811)),f775(f303(x120812,f854(x120811),f166(x120812,x120811,x120813)),f239(f857(x120812,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3934])). % 186.15/186.67 cnf(12086,plain, % 186.15/186.67 (P1(f775(f775(f334(f857(x120861,a844)),x120862),f775(f301(x120861),x120862)))), % 186.15/186.67 inference(rename_variables,[],[3542])). % 186.15/186.67 cnf(12089,plain, % 186.15/186.67 (~P1(f775(f775(f334(f856(f851(x120891),f851(x120891))),f775(f775(f241(f851(x120891),f851(x120891)),x120892),f115(x120891))),f135(x120891,x120893)))), % 186.15/186.67 inference(rename_variables,[],[4479])). % 186.15/186.67 cnf(12092,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x120921),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12094,plain, % 186.15/186.67 (~P1(f775(f63(x120941),f239(f857(x120941,a844))))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,11934,3432,3433,3484,3154,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,4338,11154,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,4381,10267,10362,4375,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3118,11412,3127,3235,3638,3947,3026,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3063,3196,11673,11896,3242,10641,3117,3137,10304,3287,4471,3813,4397,10099,10264,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,3814,10809,10928,10995,4479,10745,10935,11049,11069,11105,11111,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,12040,3541,4240,4241,4394,3487,3693,3741,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3373,4468,3954,11066,3506,3728,11537,11540,3224,3921,3877,11696,12055,3824,10638,11861,11881,3872,10812,11929,12007,3542,11706,11856,11939,11988,3910,3559,10815,10877,10962,11024,11877,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,3339,10434,10697,10742,11013,11086,11242,11492,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,11806,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,3623,10758,10764,10775,11728,3481,10980,3627,10838,10992,11018,11029,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,11117,12043,4065,10631,12064,3965,3658,3602,4475,10118,10121,10447,10450,11276,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,969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% 186.15/186.67 cnf(12095,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x120951,a844)),x120952),x120952))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12098,plain, % 186.15/186.67 (~P1(f775(f775(f334(x120981),x120982),f180(f857(x120981,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12101,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x121011,f857(x121012,a844))),x121013),x121014))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(12104,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x121041,a844)),f775(f303(x121042,x121041,x121043),f775(f305(x121042,x121041,x121043),x121044))),x121044))), % 186.15/186.67 inference(rename_variables,[],[4065])). % 186.15/186.67 cnf(12105,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x121051,a844)),x121052),x121052))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12110,plain, % 186.15/186.67 (E(f37(x121101,x121102,x121103,x121104,x121105,x121106,x121107,x121108,x121109,a25),x121102)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12113,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x121131,a844)),f775(f158(x121131),f151(x121131,x121132,x121133))),f775(f158(x121131),x121133)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(12114,plain, % 186.15/186.67 (P1(f775(f63(x121141),f775(f158(x121141),x121142)))), % 186.15/186.67 inference(rename_variables,[],[3224])). % 186.15/186.67 cnf(12117,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x121171),x121171))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(12120,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x121201),x121201))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12123,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x121231),x121231))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12134,plain, % 186.15/186.67 (P29(x121341,x121341,f7(x121341),x121342)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12141,plain, % 186.15/186.67 (~P1(f775(f775(f334(x121411),x121412),f180(f857(x121411,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12144,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x121441,x121441)),f775(f775(f241(x121441,x121441),x121442),x121442)),f300(x121441,x121443)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(12147,plain, % 186.15/186.67 (~P1(f775(f775(f334(x121471),x121472),f180(f857(x121471,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12150,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x121501,x121501)),f775(f775(f241(x121501,x121501),x121502),x121502)),f300(x121501,x121503)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(12160,plain, % 186.15/186.67 (~E(f775(f775(f140(x121601),x121602),x121603),x121603)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(12163,plain, % 186.15/186.67 (P1(f775(f775(f334(x121631),x121632),f239(f857(x121631,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(12164,plain, % 186.15/186.67 (~E(f775(a114,x121641),x121641)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12167,plain, % 186.15/186.67 (P1(f775(f775(f334(f851(x121671)),f115(x121671)),f149(x121671,x121672)))), % 186.15/186.67 inference(rename_variables,[],[3381])). % 186.15/186.67 cnf(12168,plain, % 186.15/186.67 (~E(f775(f775(f140(x121681),x121682),x121683),f115(x121681))), % 186.15/186.67 inference(rename_variables,[],[4406])). % 186.15/186.67 cnf(12171,plain, % 186.15/186.67 (P1(f775(f775(f334(x121711),f775(x121712,x121713)),f775(f303(x121714,x121711,x121712),f239(f857(x121714,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12172,plain, % 186.15/186.67 (P29(x121721,x121721,f7(x121721),x121722)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12175,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x121751,a844)),f180(f857(x121751,a844))),x121752))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(12176,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x121761,a844)),x121762),x121762))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12179,plain, % 186.15/186.67 (P1(f775(f775(f334(x121791),f775(x121792,x121793)),f775(f303(x121794,x121791,x121792),f239(f857(x121794,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12180,plain, % 186.15/186.67 (P29(x121801,x121801,f7(x121801),x121802)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12183,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(f851(x121831),f851(x121831))),f775(f775(f241(f851(x121831),f851(x121831)),f115(x121831)),f115(x121831))),f147(x121831,x121832)))), % 186.15/186.67 inference(rename_variables,[],[3960])). % 186.15/186.67 cnf(12189,plain, % 186.15/186.67 (P29(x121891,x121891,f7(x121891),x121892)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12192,plain, % 186.15/186.67 (E(f775(f775(f125(x121921),x121922),f115(x121921)),x121922)), % 186.15/186.67 inference(rename_variables,[],[3118])). % 186.15/186.67 cnf(12193,plain, % 186.15/186.67 (~E(f775(f775(f140(x121931),x121932),x121933),x121933)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(12196,plain, % 186.15/186.67 (E(f775(f775(f125(x121961),x121962),f115(x121961)),x121962)), % 186.15/186.67 inference(rename_variables,[],[3118])). % 186.15/186.67 cnf(12197,plain, % 186.15/186.67 (~E(f775(f775(f140(x121971),x121972),x121973),x121973)), % 186.15/186.67 inference(rename_variables,[],[4397])). % 186.15/186.67 cnf(12200,plain, % 186.15/186.67 (E(f775(f775(f125(x122001),x122002),f115(x122001)),x122002)), % 186.15/186.67 inference(rename_variables,[],[3118])). % 186.15/186.67 cnf(12209,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122091,a844)),x122092),f239(f857(x122091,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(12213,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x122131),x122131))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12214,plain, % 186.15/186.67 (~E(f775(a114,x122141),x122141)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12217,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122171,a844)),f180(f857(x122171,a844))),x122172))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(12220,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x122201),x122201))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12223,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122231,a844)),x122232),x122232))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12228,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122281,a844)),x122282),f775(f775(f302(x122281),x122283),x122282)))), % 186.15/186.67 inference(rename_variables,[],[3623])). % 186.15/186.67 cnf(12231,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122311,a844)),x122312),x122312))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12232,plain, % 186.15/186.67 (~P1(f775(f775(f334(x122321),x122322),f180(f857(x122321,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12235,plain, % 186.15/186.67 (~P1(f775(f775(f334(x122351),x122352),f180(f857(x122351,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12242,plain, % 186.15/186.67 (P29(x122421,x122421,f7(x122421),x122422)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12245,plain, % 186.15/186.67 (~P1(f775(f775(f334(x122451),x122452),f180(f857(x122451,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12248,plain, % 186.15/186.67 (P1(f775(f775(f334(x122481),f775(x122482,x122483)),f775(f303(x122484,x122481,x122482),f239(f857(x122484,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12249,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x122491,x122491)),f775(f775(f241(x122491,x122491),x122492),x122492)),f300(x122491,x122493)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(12252,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x122521,x122521)),f775(f775(f241(x122521,x122521),x122522),x122522)),f300(x122521,x122523)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(12255,plain, % 186.15/186.67 (P1(f775(f63(x122551),f775(f158(x122551),x122552)))), % 186.15/186.67 inference(rename_variables,[],[3224])). % 186.15/186.67 cnf(12265,plain, % 186.15/186.67 (~P1(f775(f775(f180(f857(x122651,f857(x122652,a844))),x122653),x122654))), % 186.15/186.67 inference(rename_variables,[],[4478])). % 186.15/186.67 cnf(12268,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122681,a844)),x122682),f239(f857(x122681,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(12271,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(x122711,x122711)),f775(f775(f241(x122711,x122711),x122712),x122712)),f300(x122711,x122713)))), % 186.15/186.67 inference(rename_variables,[],[3814])). % 186.15/186.67 cnf(12274,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f775(f775(f82(a850),x122741),x122742)),x122742))), % 186.15/186.67 inference(rename_variables,[],[4475])). % 186.15/186.67 cnf(12275,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x122751),f775(a114,x122751)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12278,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x122781,a844)),x122782),f239(f857(x122781,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(12281,plain, % 186.15/186.67 (E(f37(x122811,x122812,x122813,x122814,x122815,x122816,x122817,x122818,x122819,a25),x122812)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12288,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(f856(f851(x122881),f851(x122881)),f856(f851(x122881),f851(x122881)))),f507(f300(f856(f851(x122881),f851(x122881)),x122882),f135(x122881,x122883),f856(f851(x122881),f851(x122881)))),f300(f856(f851(x122881),f851(x122881)),x122882)))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,11934,12037,12134,12172,12180,12189,3432,3433,3484,3154,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,4338,11154,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,4381,10267,10362,3239,4375,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3518,3118,11412,12192,12196,12200,3127,3235,3638,3947,3026,4377,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3063,3196,11673,11896,3242,10641,11998,3116,3117,3137,10304,3287,4471,3813,4397,10099,10264,11055,12160,12193,4406,12168,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,12183,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,4394,11169,3487,3693,3741,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3568,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,3921,3877,11696,12055,3824,10638,11861,11881,3872,10812,11929,12007,12067,12113,3542,11706,11856,11939,11988,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,3339,10434,10697,10742,11013,11086,11242,11492,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,11806,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,11534,12171,12179,3623,10758,10764,10775,11728,11952,3481,10980,12095,12105,12176,12223,3958,3627,10838,10992,11018,11029,12061,12175,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,11117,12043,12052,12101,4065,10631,12064,12078,3965,3658,3602,4475,10118,10121,10447,10450,11276,11470,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616,7617,7623,7642,7651,7662,7667,7673,7674,7680,7690,7691,7693,7722,7749,7779,7816,7817,7864,7871,7872,7894,7895,7914,7915,7980,7981,7982,8002,8003,8037,8041,8045,8054,8068,8095,8099,8105,8118,8137,8143,8165,8205,8235,8247,8264,8267,8296,8323,8387,8388,8391,8392,8409,8499,8500,8501,8502,8525,8549,8571,8613,8631,8684,8725,8728,8741,8778,8796,8812,8813,8828,8829,8957,8962,8980,8996,9016,9018,9021,9024,9027,9028,9040,9041,9064,9137,9172,9173,9238,9244,9278,9289,9293,9297,9298,9312,9336,9347,9356,9357,9359])). % 186.15/186.67 cnf(12292,plain, % 186.15/186.67 (~P1(f775(f775(f334(x122921),x122922),f180(f857(x122921,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12293,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(f851(x122931),f851(x122931))),f775(f775(f241(f851(x122931),f851(x122931)),f115(x122931)),f115(x122931))),f147(x122931,x122932)))), % 186.15/186.67 inference(rename_variables,[],[3960])). % 186.15/186.67 cnf(12295,plain, % 186.15/186.67 (P1(f775(f775(f334(f856(a850,a850)),f775(f775(f241(a850,a850),f2(a850)),f775(a114,f2(a850)))),f775(f775(f281(a850,a850,a850),f300(a850,a323)),f300(a850,f300(a850,a323)))))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,3424,10867,11934,12037,12134,12172,12180,12189,3432,3433,3484,3154,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,4338,11154,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,4381,10267,10362,3239,4375,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3518,3118,11412,12192,12196,12200,3127,3235,3638,3947,3026,4377,4436,10803,11097,11100,3731,11186,3084,3049,3044,3033,3039,4045,10983,3063,3196,11673,11896,3242,10641,11998,3116,3117,3137,10304,3287,4471,3813,4397,10099,10264,11055,12160,12193,4406,12168,3174,11512,4461,3577,3288,3080,3081,10164,10462,3343,3003,3103,11178,3960,12183,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,4394,11169,3487,3693,3741,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,4467,11279,11312,11353,11383,3615,3391,3768,3211,3213,3186,4448,4391,3568,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,3921,3877,11696,12055,3824,10638,11861,11881,3872,10812,11929,12007,12067,12113,3542,11706,11856,11939,11988,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3185,10628,10694,11978,3260,11912,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,3339,10434,10697,10742,11013,11086,11242,11492,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,3246,10459,3283,3278,3699,3635,10145,11406,11439,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,3205,10646,10720,11440,11602,11806,3659,4005,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4474,10067,10070,10322,10780,11606,3934,3785,11131,11469,11473,11534,12171,12179,3623,10758,10764,10775,11728,11952,3481,10980,12095,12105,12176,12223,3958,3627,10838,10992,11018,11029,12061,12175,3452,10420,10423,10492,10673,4477,11400,4478,10543,10965,11117,12043,12052,12101,4065,10631,12064,12078,3965,3658,3602,4475,10118,10121,10447,10450,11276,11470,4476,11380,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616,7617,7623,7642,7651,7662,7667,7673,7674,7680,7690,7691,7693,7722,7749,7779,7816,7817,7864,7871,7872,7894,7895,7914,7915,7980,7981,7982,8002,8003,8037,8041,8045,8054,8068,8095,8099,8105,8118,8137,8143,8165,8205,8235,8247,8264,8267,8296,8323,8387,8388,8391,8392,8409,8499,8500,8501,8502,8525,8549,8571,8613,8631,8684,8725,8728,8741,8778,8796,8812,8813,8828,8829,8957,8962,8980,8996,9016,9018,9021,9024,9027,9028,9040,9041,9064,9137,9172,9173,9238,9244,9278,9289,9293,9297,9298,9312,9336,9347,9356,9357,9359,9361,9388])). % 186.15/186.67 cnf(12298,plain, % 186.15/186.67 (~P1(f775(f775(f334(x122981),x122982),f180(f857(x122981,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12301,plain, % 186.15/186.67 (~P1(f775(f775(f334(x123011),x123012),f180(f857(x123011,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12304,plain, % 186.15/186.67 (P1(f775(f775(f187(a25),x123041),x123041))), % 186.15/186.67 inference(rename_variables,[],[3182])). % 186.15/186.67 cnf(12307,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x123071),x123071))), % 186.15/186.67 inference(rename_variables,[],[4447])). % 186.15/186.67 cnf(12310,plain, % 186.15/186.67 (P1(f775(f775(f334(x123101),x123102),f239(f857(x123101,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(12317,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x123171,a844)),x123172),x123172))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12320,plain, % 186.15/186.67 (~P1(f775(f775(f334(x123201),x123202),f180(f857(x123201,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12323,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f2(a1)),f775(f775(f242(a1),f775(f77(a1),x123231)),x123232)))), % 186.15/186.67 inference(rename_variables,[],[3658])). % 186.15/186.67 cnf(12326,plain, % 186.15/186.67 (E(f37(x123261,x123262,x123263,x123264,x123265,x123266,x123267,x123268,x123269,a25),x123262)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12328,plain, % 186.15/186.67 (E(f37(x123281,x123282,x123283,x123284,x123285,x123286,x123287,x123288,x123289,a25),x123282)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12330,plain, % 186.15/186.67 (E(f37(x123301,x123302,x123303,x123304,x123305,x123306,x123307,x123308,x123309,a25),x123302)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12332,plain, % 186.15/186.67 (P28(x123321,x123322,f180(f857(f849(x123321),a844)))), % 186.15/186.67 inference(rename_variables,[],[3238])). % 186.15/186.67 cnf(12337,plain, % 186.15/186.67 (P39(a25,x123371,x123372,x123371)), % 186.15/186.67 inference(rename_variables,[],[3400])). % 186.15/186.67 cnf(12339,plain, % 186.15/186.67 (P39(a25,x123391,x123392,x123391)), % 186.15/186.67 inference(rename_variables,[],[3400])). % 186.15/186.67 cnf(12343,plain, % 186.15/186.67 (E(f37(x123431,x123432,x123433,x123434,x123435,x123436,x123437,x123438,x123439,a25),x123432)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12350,plain, % 186.15/186.67 (E(f37(x123501,x123502,x123503,x123504,x123505,x123506,x123507,x123508,x123509,a25),x123502)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12355,plain, % 186.15/186.67 (P29(x123551,x123551,f7(x123551),x123552)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12357,plain, % 186.15/186.67 (P29(x123571,x123571,f7(x123571),x123572)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12368,plain, % 186.15/186.67 (E(f37(x123681,x123682,x123683,x123684,x123685,x123686,x123687,x123688,x123689,a25),x123682)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12370,plain, % 186.15/186.67 (P53(x123701,x123701,f260(x123701,x123702))), % 186.15/186.67 inference(rename_variables,[],[3154])). % 186.15/186.67 cnf(12376,plain, % 186.15/186.67 (P47(x123761,x123762,f260(x123761,x123762))), % 186.15/186.67 inference(rename_variables,[],[3153])). % 186.15/186.67 cnf(12378,plain, % 186.15/186.67 (P47(x123781,x123782,f260(x123781,x123782))), % 186.15/186.67 inference(rename_variables,[],[3153])). % 186.15/186.67 cnf(12383,plain, % 186.15/186.67 (E(f180(f857(f856(x123831,x123831),a844)),f260(x123831,f180(f857(x123831,a844))))), % 186.15/186.67 inference(rename_variables,[],[3255])). % 186.15/186.67 cnf(12387,plain, % 186.15/186.67 (E(f37(x123871,x123872,x123873,x123874,x123875,x123876,x123877,x123878,x123879,a25),x123872)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12389,plain, % 186.15/186.67 (E(f37(x123891,x123892,x123893,x123894,x123895,x123896,x123897,x123898,x123899,a25),x123892)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12391,plain, % 186.15/186.67 (E(f37(x123911,x123912,x123913,x123914,x123915,x123916,x123917,x123918,x123919,a25),x123912)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12395,plain, % 186.15/186.67 (E(f37(x123951,x123952,x123953,x123954,x123955,x123956,x123957,x123958,x123959,a25),x123952)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12397,plain, % 186.15/186.67 (P31(x123971,f2(a850),f775(f775(f775(f93(x123971),x123972),f775(a27,x123973)),x123974))), % 186.15/186.67 inference(rename_variables,[],[3552])). % 186.15/186.67 cnf(12404,plain, % 186.15/186.67 (P37(x124041,f183(x124041))), % 186.15/186.67 inference(rename_variables,[],[3023])). % 186.15/186.67 cnf(12411,plain, % 186.15/186.67 (P19(x124111,f857(x124111,a844),f302(x124111))), % 186.15/186.67 inference(rename_variables,[],[3157])). % 186.15/186.67 cnf(12415,plain, % 186.15/186.67 (P41(x124151,x124152,x124153,x124154,f180(f857(x124151,a844)),x124154)), % 186.15/186.67 inference(rename_variables,[],[4127])). % 186.15/186.67 cnf(12418,plain, % 186.15/186.67 (P41(x124181,x124182,x124183,x124184,f180(f857(x124181,a844)),x124184)), % 186.15/186.67 inference(rename_variables,[],[4127])). % 186.15/186.67 cnf(12426,plain, % 186.15/186.67 (P54(x124261,f180(f857(x124261,a844)),x124262)), % 186.15/186.67 inference(rename_variables,[],[3203])). % 186.15/186.67 cnf(12430,plain, % 186.15/186.67 (E(f37(x124301,x124302,x124303,x124304,x124305,x124306,x124307,x124308,x124309,a25),x124302)), % 186.15/186.67 inference(rename_variables,[],[4337])). % 186.15/186.67 cnf(12442,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x124421),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12451,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x124511)),f775(f81(a1),f775(f102(a1),x124512))))), % 186.15/186.67 inference(rename_variables,[],[4473])). % 186.15/186.67 cnf(12457,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f775(f42(x124571),f775(f158(x124571),x124572))),f775(f181(f851(x124571)),x124572)))), % 186.15/186.67 inference(rename_variables,[],[3724])). % 186.15/186.67 cnf(12461,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x124611),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12464,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x124641),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12467,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x124671,x124672)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12470,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x124701,x124702)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12473,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x124731,x124732)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12476,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x124761,x124762)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12483,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f775(f81(a1),f775(f102(a1),x124831))),f775(f102(a1),x124832)))), % 186.15/186.67 inference(rename_variables,[],[3659])). % 186.15/186.67 cnf(12486,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x124861),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12487,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x124871),x124871))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12494,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x124941),f775(a114,x124941)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12500,plain, % 186.15/186.67 (P1(f775(f775(f334(x125001),f775(x125002,x125003)),f775(f303(x125004,x125001,x125002),f239(f857(x125004,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12501,plain, % 186.15/186.67 (~E(f775(a114,x125011),f2(a850))), % 186.15/186.67 inference(rename_variables,[],[4375])). % 186.15/186.67 cnf(12506,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x125061),x125061))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12509,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x125091,x125092)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12512,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x125121,x125122)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12515,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x125151),x125151))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12528,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x125281),f775(a114,x125281)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12533,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f52(a850,x125331,x125332)),x125331))), % 186.15/186.67 inference(rename_variables,[],[3635])). % 186.15/186.67 cnf(12542,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x125421),f775(a114,x125421)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12543,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x125431),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12552,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x125521)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(12553,plain, % 186.15/186.67 (P1(f775(f239(f857(x125531,a844)),x125532))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(12556,plain, % 186.15/186.67 (~P1(f775(f775(f233(a1),f775(f102(a1),x125561)),f2(a1)))), % 186.15/186.67 inference(rename_variables,[],[4467])). % 186.15/186.67 cnf(12557,plain, % 186.15/186.67 (P1(f775(f239(f857(x125571,a844)),x125572))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(12560,plain, % 186.15/186.67 (P1(f775(f239(f857(x125601,a844)),x125602))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(12563,plain, % 186.15/186.67 (P1(f775(f239(f857(x125631,a844)),x125632))), % 186.15/186.67 inference(rename_variables,[],[3246])). % 186.15/186.67 cnf(12571,plain, % 186.15/186.67 (~P1(f775(f775(f334(x125711),x125712),f180(f857(x125711,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12572,plain, % 186.15/186.67 (P1(f775(f63(x125721),f180(f857(x125721,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12584,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x125841))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12587,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x125871),f775(a114,x125871)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12588,plain, % 186.15/186.67 (~E(f775(a114,x125881),x125881)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12591,plain, % 186.15/186.67 (~P1(f775(f775(f334(x125911),x125912),f180(f857(x125911,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12594,plain, % 186.15/186.67 (~P1(f775(f775(f334(x125941),x125942),f180(f857(x125941,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12599,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x125991),x125991))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12606,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126061),x126061))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12610,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x126101),f775(a114,x126101)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12613,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126131),x126131))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12618,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126181),x126181))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12621,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126211),x126211))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12624,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126241),x126241))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12627,plain, % 186.15/186.67 (E(f775(f775(f3(f857(x126271,a844)),f180(f857(x126271,a844))),x126272),f180(f857(x126271,a844)))), % 186.15/186.67 inference(rename_variables,[],[3454])). % 186.15/186.67 cnf(12628,plain, % 186.15/186.67 (P1(f775(f63(x126281),f180(f857(x126281,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12631,plain, % 186.15/186.67 (E(f775(f775(f3(f857(x126311,a844)),f180(f857(x126311,a844))),x126312),f180(f857(x126311,a844)))), % 186.15/186.67 inference(rename_variables,[],[3454])). % 186.15/186.67 cnf(12632,plain, % 186.15/186.67 (P1(f775(f63(x126321),f180(f857(x126321,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12635,plain, % 186.15/186.67 (E(f775(f775(f3(f857(x126351,a844)),f180(f857(x126351,a844))),x126352),f180(f857(x126351,a844)))), % 186.15/186.67 inference(rename_variables,[],[3454])). % 186.15/186.67 cnf(12636,plain, % 186.15/186.67 (P1(f775(f63(x126361),f180(f857(x126361,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12639,plain, % 186.15/186.67 (E(f775(f775(f3(f857(x126391,a844)),f180(f857(x126391,a844))),x126392),f180(f857(x126391,a844)))), % 186.15/186.67 inference(rename_variables,[],[3454])). % 186.15/186.67 cnf(12640,plain, % 186.15/186.67 (P1(f775(f63(x126401),f180(f857(x126401,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12644,plain, % 186.15/186.67 (E(f38(x126441,x126442,x126443,x126444,x126445,x126446,x126447,x126448,x126449,a25),x126442)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12649,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),f775(a114,f2(a850))),x126491))), % 186.15/186.67 inference(rename_variables,[],[3340])). % 186.15/186.67 cnf(12650,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x126501)),x126501))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(12653,plain, % 186.15/186.67 (E(f775(f775(f3(f857(x126531,a844)),f180(f857(x126531,a844))),x126532),f180(f857(x126531,a844)))), % 186.15/186.67 inference(rename_variables,[],[3454])). % 186.15/186.67 cnf(12654,plain, % 186.15/186.67 (P1(f775(f63(x126541),f180(f857(x126541,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12658,plain, % 186.15/186.67 (P1(f775(f63(x126581),f180(f857(x126581,a844))))), % 186.15/186.67 inference(rename_variables,[],[3260])). % 186.15/186.67 cnf(12661,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126611),x126611))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12667,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x126671),x126671))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12670,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x126701),f775(a114,x126701)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12677,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x126771),f775(a114,x126771)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12680,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126801),x126801))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12691,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x126911),x126911))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12694,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x126941),x126941))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12701,plain, % 186.15/186.67 (~P1(f775(f775(f334(x127011),x127012),f180(f857(x127011,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12712,plain, % 186.15/186.67 (P1(f775(f775(f334(x127121),x127122),f239(f857(x127121,a844))))), % 186.15/186.67 inference(rename_variables,[],[3339])). % 186.15/186.67 cnf(12718,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x127181,a844)),f775(f158(x127181),f775(f126(x127181,x127182),x127183))),f775(f158(x127181),x127183)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(12724,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x127241),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12725,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x127251),x127251))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12729,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x127291),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12730,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x127301),x127301))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12735,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x127351),x127351))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12742,plain, % 186.15/186.67 (E(f775(f775(f18(x127421,x127422),x127423),x127424),x127423)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(12745,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x127451,a844)),f775(f158(x127451),f151(x127451,x127452,x127453))),f775(f158(x127451),x127453)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(12752,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x127521),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12753,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x127531),x127531))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12757,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),x127571),f2(a850)))), % 186.15/186.67 inference(rename_variables,[],[4451])). % 186.15/186.67 cnf(12758,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x127581),x127581))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12761,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x127611),x127611))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12763,plain, % 186.15/186.67 (~P1(f775(f775(f232(f857(a850,a844)),f295(a850,f775(a114,x127631),f775(a114,x127631))),f295(a850,x127632,x127631)))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,11916,12337,12339,3424,10867,11934,12037,12134,12172,12180,12189,12242,12355,3432,12001,3433,12073,3484,3153,12376,12378,3154,12370,4127,12415,12418,3157,12411,3002,3023,12404,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12326,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,4338,11154,11158,3483,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,4381,10267,10362,3239,3203,12426,4375,10713,2808,2811,2820,2826,2830,2831,2832,2833,2835,2838,2841,2842,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2904,2906,2911,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4358,3057,4359,3518,3165,3508,3758,4350,3118,11412,12192,12196,12200,3127,3235,3638,3947,3026,4377,4395,4436,10803,11097,11100,3731,11186,3238,12332,3096,3084,3049,3552,12397,3044,3844,3557,4323,3033,3012,3039,4045,10983,3063,3196,11673,11896,12031,3242,10641,11998,3116,3117,3137,10304,3287,4471,10235,3813,4397,10099,10264,11055,12160,12193,4406,12168,3174,11512,11515,4461,3577,3288,10884,3507,3255,12383,3080,3081,10164,10462,3343,3072,3003,3103,11178,3960,12183,12293,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,4394,11169,3487,3521,3693,3454,12627,12631,12635,12639,12653,3741,12034,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,12275,12494,12528,12542,12587,12610,12670,12677,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,12442,12461,12464,12486,12543,12724,12729,12752,4467,11279,11312,11353,11383,12552,12556,3615,3391,3392,12467,12470,12473,12476,12509,3768,3211,3213,3186,4448,3079,4391,3568,3879,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,12255,3921,3877,11696,12055,3824,10638,11861,11881,12068,3872,10812,11929,12007,12067,12113,3542,11706,11856,11939,11988,12086,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,12278,4472,10583,10946,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,12117,12304,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12487,12515,12599,12606,12613,12618,12621,12624,12661,12680,12691,12735,12761,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12506,12667,12694,12725,12730,12753,3185,10628,10694,11978,11981,3260,11912,12572,12628,12632,12636,12640,12654,12658,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3339,10434,10697,10742,11013,11086,11242,11492,12163,12310,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12571,12591,12594,3246,10459,10489,12553,12557,12560,12563,3283,3278,3699,3635,10145,11406,11439,12533,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,12650,3205,10646,10720,11440,11602,11806,12049,3659,11543,12483,4005,3397,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,4101,4474,10067,10070,10322,10780,11606,3934,12081,3785,11131,11469,11473,11534,12171,12179,12248,3623,10758,10764,10775,11728,11952,3481,10980,12095,12105,12176,12223,12231,3958,3627,10838,10992,11018,11029,12061,12175,3724,12457,3340,3452,10420,10423,10492,10673,4477,11400,4473,12451,4478,10543,10965,11117,12043,12052,12101,12265,4065,10631,12064,12078,3965,3658,12323,3602,11526,4475,10118,10121,10447,10450,11276,11470,12274,4476,11380,11479,3628,10417,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,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% 186.15/186.67 cnf(12764,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x127641),x127641))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12767,plain, % 186.15/186.67 (~P1(f775(f775(f232(a850),f775(a114,x127671)),x127671))), % 186.15/186.67 inference(rename_variables,[],[4460])). % 186.15/186.67 cnf(12773,plain, % 186.15/186.67 (P1(f775(f775(f334(x127731),f775(x127732,x127733)),f775(f303(x127734,x127731,x127732),f239(f857(x127734,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12774,plain, % 186.15/186.67 (P29(x127741,x127741,f7(x127741),x127742)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12779,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x127791,a844)),x127792),f239(f857(x127791,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(12780,plain, % 186.15/186.67 (P29(x127801,x127801,f7(x127801),x127802)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12784,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x127841,a844)),x127842),f239(f857(x127841,a844))))), % 186.15/186.67 inference(rename_variables,[],[3559])). % 186.15/186.67 cnf(12785,plain, % 186.15/186.67 (P29(x127851,x127851,f7(x127851),x127852)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12789,plain, % 186.15/186.67 (P29(x127891,x127891,f7(x127891),x127892)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12792,plain, % 186.15/186.67 (~P1(f775(f775(f233(f857(x127921,a844)),x127922),f180(f857(x127921,a844))))), % 186.15/186.67 inference(rename_variables,[],[4472])). % 186.15/186.67 cnf(12795,plain, % 186.15/186.67 (P29(x127951,x127951,f7(x127951),x127952)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12798,plain, % 186.15/186.67 (P29(x127981,x127981,f7(x127981),x127982)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12809,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x128091,a844)),f180(f857(x128091,a844))),x128092))), % 186.15/186.67 inference(rename_variables,[],[3627])). % 186.15/186.67 cnf(12813,plain, % 186.15/186.67 (E(f38(x128131,x128132,x128133,x128134,x128135,x128136,x128137,x128138,x128139,a25),x128132)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12817,plain, % 186.15/186.67 (~P1(f775(f775(f334(x128171),x128172),f180(f857(x128171,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12821,plain, % 186.15/186.67 (P1(f775(f775(f334(x128211),f775(x128212,x128213)),f775(f303(x128214,x128211,x128212),f239(f857(x128214,a844)))))), % 186.15/186.67 inference(rename_variables,[],[3785])). % 186.15/186.67 cnf(12822,plain, % 186.15/186.67 (P29(x128221,x128221,f7(x128221),x128222)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12832,plain, % 186.15/186.67 (~P1(f775(f775(f334(x128321),x128322),f180(f857(x128321,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12835,plain, % 186.15/186.67 (~P1(f775(f775(f334(x128351),x128352),f180(f857(x128351,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12838,plain, % 186.15/186.67 (E(f38(x128381,x128382,x128383,x128384,x128385,x128386,x128387,x128388,x128389,a25),x128382)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12840,plain, % 186.15/186.67 (~E(f775(a114,x128401),x128401)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12843,plain, % 186.15/186.67 (P1(f775(f775(f279(a850),x128431),x128431))), % 186.15/186.67 inference(rename_variables,[],[3185])). % 186.15/186.67 cnf(12845,plain, % 186.15/186.67 (~E(f775(a114,x128451),x128451)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12849,plain, % 186.15/186.67 (E(f38(x128491,x128492,x128493,x128494,x128495,x128496,x128497,x128498,x128499,a25),x128492)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12850,plain, % 186.15/186.67 (~E(f775(a114,x128501),x128501)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12854,plain, % 186.15/186.67 (E(f775(f775(f18(x128541,x128542),x128543),x128544),x128543)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(12857,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x128571),f775(a114,x128571)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12858,plain, % 186.15/186.67 (~E(f775(a114,x128581),x128581)), % 186.15/186.67 inference(rename_variables,[],[4363])). % 186.15/186.67 cnf(12861,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x128611),f775(a114,f775(f775(f82(a850),x128612),x128611))))), % 186.15/186.67 inference(rename_variables,[],[3628])). % 186.15/186.67 cnf(12862,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x128621),f775(a114,x128621)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12864,plain, % 186.15/186.67 (~E(f775(f775(f83(a850),f775(a114,f2(a850))),f35(x128641,x128642)),f775(f775(f83(a850),f775(a114,f2(a850))),f36(x128643,x128644)))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,11916,12337,12339,3424,10867,11934,12037,12134,12172,12180,12189,12242,12355,12357,12774,12780,12785,12789,12795,12798,3432,12001,3433,12073,3484,3153,12376,12378,3154,12370,4127,12415,12418,3157,12411,3002,3023,12404,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12326,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,4338,11154,11158,12644,12813,12838,3483,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12588,12840,12845,12850,12858,4381,10267,10362,3239,3203,12426,4375,10713,2808,2811,2820,2826,2830,2831,2832,2833,2835,2838,2841,2842,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2904,2906,2911,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4358,3057,4359,3518,3165,3508,3758,4350,3118,11412,12192,12196,12200,3127,3235,3638,3947,3025,3026,4377,4395,4436,10803,11097,11100,3731,11186,3238,12332,3096,3084,3049,3552,12397,3044,3844,3064,3557,4323,3033,3012,3039,4045,10983,3063,3196,11673,11896,12031,3242,10641,11998,3116,3117,3137,10304,3287,4471,10235,3813,4397,10099,10264,11055,12160,12193,12197,4406,12168,3174,11512,11515,12742,4461,10872,3147,3577,3169,3288,10884,3507,3255,12383,3080,3081,10164,10462,4445,3343,3072,3003,3126,3103,11178,3960,12183,12293,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,11002,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,4394,11169,3487,3521,3693,3454,12627,12631,12635,12639,12653,3741,12034,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,12275,12494,12528,12542,12587,12610,12670,12677,12857,3630,11403,3266,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,12442,12461,12464,12486,12543,12724,12729,12752,4467,11279,11312,11353,11383,12552,12556,3615,3391,3392,12467,12470,12473,12476,12509,3768,3211,3213,3186,4448,3079,4391,3568,3879,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,12255,3921,3877,11696,12055,3824,10638,11861,11881,12068,3872,10812,11929,12007,12067,12113,3542,11706,11856,11939,11988,12086,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,12278,12779,12784,4472,10583,10946,12792,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,12117,12304,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12487,12515,12599,12606,12613,12618,12621,12624,12661,12680,12691,12735,12761,12764,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12506,12667,12694,12725,12730,12753,3185,10628,10694,11978,11981,3260,11912,12572,12628,12632,12636,12640,12654,12658,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3339,10434,10697,10742,11013,11086,11242,11492,12163,12310,12712,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12571,12591,12594,12701,12817,12832,3246,10459,10489,12553,12557,12560,12563,3283,3278,3699,3635,10145,11406,11439,12533,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,12650,12767,3205,10646,10720,11440,11602,11806,12049,3659,11543,12483,4005,3397,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,3496,11399,4101,4474,10067,10070,10322,10780,11606,3934,12081,3785,11131,11469,11473,11534,12171,12179,12248,12500,12773,12821,3623,10758,10764,10775,11728,11952,12228,3481,10980,12095,12105,12176,12223,12231,3958,3627,10838,10992,11018,11029,12061,12175,12217,3724,12457,3340,12649,3452,10420,10423,10492,10673,4477,11400,4473,12451,4478,10543,10965,11117,12043,12052,12101,12265,4065,10631,12064,12078,12104,3965,3658,12323,3602,11526,4475,10118,10121,10447,10450,11276,11470,12274,4476,11380,11479,3628,10417,10670,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,54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0,5751,5752,5912,6297,6298,6392])). % 186.15/186.67 cnf(12871,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f2(a1)),f775(f102(a1),x128711)))), % 186.15/186.67 inference(rename_variables,[],[3283])). % 186.15/186.67 cnf(12874,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f2(a1)),f775(f102(a1),x128741)))), % 186.15/186.67 inference(rename_variables,[],[3283])). % 186.15/186.67 cnf(12875,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x128751),x128751))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12878,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x128781))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12879,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x128791),x128791))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12882,plain, % 186.15/186.67 (~E(f775(a114,x128821),f2(a850))), % 186.15/186.67 inference(rename_variables,[],[4375])). % 186.15/186.67 cnf(12885,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x128851),x128851))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12889,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x128891,a844)),f775(f158(x128891),f151(x128891,x128892,x128893))),f775(f158(x128891),x128893)))), % 186.15/186.67 inference(rename_variables,[],[3872])). % 186.15/186.67 cnf(12894,plain, % 186.15/186.67 (~P1(f775(f775(f334(x128941),x128942),f180(f857(x128941,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12897,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x128971,x128972)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12898,plain, % 186.15/186.67 (E(f775(f775(f179(a850),f775(a114,x128981)),f775(a114,x128982)),f775(a114,f775(f775(f179(a850),x128981),x128982)))), % 186.15/186.67 inference(rename_variables,[],[3354])). % 186.15/186.67 cnf(12901,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x129011,x129012)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12902,plain, % 186.15/186.67 (E(f775(f775(f236(a850),f775(a114,x129021)),f775(a114,x129022)),f775(a114,f775(f775(f236(a850),x129021),x129022)))), % 186.15/186.67 inference(rename_variables,[],[3353])). % 186.15/186.67 cnf(12905,plain, % 186.15/186.67 (P1(f775(f63(a850),f297(a850,x129051,x129052)))), % 186.15/186.67 inference(rename_variables,[],[3392])). % 186.15/186.67 cnf(12913,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x129131,a844)),f775(f158(x129131),f775(f126(x129131,x129132),x129133))),f775(f158(x129131),x129133)))), % 186.15/186.67 inference(rename_variables,[],[3824])). % 186.15/186.67 cnf(12914,plain, % 186.15/186.67 (E(f775(f775(f18(x129141,x129142),x129143),x129144),x129143)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(12917,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x129171,a844)),f775(f158(x129171),f775(f775(f159(x129171),x129172),x129173))),f775(f158(x129171),x129173)))), % 186.15/186.67 inference(rename_variables,[],[3867])). % 186.15/186.67 cnf(12918,plain, % 186.15/186.67 (E(f775(f775(f18(x129181,x129182),x129183),x129184),x129183)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(12922,plain, % 186.15/186.67 (E(f775(f775(f18(x129221,x129222),x129223),x129224),x129223)), % 186.15/186.67 inference(rename_variables,[],[3174])). % 186.15/186.67 cnf(12929,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x129291,a844)),x129292),x129292))), % 186.15/186.67 inference(rename_variables,[],[3481])). % 186.15/186.67 cnf(12935,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),f2(a1)),f775(f102(a1),x129351)))), % 186.15/186.67 inference(rename_variables,[],[3283])). % 186.15/186.67 cnf(12939,plain, % 186.15/186.67 (~P1(f775(f775(f334(x129391),x129392),f180(f857(x129391,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12942,plain, % 186.15/186.67 (P1(f775(f775(f232(f857(x129421,a844)),f775(f158(x129421),f160(x129421,x129422,x129423))),f775(f158(x129421),x129422)))), % 186.15/186.67 inference(rename_variables,[],[3873])). % 186.15/186.67 cnf(12946,plain, % 186.15/186.67 (~P1(f775(f775(f334(x129461),x129462),f180(f857(x129461,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12949,plain, % 186.15/186.67 (~P1(f775(f775(f334(x129491),x129492),f180(f857(x129491,a844))))), % 186.15/186.67 inference(rename_variables,[],[4463])). % 186.15/186.67 cnf(12950,plain, % 186.15/186.67 (E(f38(x129501,x129502,x129503,x129504,x129505,x129506,x129507,x129508,x129509,a25),x129502)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12951,plain, % 186.15/186.67 (P29(x129511,x129511,f7(x129511),x129512)), % 186.15/186.67 inference(rename_variables,[],[3424])). % 186.15/186.67 cnf(12955,plain, % 186.15/186.67 (E(f38(x129551,x129552,x129553,x129554,x129555,x129556,x129557,x129558,x129559,a25),x129552)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12961,plain, % 186.15/186.67 (E(f38(x129611,x129612,x129613,x129614,x129615,x129616,x129617,x129618,x129619,a25),x129612)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12962,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x129621),x129621))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12965,plain, % 186.15/186.67 (E(f38(x129651,x129652,x129653,x129654,x129655,x129656,x129657,x129658,x129659,a25),x129652)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12966,plain, % 186.15/186.67 (P1(f775(f775(f232(a1),x129661),x129661))), % 186.15/186.67 inference(rename_variables,[],[3184])). % 186.15/186.67 cnf(12969,plain, % 186.15/186.67 (E(f38(x129691,x129692,x129693,x129694,x129695,x129696,x129697,x129698,x129699,a25),x129692)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(12973,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x129731),f775(a114,x129731)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12975,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),x129751),x129751))), % 186.15/186.67 inference(rename_variables,[],[3183])). % 186.15/186.67 cnf(12976,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x129761))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12979,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),x129791),f775(a114,x129791)))), % 186.15/186.67 inference(rename_variables,[],[3252])). % 186.15/186.67 cnf(12982,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x129821))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12986,plain, % 186.15/186.67 (P1(f775(f775(f232(a850),f2(a850)),x129861))), % 186.15/186.67 inference(rename_variables,[],[3205])). % 186.15/186.67 cnf(12987,plain, % 186.15/186.67 (P1(f775(f775(f233(a850),f2(a850)),f775(a114,x129871)))), % 186.15/186.67 inference(rename_variables,[],[3266])). % 186.15/186.67 cnf(12988,plain, % 186.15/186.67 (E(f38(x129881,x129882,x129883,x129884,x129885,x129886,x129887,x129888,x129889,a25),x129882)), % 186.15/186.67 inference(rename_variables,[],[4338])). % 186.15/186.67 cnf(13062,plain, % 186.15/186.67 (P1(f775(f775(f233(a1),f2(a1)),f775(f77(a1),f80(a1))))), % 186.15/186.67 inference(scs_inference,[],[3400,11899,11916,12337,12339,3424,10867,11934,12037,12134,12172,12180,12189,12242,12355,12357,12774,12780,12785,12789,12795,12798,12822,12951,3432,12001,3433,12073,3484,3153,12376,12378,3154,12370,4127,12415,12418,3157,12411,3002,3023,12404,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12326,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,4338,11154,11158,12644,12813,12838,12849,12950,12955,12961,12965,12969,12988,3483,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12588,12840,12845,12850,12858,4381,10267,10362,3239,3203,12426,4375,10713,12501,12882,2808,2811,2820,2821,2826,2830,2831,2832,2833,2835,2838,2841,2842,2843,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2891,2904,2906,2911,2914,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4358,3057,4359,3518,3165,3508,3758,4350,3118,11412,12192,12196,12200,3127,3235,3638,3947,3025,3026,4377,4395,4436,10803,11097,11100,3731,11186,3238,12332,3096,3084,3049,3552,12397,3044,3844,3064,3557,4323,3033,3012,3039,4045,10983,3063,3196,11673,11896,12031,3242,10641,11998,3116,3117,3137,10304,3287,4471,10235,3813,4397,10099,10264,11055,12160,12193,12197,4406,12168,3174,11512,11515,12742,12854,12914,12918,12922,4461,10872,3147,3577,3169,3288,10884,3507,3280,3255,12383,3080,3081,10164,10462,4445,3343,3072,3003,3126,3103,11178,3960,12183,12293,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,11002,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,3364,4394,11169,3487,3521,3693,3454,12627,12631,12635,12639,12653,3741,12034,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,12275,12494,12528,12542,12587,12610,12670,12677,12857,12862,12973,12979,3630,11403,3266,11527,12987,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,12442,12461,12464,12486,12543,12724,12729,12752,12757,4467,11279,11312,11353,11383,12552,12556,3615,3391,3392,12467,12470,12473,12476,12509,12512,12897,12901,12905,3394,3768,3353,12902,3354,12898,3211,3213,3186,4448,3079,4391,3568,3879,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,12255,3921,3877,11696,12055,3824,10638,11861,11881,12068,12718,12913,3867,12917,3872,10812,11929,12007,12067,12113,12745,12889,3873,12942,3542,11706,11856,11939,11988,12086,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,12278,12779,12784,4472,10583,10946,12792,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,12117,12304,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12487,12515,12599,12606,12613,12618,12621,12624,12661,12680,12691,12735,12761,12764,12879,12975,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12506,12667,12694,12725,12730,12753,12758,12875,12885,12962,12966,3185,10628,10694,11978,11981,12843,3260,11912,12572,12628,12632,12636,12640,12654,12658,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3339,10434,10697,10742,11013,11086,11242,11492,12163,12310,12712,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12571,12591,12594,12701,12817,12832,12835,12894,12939,12946,12949,3246,10459,10489,12553,12557,12560,12563,3283,12871,12874,12935,3278,3699,3635,10145,11406,11439,12533,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,12650,12767,3205,10646,10720,11440,11602,11806,12049,12584,12878,12976,12982,12986,3659,11543,12483,4005,3397,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,4181,3496,11399,4101,4474,10067,10070,10322,10780,11606,3934,12081,3785,11131,11469,11473,11534,12171,12179,12248,12500,12773,12821,3623,10758,10764,10775,11728,11952,12228,3481,10980,12095,12105,12176,12223,12231,12317,12929,3958,3627,10838,10992,11018,11029,12061,12175,12217,12809,3724,12457,3340,12649,3452,10420,10423,10492,10673,4477,11400,4473,12451,4478,10543,10965,11117,12043,12052,12101,12265,4065,10631,12064,12078,12104,3965,3658,12323,3602,11526,4475,10118,10121,10447,10450,11276,11470,12274,4476,11380,11479,3628,10417,10670,12861,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893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6806,6831,6855,6864,6866,6870,6913,6936,6937,6953,6954,6956,6987,7034,7035,7131,7200,7201,7202,7203,7219,7259,7273,7317,7318,7327,7336,7338,7350,7385,7386,7387,7388,7533,7534,7540,7541,7543,7545,7621,7755,7758,7760,7761,7776,7814,7891,7935,7989,8008,8009,8081,8178,8245,8246,8248,8280,8319,8348,8349,8440,8441,8442,8443,8575,8792,8793,8853,8868,8922,8923,9037,9068,9091,9121,9152,9334,9578,9760,9817,9820,5490,5751,5752,5912,6297,6298,6392,6412,6413,6800,6854,7072,8233,8435,8512,8718,8879,8880,8945,8946,9188,9189,9190,9191,9390,9641,9818,9941,9949,10002,10003,6372,7313,7575,7576,8340,8341,8765,8779,9642,10001,4517,4554,4555,4556,4611,4619,4748,4762,4763,4791,4792,4819,4877,4879,4937,5049,5077,5110,5111,5113,5118,5120,5121,5144,5212,5233,5364,5432,5544])). % 186.15/186.67 cnf(13114,plain, % 186.15/186.67 (~P1(f775(f775(f233(a850),f2(a850)),f37(x131141,f2(a850),x131142,x131143,x131144,x131145,x131146,x131147,x131148,a25)))), % 186.15/186.68 inference(scs_inference,[],[3400,11899,11916,12337,12339,3424,10867,11934,12037,12134,12172,12180,12189,12242,12355,12357,12774,12780,12785,12789,12795,12798,12822,12951,3432,12001,3433,12073,3484,3153,12376,12378,3154,12370,4127,12415,12418,3157,12411,3002,3023,12404,4385,4337,10037,10040,10046,10108,10111,10202,10205,10486,10497,11138,11153,11157,11198,11201,11204,11207,11219,11250,11263,11290,11293,11304,11309,11315,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12326,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,4338,11154,11158,12644,12813,12838,12849,12950,12955,12961,12965,12969,12988,3483,3065,4363,10043,10053,10064,10073,10172,10175,10178,10283,10389,10557,10689,10822,11058,11141,11148,11164,11212,11215,11318,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12588,12840,12845,12850,12858,4381,10267,10362,3239,3203,12426,4375,10713,12501,12882,2808,2811,2820,2821,2826,2830,2831,2832,2833,2835,2838,2841,2842,2843,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2891,2904,2906,2911,2914,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4358,3057,4359,3518,3165,3508,3758,4350,3118,11412,12192,12196,12200,3127,3235,3638,3947,3025,3026,4377,4395,4436,10803,11097,11100,3731,11186,3238,12332,3096,3084,3049,3552,12397,3044,3844,3064,3557,4323,3033,3012,3039,4045,10983,3063,3196,11673,11896,12031,3242,10641,11998,3116,3117,3137,10304,3287,4471,10235,3813,4397,10099,10264,11055,12160,12193,12197,4406,12168,3174,11512,11515,12742,12854,12914,12918,12922,4461,10872,3147,3577,3169,3288,10884,3507,3280,3255,12383,3080,3081,10164,10462,4445,3343,3072,3003,3126,3103,11178,3960,12183,12293,3814,10809,10928,10995,12144,12150,12249,12252,12271,4479,10745,10935,11049,11069,11105,11111,12089,4480,10849,10938,11052,11108,4481,10941,11002,4482,11005,4483,3100,3381,12040,12167,3541,4240,4241,3364,4394,11169,3487,3521,3693,3454,12627,12631,12635,12639,12653,3741,12034,3367,3618,3252,10183,10186,10299,10376,10428,10431,10465,10554,10793,11571,11619,11703,11771,11849,11887,11960,11963,12275,12494,12528,12542,12587,12610,12670,12677,12857,12862,12973,12979,3630,11403,3266,11527,12987,3449,4451,10076,10079,10105,10565,10580,10702,11120,11181,11585,11593,11825,11828,11921,12092,12442,12461,12464,12486,12543,12724,12729,12752,12757,4467,11279,11312,11353,11383,12552,12556,3615,3391,3392,12467,12470,12473,12476,12509,12512,12897,12901,12905,3394,3768,3353,12902,3354,12898,3211,3213,3186,4448,3079,4391,3568,3879,3373,4468,3954,11066,3506,3728,11537,11540,3224,12008,12114,12255,3921,3877,11696,12055,3824,10638,11861,11881,12068,12718,12913,3867,12917,3872,10812,11929,12007,12067,12113,12745,12889,3873,12942,3542,11706,11856,11939,11988,12086,3910,3559,10815,10877,10962,11024,11877,11953,12209,12268,12278,12779,12784,4472,10583,10946,12792,3182,10195,10290,10414,10472,11255,11262,11485,11496,11530,11567,11676,11731,11946,12117,12304,3183,10532,10586,10589,10622,10649,10683,10727,10761,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12487,12515,12599,12606,12613,12618,12621,12624,12661,12680,12691,12735,12761,12764,12879,12975,3184,10280,10477,10560,10686,11321,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12506,12667,12694,12725,12730,12753,12758,12875,12885,12962,12966,3185,10628,10694,11978,11981,12843,3260,11912,12572,12628,12632,12636,12640,12654,12658,4447,10142,10230,10341,10371,10604,10652,10659,10972,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3339,10434,10697,10742,11013,11086,11242,11492,12163,12310,12712,4463,10613,10625,10734,10752,10755,10806,10891,10901,10913,10949,10977,10989,11021,11061,11077,11080,11083,11114,11125,11128,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12571,12591,12594,12701,12817,12832,12835,12894,12939,12946,12949,3246,10459,10489,12553,12557,12560,12563,3283,12871,12874,12935,3278,3699,3635,10145,11406,11439,12533,4460,10096,10453,10456,10894,10910,11369,11425,11474,11493,11603,11646,11649,11652,11655,12650,12767,3205,10646,10720,11440,11602,11806,12049,12584,12878,12976,12982,12986,3659,11543,12483,4005,3397,4458,3670,3707,4439,4440,4442,3160,3161,4441,4443,4181,3496,11399,4101,4474,10067,10070,10322,10780,11606,3934,12081,3785,11131,11469,11473,11534,12171,12179,12248,12500,12773,12821,3623,10758,10764,10775,11728,11952,12228,3481,10980,12095,12105,12176,12223,12231,12317,12929,3958,3627,10838,10992,11018,11029,12061,12175,12217,12809,3724,12457,3340,12649,3452,10420,10423,10492,10673,4477,11400,4473,12451,4478,10543,10965,11117,12043,12052,12101,12265,4065,10631,12064,12078,12104,3965,3658,12323,3602,11526,4475,10118,10121,10447,10450,11276,11470,12274,4476,11380,11479,3628,10417,10670,12861,3629,3894,4488,4493,4499,4561,4564,4592,4610,4617,4618,4654,4683,4689,4793,4794,4831,4854,4855,4878,4880,4893,4897,4917,4923,4940,4944,4945,4950,4955,4956,4978,5002,5003,5013,5018,5024,5069,5070,5078,5087,5089,5090,5099,5101,5109,5114,5127,5133,5136,5137,5141,5174,5184,5191,5193,5194,5197,5198,5199,5207,5208,5211,5215,5216,5217,5224,5228,5229,5230,5238,5241,5243,5249,5260,5267,5280,5282,5290,5291,5295,5298,5323,5329,5339,5340,5341,5356,5368,5390,5396,5414,5415,5418,5437,5445,5446,5448,5449,5458,5459,5473,5477,5486,5487,5489,5504,5507,5518,5529,5536,5549,5555,5561,5562,5563,5566,5571,5608,5610,5613,5615,5618,5619,5620,5622,5624,5626,5629,5636,5650,5664,5670,5671,5690,5691,5696,5697,5699,5702,5705,5706,5711,5755,5769,5777,5781,5793,5803,5820,5838,5841,5851,5878,5893,5920,5940,5941,5944,5958,5960,5961,5963,5976,5977,5980,5982,5985,5986,6000,6006,6007,6008,6011,6013,6055,6065,6074,6109,6111,6113,6115,6125,6127,6130,6136,6138,6142,6145,6153,6160,6161,6162,6168,6194,6201,6208,6244,6245,6249,6250,6251,6252,6253,6254,6255,6262,6299,6300,6309,6329,6330,6355,6359,6370,6371,6379,6410,6411,6426,6448,6449,6468,6471,6472,6518,6526,6551,6592,6608,6617,6626,6627,6628,6629,6651,6652,6658,6670,6673,6676,6678,6679,6680,6682,6696,6709,6711,6712,6723,6726,6783,6796,6798,6804,6818,6821,6822,6859,6874,6902,6935,6985,7016,7073,7101,7104,7162,7174,7241,7243,7258,7268,7271,7272,7290,7296,7298,7351,7361,7367,7370,7383,7428,7431,7435,7482,7483,7501,7564,7571,7590,7614,7636,7650,7666,7675,7683,7712,7714,7716,7724,7768,7778,7803,7861,7893,7927,7972,7987,8075,8123,8142,8166,8185,8207,8306,8308,8314,8334,8338,8352,8373,8384,8386,8398,8404,8408,8432,8447,8448,8459,8460,8461,8467,8468,8473,8474,8475,8476,8477,8495,8496,8497,8505,8517,8519,8533,8535,8541,8546,8567,8568,8597,8610,8614,8632,8653,8654,8656,8657,8667,8668,8690,8699,8706,8707,8708,8709,8732,8733,8744,8780,8786,8790,8803,8806,8808,8809,8816,8825,8890,8919,8920,8921,8935,8949,8955,8982,8983,8984,8985,8986,8989,9026,9029,9053,9087,9097,9098,9108,9118,9119,9133,9143,9145,9164,9186,9247,9285,9286,9287,9313,9314,9331,9348,9355,9366,9389,9407,9417,9418,9419,9420,9421,9436,9441,9476,9477,9483,9484,9520,9521,9546,9570,9572,9573,9588,9594,9618,9647,9694,9731,9744,9746,9750,9751,9753,9762,9763,9783,9788,9809,9814,9885,9961,9962,10013,2,8,9,4502,4518,4549,4550,4552,4576,4584,4585,4596,4643,4645,4688,4716,4808,4809,4825,4844,4900,4903,4904,4907,4908,4920,4930,4942,4943,4953,4962,4973,4974,4992,4997,4998,4999,5000,5001,5009,5012,5019,5083,5093,5124,5134,5139,5155,5173,5180,5181,5183,5188,5203,5205,5206,5213,5220,5221,5234,5235,5236,5237,5239,5240,5245,5246,5247,5248,5276,5277,5278,5286,5287,5288,5289,5318,5334,5336,5338,5375,5377,5378,5380,5381,5383,5384,5386,5395,5400,5402,5404,5405,5406,5407,5408,5409,5416,5426,5429,5440,5452,5453,5456,5466,5469,5470,5471,5496,5506,5520,5521,5530,5531,5533,5535,5539,5573,5577,5579,5637,5672,5673,5686,5689,5692,5693,5694,5695,5703,5707,5717,5718,5720,5721,5729,5750,5785,5798,5799,5800,5804,5814,5828,5832,5833,5834,5837,5853,5864,5865,5895,5896,5900,5922,5926,5929,5947,5952,5953,5978,5981,5989,5996,5998,6005,6009,6017,6018,6019,6020,6058,6059,6075,6129,6163,6165,6166,6190,6191,6193,6197,6198,6204,6218,6237,6257,6258,6263,6275,6276,6279,6292,6313,6318,6320,6334,6335,6339,6341,6342,6343,6345,6347,6348,6349,6357,6364,6365,6366,6367,6373,6375,6382,6419,6425,6440,6443,6444,6445,6483,6485,6487,6492,6493,6504,6507,6522,6547,6548,6549,6550,6561,6565,6582,6586,6609,6630,6646,6647,6648,6653,6666,6688,6690,6692,6694,6697,6698,6705,6707,6720,6728,6768,6771,6772,6788,6789,6790,6791,6811,6812,6830,6857,6879,6889,6891,6892,6894,6896,6897,6931,6932,6933,6938,6939,6941,6943,6944,6945,6967,6975,6976,6988,6998,7040,7049,7055,7063,7074,7079,7081,7087,7095,7108,7125,7142,7144,7154,7160,7221,7223,7224,7225,7233,7234,7240,7242,7267,7312,7331,7348,7364,7365,7382,7410,7414,7439,7466,7484,7487,7488,7498,7516,7517,7519,7521,7523,7525,7526,7527,7579,7580,7613,7615,7616,7617,7623,7642,7651,7662,7667,7673,7674,7680,7690,7691,7693,7722,7749,7779,7816,7817,7864,7871,7872,7894,7895,7914,7915,7980,7981,7982,8002,8003,8037,8041,8045,8054,8068,8095,8099,8105,8118,8137,8143,8165,8205,8235,8247,8264,8267,8296,8323,8387,8388,8391,8392,8409,8499,8500,8501,8502,8525,8549,8571,8613,8631,8684,8725,8728,8741,8778,8796,8812,8813,8828,8829,8957,8962,8980,8996,9016,9018,9021,9024,9027,9028,9040,9041,9064,9137,9172,9173,9238,9244,9278,9289,9293,9297,9298,9312,9336,9347,9356,9357,9359,9361,9388,9504,9583,9721,9722,9792,9862,9942,9953,9958,3,2549,2552,2563,2564,2565,2571,2572,2574,2575,2583,2584,2585,2588,2592,2594,2595,2596,2599,2600,2601,2602,2607,2608,2612,2613,2615,2625,2626,2627,2630,2631,2632,2635,2637,2648,2650,2651,2660,2675,2677,2679,2681,2682,2683,2685,2699,2700,2716,2726,2731,2733,2745,2748,2749,2750,2763,2765,2768,2777,2778,2789,2799,2800,2801,2802,5170,5343,5349,5350,5427,5519,5548,5580,5596,5602,5604,5665,5666,5667,5668,5684,5719,5848,5894,5919,5955,5990,5994,6143,6150,6188,6189,6210,6212,6214,6220,6221,6222,6223,6224,6225,6226,6227,6228,6315,6389,6390,6481,6516,6517,6558,6559,6706,6719,6780,6801,6802,6806,6831,6855,6864,6866,6870,6913,6936,6937,6953,6954,6956,6987,7034,7035,7131,7200,7201,7202,7203,7219,7259,7273,7317,7318,7327,7336,7338,7350,7385,7386,7387,7388,7533,7534,7540,7541,7543,7545,7621,7755,7758,7760,7761,7776,7814,7891,7935,7989,8008,8009,8081,8178,8245,8246,8248,8280,8319,8348,8349,8440,8441,8442,8443,8575,8792,8793,8853,8868,8922,8923,9037,9068,9091,9121,9152,9334,9578,9760,9817,9820,5490,5751,5752,5912,6297,6298,6392,6412,6413,6800,6854,7072,8233,8435,8512,8718,8879,8880,8945,8946,9188,9189,9190,9191,9390,9641,9818,9941,9949,10002,10003,6372,7313,7575,7576,8340,8341,8765,8779,9642,10001,4517,4554,4555,4556,4611,4619,4748,4762,4763,4791,4792,4819,4877,4879,4937,5049,5077,5110,5111,5113,5118,5120,5121,5144,5212,5233,5364,5432,5544,5545,5569,5570,5574,5609,5632,5634,5642,5648,5732,5811,5870,5914,5937,5959,6010,6056,6132,6256,6423,6462,6638,6639,6797,6867,6906])). % 186.15/186.68 cnf(13299,plain, % 186.15/186.68 (P1(f775(f775(f233(a1),f775(f775(f3(a1),x132991),f80(a1))),x132991))), % 186.15/186.68 inference(rename_variables,[],[10559])). % 186.15/186.68 cnf(13302,plain, % 186.15/186.68 (P1(f775(f775(f233(a850),x133021),f775(a114,f775(f775(f82(a850),x133022),x133021))))), % 186.15/186.68 inference(rename_variables,[],[3628])). % 186.15/186.68 cnf(13305,plain, % 186.15/186.68 (P1(f775(f775(f232(f857(x133051,a844)),f775(f158(x133051),f151(x133051,x133052,x133053))),f775(f158(x133051),x133053)))), % 186.15/186.68 inference(rename_variables,[],[3872])). % 186.15/186.68 cnf(13313,plain, % 186.15/186.68 (E(f38(x133131,x133132,x133133,x133134,x133135,x133136,x133137,x133138,x133139,a25),x133132)), % 186.15/186.68 inference(rename_variables,[],[4338])). % 186.15/186.68 cnf(13321,plain, % 186.15/186.68 (~P1(f775(f775(f334(a850),x133211),f775(f257(a850),f2(a850))))), % 186.15/186.68 inference(rename_variables,[],[11560])). % 186.15/186.68 cnf(13329,plain, % 186.15/186.68 (~P1(f775(f775(f334(a850),x133291),f775(f257(a850),f2(a850))))), % 186.15/186.68 inference(rename_variables,[],[11560])). % 186.15/186.68 cnf(13337,plain, % 186.15/186.68 (~P1(f775(f775(f334(x133371),x133372),f180(f857(x133371,a844))))), % 186.15/186.68 inference(rename_variables,[],[4463])). % 186.15/186.68 cnf(13352,plain, % 186.15/186.68 (~P1(f775(f775(f232(a850),f775(f775(f83(a850),f775(a114,x133521)),f775(a114,x133521))),x133521))), % 186.15/186.68 inference(rename_variables,[],[10491])). % 186.15/186.68 cnf(13355,plain, % 186.15/186.68 (E(f38(x133551,x133552,x133553,x133554,x133555,x133556,x133557,x133558,x133559,a25),x133552)), % 186.15/186.68 inference(rename_variables,[],[4338])). % 186.15/186.68 cnf(13375,plain, % 186.15/186.68 (~E(f775(f775(f140(x133751),x133752),x133753),x133753)), % 186.15/186.68 inference(rename_variables,[],[4397])). % 186.15/186.68 cnf(13389,plain, % 186.15/186.68 (~P1(f775(f775(f334(f856(x133891,x133891)),x133892),f260(x133891,f180(f857(x133891,a844)))))), % 186.15/186.68 inference(rename_variables,[],[10751])). % 186.15/186.68 cnf(13401,plain, % 186.15/186.68 (E(f775(x134011,f703(f775(x134011,x134012),f775(f227(x134013),x134012),x134011,x134014,x134013)),f775(x134011,x134012))), % 186.15/186.68 inference(rename_variables,[],[10921])). % 186.15/186.68 cnf(13433,plain, % 186.15/186.68 (P1(f775(f775(f232(a850),x134331),f775(f775(f83(a850),x134331),x134331)))), % 186.15/186.68 inference(rename_variables,[],[3452])). % 186.15/186.68 cnf(13474,plain, % 186.15/186.68 (E(f775(x134741,f703(f775(x134741,x134742),f775(f227(x134743),x134742),x134741,x134744,x134743)),f775(x134741,x134742))), % 186.15/186.68 inference(rename_variables,[],[10921])). % 186.15/186.68 cnf(13537,plain, % 186.15/186.68 ($false), % 186.15/186.68 inference(scs_inference,[],[3213,3211,3615,3960,3186,4477,3814,3260,4479,4442,3630,4463,13337,3266,3872,13305,3785,4397,13375,4461,3635,3205,3340,3452,13433,3628,13302,4338,13313,13355,3541,4480,4447,4460,4478,4475,3433,10128,12864,10188,11629,11529,11122,13062,12051,12288,12295,10741,12045,10559,13299,4272,10921,13401,13474,10239,10496,3243,11010,12763,10509,11442,11992,11985,13114,12094,11560,13321,13329,11617,10909,10751,13389,10754,10491,13352,10959,2967,5620,6130,8308,4611,5291,4488,4855,8448,6638,6410,7712,8690,8,5960,7243,8919,5193,5650,5914,7501,4794,6115,4493,5049,5224,5432,5610,5615,6201,6629,5705,4499,8985,5732,4950,7778,9313,9962,5608,4689,4937,9731,4555,5793,8744,7077,8597,5697,8786,9029,5458,5958,7803,8610,6011,6309,7972,8568,5099,5642,9694,9407,4618,5280,8432,5191,4762,8460,5769,9,6074,8935,6670,5199,5118,7383,9186,5114,6355,8384,9520,5229,5295,5002,5212,5340,6138,8207,9744,5136,7724,5562,6249,8982,8921,5069,5127,5208,6902,7650,8338,8398,4592]), % 186.15/186.68 ['proof']). % 186.15/186.68 % SZS output end Proof % 186.15/186.68 % Total time :167.100000s %------------------------------------------------------------------------------